The Ionosphere and Radio Navigation I: Operating ... - CiteSeerX

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reasonable guess of the receiver location. The challenge of the simple concept underlying radio navigation is to make it
The ionosphere, radio navigation, and global navigation satellite systems Paul M. Kintner* and Brent M. Ledvina School of Electrical and Computer Engineering, Cornell University, Ithaca, NY 14853, USA *

Corresponding author. Tel.: 607-255-5304; Fax: 607-255-6236. E-mail address: [email protected] (P.M. Kintner).

______________________________________________________________________________ Abstract This article is a review of Global Navigation Satellite Systems for space scientists who are interested in how GNSS signals and observables can be used to understand ionospheric dynamics and, conversely, how ionospheric dynamics affect the operational capabilities of GPS. The most common form of GNSS is the Global Positioning System (GPS); we will first review its operating principles and then present a discussion of errors, of which ionospheric propagation is the most significant. Methods and systems for mitigating errors will be introduced, along with a discussion of modernization plans for GPS and for entirely new systems such as Galileo. In the second half of this article the effects of the ionosphere on GPS signals will be examined in more detail, particularly ionospheric propagation, leading to a discussion of the relation of TEC to ranging errors. Next, the subject of scintillations will also be introduced and connected to the presence and scale sizes of irregularities. The importance of TEC gradients and scintillations will then be examined in the cases of the equatorial and midlatitude ionospheres.

______________________________________________________________________________ Even though GPS has recently become a commercial success, it has a longer history. GPS was originally designed in the mid-1970s when atomic clocks became available for satellites. Those original design protocols are still in use today, even though technology has changed substantially over the intervening period. GPS became operational in 1994 when a reliable constellation of satellites was inaugurated. Finally, GPS became a true civilian application when the deliberate degradation of the SPS civilian signal was turned off on May 1, 2000. This last action made unaided civilian receivers accurate at the level of 15 m or better. The subject of GPS is usually introduced by dividing it into three categories: control, space, and ground segments. The control segment operates the satellites, determines their positions accurately, calibrates the satellite clocks, and purchases the satellites and launch services. The space segment consists of the satellites, their signals and codes, and the navigation message containing the information necessary for the receivers to determine the satellite positions. The ground segment is generally thought of as the receivers and possibly differential aiding techniques, although differential aiding now

I. Introduction In the past several years small radio navigation receivers have proliferated in the civilian market place, generally under the name of GPS or Global Positioning System. Appearing as handheld units or built into cars, mobile phones, and airplanes, these commercial applications originated from a Cold War military application. In creating GPS the United States Congress required the U.S. military to make available a civilian component of GPS, called the Standard Positioning Service (SPS). SPS is free, is available worldwide to anyone, and is guaranteed by a presidential executive order not to be interrupted. The largest source of error in SPS is produced by the ionosphere. In addition to the SPS the U.S. military provides an encrypted Precise Positioning Service (PPS) for their own use. Despite the encryption, PPS sometimes can be used in lowdynamic environments to characterize the ionosphere and to measure total electron content. In this article we will review the operation and design of GPS and then examine how GPS can be used to characterize the ionosphere and, conversely, how the ionosphere affects GPS.

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frequently uses geostationary satellites to relay range corrections. Since most space scientists have only a passing acquaintance with GPS and GNSS, we will devote the first section of this paper to understanding the operating principles behind GPS so that the ionospheric effects on GPS can be understood. We will begin with a few remarks about radio navigation and then discuss the space segment, observables, receiver operation, the navigation solution, ranging errors, dilution of precision (the mapping of ranging errors into the navigation solution), differential GPS, and finally, the future of GPS, modernization, and Galileo.

addressed to make a robust, efficient, reliable system. B. GPS orbits and the space segment The GPS satellite constellation is comprised of 24 or more satellites (some are orbited as spares). The ephemerides for the satellites are a semimajor axis of 26,660 km, an eccentricity near zero (circular orbits), and an inclination of 55°. The satellites are placed in six orbital planes whose ascending nodes are spaced at intervals of 60° around the equator. Typically, four satellites are in each orbital plane. These orbits yield a period of 12 sidereal hours and once every two orbits (one sidereal day) the satellites return to their same locations, with respect to the earth, within a few km. The GPS orbits place the satellites well above the F region and at an earth-centered distance of about 4 earth radii, mostly above the plasmasphere depending on the location of the plasmapause and the satellite distance from the magnetic equator. These orbits are also well-centered on the radiation belts. Consequently, the GPS satellite lifetimes are typically 8-10 years, yielding a time scale for changing navigation technology since funding sources are reluctant to replace satellites until they cease functioning.

II. Principles of radio navigation A. Introduction The principle of radio navigation is remarkably simple. Suppose that a transmitter exists at location ( X 1 , Y1 , Z1 ) and transmits a pulse at time t1T that is received by a user at time t1R . The user knows that they are located at a distance r1 = c ⋅ (t1R − t1T ) from the transmitter, which locates the user on a sphere centered at ( X 1 , Y1 , Z1 ) . If a second transmitter is located at ( X 2 , Y2 , Z 2 ) and transmits a pulse at time t 2T that is received by a user at time t 2 R , then the user knows that they are also located on a sphere of radius r2 = c ⋅ (t2 R − t2T ) centered at ( X 2 , Y2 , Z 2 ) . Since the user must be located on both spheres, the user location is restricted to the intersection of the two spheres. Next, a third transmitter at location ( X 3 , Y3 , Z 3 ) launches a pulse that is received and restricts the user to being on a third sphere. The intersection of the third sphere with the circle produced by the first two spheres is two points. Generally the two points of intersection are sufficiently far apart so that one can determine their position uniquely from ancillary information. The intersection of three spheres leads to a set of three simultaneous quadratic equations which must be solved within the receiver. Usually this is done using the Newton-Raphson method and a reasonable guess of the receiver location. The challenge of the simple concept underlying radio navigation is to make it real. How does the receiver know the location of the transmitters or satellites? How are the pulses created and sent? How is accurate time maintained, synchronized, or transferred, especially for an inexpensive receiver (see section IIE)? All of these challenges must be

SVID/Last Position Positive Elevation Negative Elevation 15

0 0 30 60

270

90

90

180 GPS time range : 124213.00 sec to 210433.00 sec

Fig. 1. The apparent motion of a GPS satellite from the viewpoint of a fixed observer. The solid line is above the horizon and the dashed line is below the horizon.

From the viewpoint of an observer the satellites appear to follow the stitching on the cover of a baseball, as shown in Fig. 1. The motion is primarily pro-grade, west to east, although there is also a substantial north-south component. This somewhat complicated motion will also make the

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interpretation of scintillation drift measurements between multiple receivers complicated as well. The view in Fig. 1 is from Ithaca, NY, USA at a latitude of 42.44 N and a longitude of 76.48 W. This is a midlatitude view but the views from other latitudes are equally complicated. GPS satellites broadcast on two frequencies called L1 and L2. These frequencies are exactly L1 = 1.57542 GHz and L2 = 1.2276 GHz to the extent physically possible, that is, all satellites transmit on the same two frequencies. To enable a receiver to distinguish the satellites, each carrier frequency is modulated with one or more pseudorandom codes. Currently, two codes are used: the coarse acquisition code called C/A at 1.023 Mbps and the precise code called P at 10.23 Mbps. In addition, the P code is currently encrypted into the Y code and is called the P(Y) code, which is only accessible to the civilian community in special circumstances. The C/A code and P(Y) code are both transmitted on L1 in quadrature. However, only the P(Y) code is transmitted on L2. The C/A code is used by the civilian community for navigation and timing. It is a relatively short code, implying a relatively small dynamic range, about 21 dB. On the other hand, the P(Y) code is much longer with a larger dynamic range, making it more robust. Since the P code is the only code transmitted on both L1 and L2, it is the only code that can be used to determine total electron content (TEC). Unfortunately, since the P code is also encrypted into the P(Y) code, civilian receivers capable of measuring TEC are expensive, heavy, and have low signal-to-noise ratios. This will change as GPS is modernized in the next decade and with the introduction of European GPS, called Galileo, but until the next solar maximum TEC measurements will be problematic. We will discuss GPS and TEC measurements in more detail in section IIIA.

1 ms. The receiver contains replicas of each of the 32 C/A codes. To “receive” a signal from a specific satellite the entire L1 bandwidth of the C/A code is converted to baseband, digitized, and then sent to a correlator channel (see Fig. 2). At this point the signal still contains the C/A codes of all the satellites in view. Next the correlator channel compares the incoming bit stream with a C/A code replica generated in the receiver through a process of cross-correlation. If the C/A code replica is aligned in phase and repetition rate with an incoming satellite C/A code, then the process of correlation will yield a peak value. The process of tracking is to maintain alignment between the incoming C/A code and the receiver-generated replica, typically with a delay-lock loop and either a frequency-lock loop or a phase-lock loop. In practice, there are two correlator channels per tracked satellite. One channel leads the incoming signal by a ¼ chip and the other lags the signal by a ¼ chip. By comparing the two correlators the controller can track by either increasing or decreasing the C/A code replica repetition rate.

Fig. 2. Schematic of a GPS receiver.

Before tracking can occur the signal must be acquired. This is the process of searching through code space, code phase space, and Doppler shift space to find the signals. In a cold start these 3 spaces must be searched without prior knowledge of the satellites in view or the frequency offset of the receiver oscillator. Acquiring the minimum four satellite signals for setting the receiver oscillator can take 10-15 minutes. In a warm start, the receiver knows which satellites are above the horizon and their expected Doppler shifts so that once one satellite signal is acquired, the remaining satellite signals can be acquired much more rapidly. We will see later that the issue of acquiring signals that have been “temporarily lost” is problematic when we discuss scintillations. The range from the receiver to the satellite is determined from the arrival time of the C/A code, assuming that the receiver has an accurate clock.

C. GPS observables, ranging, and the navigation message The GPS signal is sometimes called a spreadspectrum or Code Division Multiple Access (CDMA) signal since all the satellites transmit on the same two frequencies but are modulated by unique pseudorandom codes with minimal overlap. For this discussion we will only consider the L1 C/A code, but these remarks will apply to the P(Y) code. There are 32 C/A codes, each of which is 1023 bits so the code repeats itself every

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Since the receiver clocks are generally not accurate, this range estimate is generally called the pseudorange and, in the next section, we will show how the receiver compensates for inaccurate clocks. In addition to the pseudorange, the receiver can also estimate the received signal phase if a phase-lock loop is used for tracking. This observable requires a phase-stable oscillator and can only be measured in a relative sense, that is, the change in signal phase can be measured but no unique method exists to directly measure the absolute number of wavelengths between the receiver and the satellite in a short time period. This lack of information is referred to as the integer ambiguity. The signal phase observable is used for accurately surveying or measuring tectonic drifts where the change in position between two receivers is required. Finally, the Doppler shift of the signal can also be measured and this observable can be used to directly calculate the receiver velocity much more accurately than by differentiating the receiver position calculated with pseudoranges. The C/A code is modulated at a much slower rate with the navigation message. The navigation message is at 50 bps compared to 1.023 Mbps for the C/A code so that each bit contains 20 repetitions of the C/A code. The navigation message contains all of the information for the receiver to determine the satellite positions through a set of parameters called the ephemerides. These parameters contain the classical Keplerian ephemerides plus first-order secular and harmonic corrections and must be updated about every four hours to yield accurate satellite positions. At the rate of 50 bps each satellite transmits its specific ephemerides once every 30 s. During start up this means that each satellite signal must be received with no errors for up to one minute before navigation can begin.

the code arrival time the receiver can estimate the pseudorange given by

P = ρ + c ⋅ (δ S − δ R )

(1)

where P is the pseudorange and ρ is the real range. The pseudorange P contains two primary sources of error. The two error sources are a) errors in the inaccurate receiver clock, called the receiver clock offset (δR); and b) errors in the time of the satellite signal, called the satellite clock offset (δ S). In addition, propagation at less than the speed of light through the ionosphere and atmosphere will yield errors to be discussed later. The satellite clock error is monitored by the control segment and modeled with three coefficients that are included in the navigation message so that δ S can be calculated within the receiver. This receiver clock offset (error) is determined in the process of navigation, shown next. Note that an important property of δR is that it is the same for all satellite signals and pseudoranges since it is a property of the receiver. The real range ρ is the distance from the jth satellite to the receiver. We will denote the satellite’s position as (Xj, Yj, Zj) and the receiver’s position as (X, Y, Z). Recall that the satellite position is calculated by the receiver from the ephemerides in the navigation message. Given these definitions we can write down an equation from the measured pseudorange in terms of the receiver location, which is

P j − cδ j =

(X

j

− cδ R

− X ) + (Y j − Y ) + (Z j − Z ) 2

2

2

(2)

Note that the left-hand side of Eq. (2) contains measured or calculated quantities while the right side contains the four unknowns of X, Y, Z, and δR. Hence, to solve for the four unknowns a minimum of four satellites is required to yield four equations. Since Eq. (2) is nonlinear, typically this is done using the multi-dimensional NewtonRaphson method and a reasonable guess of the initial receiver position (Parkinson et al., 1996). If more than four satellites are being observed, the problem is over-determined and can be solved in a least squares sense to yield an optimal receiver location. In writing down Eq. (2) and describing the solution we have glossed over some details related to coordinate frame issues. The pseudorange is

D. Navigation solution To navigate successfully the receiver must first execute a series of actions. Initially it must acquire a satellite in the correlator for tracking. From a cold start this may take several minutes per satellite. Next it must track the satellite with no bit errors for the 30 s length of one navigation message, which may take up to one minute. For safety purposes many receivers obtain contiguous navigation messages and compare their contents to assure accurate data reception. At this point, from

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Table 1. Ranging errors for GPS receivers. Source

Cause

Unaided L1

L1/L2

Satellite

Orbital Specification Clock Accuracy Ionosphere and Plasmasphere Dry Atmosphere Wet Atmosphere Multipath

3m 2m 5-15 m 3m 0.3 m 3-5 m 1m 7-17 m

3m 2m 1m 3m 0.3 2-3 m 1m 5-6 m

Propagation

Receiver Total

Differentially Corrected L1 1m 1m 1m 0.5 m 0.1 m 3-5 m 1m 3-6 m

a) that ionospheric propagation dominates the unaided L1 error budget, b) for a dual-frequency receiver (L1/L2) most of the ionospheric propagation error is removed, and c) that differential corrections remove most errors except for multipath. Finally, we should add the caveat that all of the systems have weaknesses. For example, differential corrections only have small ionospheric errors if there are small ionospheric gradients, which is not always true, especially at the equator and even at midlatitudes (Vo and Foster, 2001).

calculated in ECEF (Earth Centered, Earth Fixed) because the ephemerides are expressed in this frame. The pseudorange is determined at some time t. However, the satellite transmits its code at an earlier time compared to t and the difference between the two times is the propagation time of the signal. So, the satellite position must be calculated at the time of reception minus the propagation time. This is a correction of few hundred meters. Next the ECEF coordinate frame rotates during the time of propagation and the frame must be unwound to its position at the time the signal is transmitted (Kaplan, 1996). E. Ranging errors and navigation solution errors The utility of GPS resides in its accuracy. There are many different navigational systems but none of them approach GPS for absolute or relative accuracy. The error in the navigation solution arises from the errors in ranging to the satellites. The ranging errors in turn have a component in the satellites (clocks and orbital specification), propagation (plasmasphere, ionosphere, atmosphere, and multipath) and in the receiver (tracking and intermodulation). Ranging errors have been the focus of many investigations and are dependent on a variety of factors, many of which are application dependent. Table 1 is a conservative estimate of error sources. The actual values are so dependent on a specific application or implementation of a technique that these values should be taken as approximate. Later we will discuss ionospheric propagation, dual-frequency receivers (L1/L2), and differential corrections. Now we will just examine the major trends in this table, which are

Fig. 3. Schematic drawing showing how satellite geometry affects the mapping of ranging error to navigational error.

Table 1 lists ranging errors. To calculate navigation errors, the ranging errors must be mapped to the navigation solution. This process is dependent on the satellite geometry as seen by the receiver. Fig. 3 illustrates how satellite geometry yields different errors for the navigation solution when the ranging errors are identical. Each measured range has some error associated with it that is drawn as a double circle in Fig. 3. The navigation solution, then, will fall into the intersection of these double circles. On the left-

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hand side the satellite geometry is such that circles meet at nearly right angles and the intersecting area is small. On the right-hand side the double circles are nearly parallel, so their intersection is much larger than on the left-hand side, yielding much larger navigation errors. The factor mapping the ranging solution to the navigation solution is called dilution of precision (DOP). DOP is calculated from the design matrix containing the unit vectors

 xˆ1  2  xˆ A= 3 ˆ x  xˆ 4 

yˆ 1 yˆ 2

zˆ1 zˆ 2

yˆ 3 yˆ 4

zˆ 3 zˆ 4

− 1  − 1 − 1 − 1

human body will block signals. Now we can return to Table 1 and estimate navigational errors. At this point we should note that occasionally GDOP is less than 2 but never reaches its optimal value of 1.6 for earth-bound receivers. However, GDOP can frequently be larger than 3, especially in conditions where there is not a clear view of the sky down to the horizon. In poor viewing conditions GDOP can easily become 10 or worse. If we use the typical GDOP factors of 2-3, this implies a total navigational error of 14 to 51 m for an unaided L1 receiver. F. Differential GPS (DGPS)

(3)

Differential techniques, both in general and with GPS, rely on one or more reference stations at well-known locations, making ranging measurements, comparing them with their known location and the computed satellite location, and computing the residuals. These residuals represent the ranging error. Generally they lump together the satellite clock errors, orbit errors, and propagation errors except for multipath. Using a variety of systems, the ranging errors are then broadcast to mobile receivers where they are applied as corrections to the pseudoranges. This concept works well when the reference receiver and the mobile receiver have a common error source. For example, the ionospheric propagation error is the same because both receivers observe through the same ionosphere. This in turn sets limits on ionospheric gradients for a given level of accuracy. In addition, differential corrections are scalars while orbital errors are vectors. So if the reference and mobile receivers are too far apart, the orbital corrections will have their own errors. A quantitative consideration of these factors is beyond the scope of this review. Table 1 (Ranging Errors) indicates how navigation errors improve with differential corrections. Many different operational differential systems are used to aid single-frequency receivers. For maritime applications, usually there are national systems with local reference receivers and limited ranges. Frequently, national systems will overlap with compatible protocols. Some maritime services use short range (a few hundred km), lowfrequency signals to transmit corrections while others use geostationary satellites. For example, the U.S. Coast Guard’s differential GPS system transmits near 300 kHz and is compatible with the Canadian DGPS system. Larger regional systems rely on geosynchronous satellites to relay the

from the receiver to the satellite and in the direction of time. Eq. (3) shows the design matrix A for a minimum four-satellite solution. Additional satellites add more rows. The Q matrix is calculated from the design matrix as

(

T

QX ≡ A A

)

−1

 qxx   q yx = q  zx q  tx

qxy q yy

qxz q yz

qzy qty

qzz qtz

qxt   q yt  qzt   qtt 

(4)

The Q matrix maps the ranging covariance matrix into the navigation covariance matrix (see, for example, Parkinson et al., 1996, p. 195). In its simplest form it provides a scaling factor from the pseudorange errors (σPR) to the navigational errors. For example, the trace of the Q matrix can be used to define the geometrical dilution of precision (GDOP) through

σ xx2 + σ yy2 + σ zz2 + σ tt2 = q xx + q yy + q zz + qtt σ PR = GDOP ⋅ σ PR

(5)

where x, y, and z represent the ECEF coordinates and σ is the error in a particular component of the process. By appropriate rotations of the Q matrix, similar dilution of precision scaling factors can be generated for local horizontal and vertical directions. Typical GDOP factors range from 2 to 3 depending on the satellites above the horizon, their positions, and which satellites can be seen by the receiver. Buildings, foliage and, of course, the

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differential corrections and many of them use the L1 frequency and C/A codes not assigned to specific GPS satellites, simplifying receiver design. Examples of these systems include the U.S. WAAS (Wide Area Augmentation System), EGNOS (European Geostationary Navigation Overlay Service), and MSAS (Multifunctional Transport Satellite-based Augmentation System), which covers the Pacific Ocean and parts of Asia. Together, these three systems provide continuous global coverage, although the quality of the corrections may vary depending on the reference receiver locations. The utility of these systems varies with the application. For automotive and maritime navigation the quality, reliability, and correction integrity are more than adequate. However, for commercial aviation the standards are much higher and substantial effort is made to assure that either the broadcast corrections are valid or that the user knows when the system utility may be suspect. In the latter case, reference receiver spacings, knowing which ionospheric density gradients are permissible, and gradient detection all become paramount.

satellite replacement, so the modernization period will take roughly a decade. The orbits will remain unchanged, although there may be a few more satellites than the current level of 24. The first level of modernization will include new military and civilian signals. In addition to the C/A code on L1 and the P(Y) code on both L1 and L2, there will be a new civilian code on L2 and a new M code on both L1 and L2. The new L2 civilian code can be either the C/A code or two interleaved medium length and long length codes that should provide more robust tracking in the presence of scintillations. Less has been publicized about the new M code, although one suspects that it will be more difficult to jam. These signals will be incorporated in the Block II R-M satellites beginning in late 2004. The second level of GPS modernization will begin in 2006 with the Block IIF spacecraft when a new L5 signal is added (1176.45 MHz). The L5 signal is planned for safety-of-life applications and will use a frequency band protected for aviation. Galileo is the European entry into the GNSS arena. This system will be a completely original design without the legacy requirements of GPS. The system is based on a business plan instead of military need. Likely a fee will be levied to use some or even most of the services. Currently the design includes 30 spacecraft in a slightly higher inclination and higher orbits compared to GPS. The transmission plan calls for 10 signals on 6 frequencies, some containing data and some containing no data. The final design is still being created and, to some extent, negotiated as this article is being written. International issues involving the frequency for Galileo’s Public Regulated Service, which is their encrypted code for security applications, along with considerations of interference and compatibility with GPS, are serious concerns on both sides of the Atlantic. The announced schedule for implementing Galileo is ambitious. The first launch of a prototype spacecraft is scheduled for 2005 and the stated goal for an operational system is 2008.

G. Modernization and Galileo “If I could predict the future, I would not be working for a living.” Anon. During the period leading up to the next solar maximum, and certainly within ten years, there will be major changes in Global Navigation Satellite Systems. There are two major changes ahead. First, GPS will evolve into a more modern system and second, Europe will introduce its own satellite-based navigation system called Galileo. GPS was designed in the 1970s by scientists and engineers who may well have used slide rules and ran computer programs with punch cards. The system architecture was created in an environment where VLSI barely existed and no microprocessors existed. That the system is so successful today is a tribute to their vision and foresight. Nonetheless, the possibilities of current technology and what users want have advanced in major leaps. The first level of GPS modernization is scheduled to begin with launches in 2004. To understand the pace of modernization, one must first realize that GPS satellites have roughly a ten-year lifetime limited primarily by radiation belt damage to the solar arrays. The U.S. Congress is not eager to finance functional

III. The Ionosphere and Radio Navigation: Ionospheric Effects on GNSS A. Propagation in a plasma The largest error source in GPS ranging is propagation through the ionosphere where the signal group velocity slows down and phase

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velocity speeds up. For frequencies well above the electron gyrofrequency (about 1 MHz), the electromagnetic dispersion relation can be derived from Maxwell’s equations in an electron gas. Beginning with the two curl equations, r r r& r r& ∇ × H = J + D ; ∇ × E = −B (6) r r assuming a plane r r wave form for E and B of v r ψ = ψ o exp( j (k ⋅ r − ωtr)) , and r that the current density is given by J = ne qv e where ne is the electron r density, q is the charge on an electron, and v e is the instantaneous electron velocity in response to the electric field, a Fourier decomposition yields the result that the group velocity is 2 v g = c 1 − ω pe /ω2

δt =



∫v

ρ*

g

−∫ ρ

dρ vg

(9)

By employing the approximations discussed above we obtain 2 1 ω δt = ∫ pe2 dρ (10) c ρ * 2ω as the time delay. In mks units this reduces to

δt =

40.3 ne dρ cf 2 ρ∫*

(11a)

where

(7)

∫ n dρ

(11b)

e

ρ*

and the phase velocity is

vφ =

c 2 1 − ω pe /ω2

is called the total electron content or TEC. The TEC is the number of electrons found in a 1 meter square column from the receiver to the satellite. For convenience, the quantity of 1016 electrons per meter2 is called a total electron content unit or TECU. One TECU yields a cδt delay or ranging error of 16 cm. Typical daytime TEC values are a function of solar cycle and magnetic storms but typical midlatitude values are about 30 TECU and equatorial values are about 50 TECU. These values are, of course, quite variable with diurnal, seasonal, solar cycle, and storm time variations. Dual-frequency GPS receivers operate by comparing the time delay between two different frequencies, in this case L1 at 1.57442 GHz and L2 at 1.2276 GHz. Even though δt cannot be measured at one frequency with a standard receiver clock, the difference in δt at two different frequencies can be measured. If we define ∆(δt ) = δt L1 − δt L 2 , then the difference in arrival time for two codes transmitted at identical times but at different frequencies becomes:

(8a)

2 = ne q 2 / εme . Hence, the only variables where ω pe that can vary in either space or time are the electron density and plasma frequency, ω pe . Note that the product of the phase velocity and the group velocity is just the square of the speed of light. Furthermore, as the group velocity slows down the phase velocity speeds up. For the remainder of this discussion we will focus on the group velocity but since the group delay is equal and opposite to the phase advance, calculating the phase advance is straightforward. Since the largest plasma frequencies in the ionosphere are the order of 10 MHz while the GPS 2 / ω 2 is L1 signal is 1.6 GHz, the quantity ω pe much less than one and we can approximate the group velocity as

 ω2  v g = c1 − pe2   2ω 

(8b)

∆(δt ) =

To calculate the delay produced by the ionospheric electron density we calculate the difference in propagation times for a path ρ* with an ionosphere and a path ρ without an ionosphere. The extra time delay is given by the difference in the two path integrals as

40.3 × TEC  f L21 − f L22   2 2  c  f L1 f L 2 

(12)

When the P code is not encrypted, the process of estimating TEC from the difference in arrival time of the P code on two different frequencies is straightforward. For the encrypted P code, called the P(Y) code, the situation is somewhat more complicated. In this case one can cross-correlate

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the two codes to find the difference in arrival time, even though the code is unknown (HofmannWellenhof et al., 2001). Because this process is rather noisy and requires averaging, it will not work for a moving receiver. Current civilian receivers estimating TEC without the encryption key are also expensive and heavy.

individual satellites yield different results by up to 5 ns. Next, the model delay is not a very good approximation: during the day the dual-frequency calculated delay can be double the model estimate. During a magnetic storm or equatorial spread F, the model becomes even less valid when it cannot accommodate large temporal and spatial variations. B. Scintillations Scintillations occur when a plane wave traverses a region of irregularities containing fluctuations in the index of refraction. Before entering the region of irregularities the plane wave possesses a front of constant phase. After exiting the region of irregularities the previously constant phase front varies in phase, depending on the nature of the index of refraction irregularities. Well below the region of irregularities, the wave fronts add to form destructive or constructive interference. This overly simplified picture has been examined more rigorously from a variety of viewpoints (Salpeter, 1967, Rino and Owen, 1980; Yeh and Liu, 1982). Here we may only summarize the highlights. Following the development of Yeh and Liu (1982), the wave equation for the electric field reduces to a rscalar equation of the form ∇ 2 E + k 2 [1 + ε 1 (r )]E = 0 . This equation is called the Helmholtz equation. For electromagnetic waves in a plasma and well above the plasma frequency, it assumes that dielectric permittivity, r ε1 (r ) , is described by a field of density irregularities. The quantity k is the electric field wave vector. The action of the irregularity layer is to change the wave phase. If we assume the wave is propagating in the z direction and the irregularity layer is in the x and y directions, then the emerging electric field will have an altered phase of the form exp(iφ (x, y )) exp(ikz ) . The phase field φ (x, y ) is produced by the density irregularities and the phase screen model assumes that this is the only perturbation to the waves. Assuming that the observer distance to the irregularities is much larger than the irregularity thickness, that the irregularity thickness is much larger than the electric field wavelength, and that the directional scattering is only to small angles in the forward direction, a relationship for power and phase can be found. Again, we use the notation of Yeh and Liu (1982) where the power spectra for the log amplitude is Φ Χ (κ ⊥ ) and the power spectra for phase deviations is Φ S (κ ⊥ ) . Then,

Fig. 4. Measured ionospheric time delays (blue) compared to the model delay (red).

We should note that most L1 C/A receivers employ an ionospheric model (Klobuchar, 1987) that uses 8 parameters in the navigation message to estimate ranging errors. The parameters are updated for solar cycle and magnetic storm conditions. Recall that this model was developed in the 1970s when there was substantially less computational power and we knew less about the ionosphere. Fig. 4 shows a comparison between the model estimate and the dual-frequency calculation of TEC for a quiet period near solar maximum at Ithaca, NY. The delay is given in nsec where 10 ns is equivalent to 3 m of range error or 18.75 TECU. The red line is the delay estimated from the ionospheric model contained in the navigation message. The blue lines are individual satellite measurements converted to equivalent vertical TEC by inverting the effect of the slant factor through the ionosphere. Next, the average of the VTEC measurements is plotted as a black line. Several conclusions can be drawn from this figure. First, biases exist in the dualfrequency measurement at both the satellite and the receiver, yielding negative and non-physical delays. In this case the bias could be the order of 5 ns for two of the satellites. Next, there is substantial spatial variability in the ionospheric TEC so, after correcting for the slant factor, the

9

r Φ Χ (κ ⊥ ) = 2πLλ2 re2 sin 2 (κ ⊥2 z / 2k )Φ ∆N (κ ⊥ ,0 )

where V ′ is the apparent velocity and t0 is the time at which the autocorrelation function takes on the maximum value of the cross-correlation function. Briggs et al. also define a characteristic velocity, which is a measure of the scintillation fade pattern change rate in the true velocity reference frame, given by

(13)

and r Φ S (κ ⊥ ) = 2πLλ2 re2 cos 2 (κ ⊥2 z / 2k )Φ ∆N (κ ⊥ ,0 )

(14)

where the amplitude or phase power spectrum is measured at the receiver location z but the density spectrum is evaluated in the irregularity r layer whose bottom is z=0. As long as Φ ∆N (κ ⊥ ,0 ) is a power law not falling steeper than κ ⊥−2 , the first peak in the log amplitude power Φ Χ (κ ⊥ ) will occur near κ ⊥2 z / 2k = π / 2 . This defines the Fresnel length of l f = 2λz , which is the length scale associated with the first maximum in the Fresnel filter. For our purposes only the first maximum is relevant since the irregularity power spectrum is significantly smaller when κ ⊥2 z / 2k = 3π / 2 . The expression for Φ Χ (κ ⊥ ) describes the spatial log-amplitude power spectrum. In general the spatial spectrum is not measured because of the unrealistic constraint of populating space with receivers measuring power. Instead the temporal spectrum is measured at one or a few receivers. With multiple receivers, some of the spatial features of the phase screen approach can be investigated, such as size and speed. We introduce this subject next.

VC =

,

(16)

D. Equatorial spread F and GPS In this section we will introduce the application of GPS receivers to investigating equatorial spread F and scintillations. There is long history of investigating spread F with other techniques for measuring TEC or scintillation drift that are too numerous to review here (Woodman, 1972; Fejer et al., 1981; Basu et al., 1986; Vacchione et al., 1987; Basu et al., 1996; Valladares et al., 1996). The advantage of GPS is a comparatively larger number of satellites, 6-9 compared to 1-2 for most geostationary experiments. Fig. 5 shows a typical GPS observation of a spread-F bubble from near the equatorial anomaly at Cachoeira Paulista, Brazil. The left-hand panel shows the track of the satellite across the sky in elevation and azimuth. The x’s on the track are one hour’s tick marks. On the right, the lower panel shows measured TEC beginning at a large value, in part because the time (1900 LT) just follows local sunset and in part because the low elevation of the satellite implies a long slant path. As the elevation increases the TEC decreases reaching a minimum near 2100 LT when the elevation is a maximum, and then the situation

A basic application of receivers that measure ionospheric scintillations is investigating the speed of scintillations using spaced receivers. In Briggs et al. (1950) an approach to measuring the drift speed of scintillation fade patterns is developed through the cross-correlation function between two receivers separated by a distance ξ0. The maximum value of the cross-correlation function at time lag τ0 yields an “apparent velocity” through ξ0/τ0. However, the true velocity is that given by the motion of an observer in which the scintillation fade pattern evolves most slowly in time and, in general, it is not the same as the apparent velocity. Briggs et al. have shown that the true velocity is related to the apparent velocity by

V′ , 1 + t02 τ 02

1 + τ 02 t02

where the denominators of the two equations above are slightly different. The fundamental contribution of Briggs et al. is the realization that spaced receivers will observe two dynamic processes. The first is the translation of the scintillation pattern from an upstream receiver to a downstream receiver. The second is the evolution of the scintillation pattern during the translation time. The apparent velocity mixes together both processes. The true velocity is the velocity at which the observed evolution of the scintillation pattern is a minimum and the characteristic velocity is a measure of how fast the scintillation pattern evolves.

C. Measuring scintillation velocity with spaced receivers

V =

V′

(15)

10

scintillations”. Fig. 6 shows an example of these fluctuations. In this example the onset of a spread-F event about mid-way through the 700 s record can be seen. Starting at 400 s, the amplitude scintillation commences while the phase scintillations begin somewhat earlier. This comparison between amplitude and phase scintillations demonstrates their partially common origin. “Phase scintillations” can be produced either by fluctuations in the TEC (refractive) or by Fresnel scattering (diffractive). The lower frequency and larger amplitude fluctuations are from long scale-length (the order of 10 km) TEC variations translating across the receiver line-ofsight while the lower amplitude but faster phase fluctuations seen after 450 s are produced in part by a diffractive process. The rapid changes in phase are a concern for semi-codeless dualfrequency GPS receivers, which frequently will not track in this environment (Kelley et al., 1996).

reverses with the TEC increasing as the elevation decreases. The top panel shows the GPS L1 signal power for satellite PRN 14 during its pass over the receiver. As the satellite rises the signal strength increases because the satellite, in a circular orbit, is approaching the receiver. The signal power reaches a maximum at the highest elevation and then declines again as the satellite approaches the northern horizon. Power (dB)

CACHOEIRA PAULISTA BRAZIL 0

PRN 14

0

40 35 30

20

TEC [TECU]

60 30

180

PRN 14

45

25

90

270

98.11.10.

50

AZIMUTH : ELEVATION

100 80 60 40 20 0

2000

2200

0000

0200

Local Time (h)

Fig. 5. Elevation and azimuth satellite trajectory (left panel), signal amplitude (upper right panel) and total electron content (lower right panel).

Amplitude Scintillation of GPS L1 Signal 98.11.10.

D

Power (dB)

The spread-F event in Fig. 5 is obvious as the irregularity decreases in TEC between 2200 LT and 2300 LT when a bubble passes between the receiver and the satellite. Associated with the bubble are irregularities at the Fresnel length (about 400 m) that produce rapid fluctuations up to 15 dB in L1 power, both increasing and decreasing which is characteristic of scintillations.

PRN 14

E F G

↑5 dB ↓

22:30

22:31 Local Time (h)

22:32

Cross Correlation

PRN 2 010118 Rx-X0



0.5

DE (79 m)



j=26

EF (50 m)

ρ

40



j=42

Power

45

35

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30 25 20 0



1

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→←

j=67

DF (129 m)

j=2

GE (70 m)

ρ

power [dB]



1

Integrated Carrier Phase (filtered)

3

0

Cycles

2 100

1

0

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Offset Number

100

0

100

Offset Number

0

Fig. 7. GPS signal amplitude and cross-correlation functions for four closely spaced receivers.

-1 -2

0

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300

400 Time (sec)

500

600

700

Kil et al. (2000, 2002) examined spread-F GPS amplitude scintillations in more detail to understand their velocity. Three antennas (D, E, and F) were placed in the west-to-east direction with spacings of (D-E) 79 m and (E-F) 50 m. North (70 m) of the E antenna was the G antenna.

Fig. 6. GPS L1 signal amplitude (upper panel) and signal phase (lower panel).

Note that the spread-F L1 amplitude scintillations are also accompanied by L1 “phase

11

were spaced too closely. They were able to show that the estimated ionospheric velocities at Cachoeira Paulista near the equatorial anomaly were similar to but consistently 10-20% larger than the equatorial ionospheric velocities estimated using radar (Kil et al., 2002). A second experiment (Kintner et al., 2004) examined scintillation drifts using a large array with east-west spacings up to 715 m and northsouth spacing of up to 1 km. The results of their east-west velocity study are shown in Fig. 8. The upper panel shows the true velocity as a function of local time, the middle panel shows the characteristic velocity, and the lower panel shows the ratio of τ 0 t0 versus local time. Several important conclusions may be drawn from this figure. First, the true velocity declines during the course of the night. Next, the true velocity is always much larger than the characteristic velocity. This point is emphasized in the bottom panel where τ 0 t0 is displayed and this ratio is almost always larger than 4 with a mean of about 10. Since the correction to the apparent velocity is t02 τ 02 (Eq. 15), the error in assuming that the apparent velocity is equal to the true velocity is 6% for the worst case and 1% typically.

The upper panel of Fig. 7 shows an example of L1 amplitude scintillations for the four antennas and the time records are virtually identical. Next, the cross-correlation function between the various antennas was calculated in time units of j=20 ms to yield the velocity. For example, the apparent velocity estimate from antenna pair EF is 50 m divided by 520 ms or about 100 m/s, which is a typical ionospheric velocity when the ionospheric puncture point velocity of the satellite signal is taken into account. In this case the maximum 500 160

Velocity (m/s)

400

140 120

300

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40

Number of Occurrences

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S4>0.5 El>10

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140

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18

East

West

φ Projection

Elevation

North Azimuth+180 o

20 18

20

22 Local time (hrs)

24

Fig. 9. Projection of the magnetic field along the GPS signal path to the horizontal plane. [After Kintner et al. (2004). Reprinted by permission of the American Geophysical Union.]

02

Fig. 8. The distribution of measured true velocities (upper panel), characteristic velocity (middle panel), and the ratio between true and characteristic velocities (lower panel). [After Kintner et al. (2004). Reprinted by permission of the American Geophysical Union.]

This second experiment produced another interesting and unexpected result (Kintner et al., 2004). Attempts to measure the north-south length of the scintillation pattern by comparing scintillations on the magnetic north-south 1 km baseline showed that the scintillation pattern was greatly elongated in the magnetic field direction

cross-correlation values are near 1, implying that the true and apparent velocities are equal. Kil et al. also tried to estimate the characteristic velocity but were unable to do so because the antennas

12

The east-west fade width will also depend on projection angle. When these two factors are accounted for, the measured widths should be a constant equal to the Fresnel length for vertical propagation. Fig. 11 shows the probability distribution for scintillation pattern widths after correcting for elevation and projection angle. The most probable values are near 400 m as expected for a scattering layer of 350-400 km altitude. Interestingly, by allowing data for signal paths within 60° of the magnetic field, the most likely Fresnel length is unchanged but a tail of events with smaller widths is produced.

but with a twist. Fig. 9 illustrates this twist where the projection of a magnetic field line maps into the horizontal plane angles that depend on the direction of the satellite signal. If the density irregularities are organized along the magnetic field and the scintillations are produced by a thin screen process where they diffract in one local volume within the F region, then one expects the scintillation pattern to also reflect this projection. The projection angle, φ, shown in Fig. 9 can be calculated from the magnetic dip angle and satellite elevation and azimuth or it can be measured from the cross-correlations of the eastwest, north-south receiver grid. The resulting calculation and projection angle can then be compared as in Fig. 10, where the calculated projection is compared against the measured projection angle. Events where the satellite vector was within 60° of being parallel to the magnetic field have been omitted to assure that the thin screen assumption is correct. The red line represents a perfect fit of the data to the model. Each data point represents one 40 s long sample and, of the 3046 total points, all but a few hundred confirm the validity of this simple model. Data from satellites where signals were within 60° of the magnetic field sometimes agreed with the model and sometimes did not.

0.12

Measured projection angle from U,W, and Z receivers

Frequency in 25 m bin

0.08

All data

0.06 0.04 0.02 0

0

250

500 Length (m)

750

1000

Fig. 11. Width of scintillation pattern fades after correcting for elevation and projection angle. [After Kintner et al. (2004). Reprinted by permission of the American Geophysical Union.]

100 80

Paths more than 60o from the magnetic field

0.1

60 degree cone filter, 3046 pts

60 40 20

The approach of using scintillation pattern velocities to estimate ionospheric velocities has been considered rigorously by Ledvina et al. (2004), in which general satellite velocities and general ionospheric velocities are included. To validate the approach, several simulations were created. The conclusion of this study is that the results of Kil et al. (2002), in which the equatorial anomaly west-east velocity was somewhat larger than the radar-derived velocities, are valid. The general conclusion from these experiments and studies is that scintillation patterns measured with GPS receivers are primarily spatial objects translating across the horizontal plane with little temporal evolution in the moving or resonant reference frame. This conclusion has important implications for using GPS in high reliability applications. GPS receivers operate by tracking a pseudorandom code. For the C/A code, the code length is 1 ms. For relatively short interruptions

0 -20 -40 -60 -80

-100 -100 -80

-60

-40

-20

0

20

40

60

80

100

Calculated projection angle from satellite elevation and azimuth

Fig. 10. A comparison of measured and computed projection angles for satellites with signal paths greater than 60° from the magnetic field.

By understanding the projection model it becomes possible to estimate the width of the scintillation patterns. The east-west fade width will depend on the distance to the scattering source and hence, needs to be adjusted for satellite elevation, assuming a constant scattering height.

13

E. Midlatitude ionospheric irregularities and storms

of the signal, and in situations in which dynamics are not extreme, most receiver tracking loops can follow the signal during a scintillation fade, typically lasting a few hundred milliseconds. However, the length of the scintillation fade is a function of the scintillation pattern speed and the receiver speed. In some cases the scintillation pattern speed can also become slow when the signal ionospheric puncture point (IPP) velocity is in the opposite direction and magnitude similar to the ionospheric drift. Fig. 12 shows this situation where the IPP velocity nearly cancels the ionospheric drift velocity, producing unusually long fades at a stationary receiver, and the fade amplitudes are large (15-20 dB). The straight lines in the signal amplitude are examples of loss of tracking. These are relatively minor examples of tracking loss unless the situation is life-critical.

By midlatitude we mean those locations poleward of the Appleton anomalies or tropical arcs. In the region just poleward, say, Hawaii, the disturbances appear to be related to equatorial spread-F dynamics penetrating to high altitudes (Makela et al., 2004). At yet higher latitudes a different phenomenon occurs during magnetic storms where large amounts of the ionosphere are swept poleward, in some cases to the polar cap, during magnetic storms (Foster et al., 2002). This latter phenomenon is a relatively recent discovery and its cause and consequences are still being investigated. The significance of midlatitude irregularities and storms to GPS and GNSS is similar to the significance of equatorial spread F. Ionospheric gradients and scintillations will disrupt or degrade GNSS operations. 07:22 UT

08:59 UT

4

8

12

16

20

24

28

07:11 UT

192

196

200

208

192

196

200

204

208

192

196

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S4 index, GPS Satellites 15, 17, 18

1.5

Fig. 12. Examples of GPS signal tracking loss of lock.

204

S4

1.0

For moving receivers that are in resonance with the drift pattern, the fades can be potentially much longer with even longer tracking losses, creating several progressively worse implications. The first consequence of tracking loss is an increase in the dilution of precision depending on the satellite(s) lost, producing an increase in navigational errors (see section IIE). For extreme cases in which scintillations fill the sky, the number of satellites successfully tracked may fall below the four required for calculating navigational solutions (S. Basu, personal communication, 2004). Finally, receivers that are newly acquiring signals will not be able to obtain the ephemerides unless there is a 30 s period with no fades yielding a bit loss, which is a more stringent condition than tracking. For most receivers the continuous bit tracking condition is 60 seconds to assure that no bit errors have occurred.

0.5 0.0 6

7

8

9

10

11

12

13

UT

Fig. 13. Images of spread-F-like bubbles and associated GPS S4 scintillation index measured from Hawaii.

An experiment combining 630 nm images with GPS scintillation measurements from Hawaii has revealed in dramatic detail the relationship between plasma bubbles and GPS scintillations. In Fig. 13 the three images on top show the evolution of 630 nm light, as a proxy for electron density, over roughly a two hour period. Fingers of reduced emissions clearly indicate the presence of plasma bubbles. The GPS IPP tracks are shown as color lines in the images and then, below the images, the S4 index for scintillations is shown for each of the three satellites. The S4 index reaches and exceeds 1 for each of the satellites over extend

14

daytime map since 21:44 UT corresponds to 15:44 EST (local time on the east coast of the USA). Typical VTEC values at midlatitudes for the daytime, declining phase of the solar cycle, and near equinox are 25-35. Each station measured TEC from 5-8 satellites that were converted to an equivalent vertical TEC (VTEC) by including the slant factor. Coverage over the oceans is minimal and only occurs via islands with CORS stations (Hawaii in this case) or where costal CORS stations observe low elevation satellites with ionospheric puncture points (IPP) over the ocean. Coverage over Canada, the arctic, and Central America/Caribbean is sparse because of the few cooperating CORS sites. Nonetheless, the coverage is adequate to determine major features, including spatial gradients.

periods and, for one 10 minute period, the S4 index exceeds 1 for two satellites simultaneously. During this event many of the equatorial spread-F features occurred at somewhat higher latitudes. Kelley et al. (2002) point out that these features sometimes extend poleward of the imager on Maui, implying that affected magnetic field lines map to 1500 km altitude at the equator. Both the implied density gradients in the 630 nm images and the scintillations imply that the use of GNSS at Hawaii will require careful implementation. The statistical results from Hawaii are also consistent with a spread-F interpretation. The occurrence rates maximize near the equinoxes and, since the experiment was initiated near solar maximum, the intensity of the scintillations has been declining, as expected. Also, the local time behavior shows a maximum in the S4 index in the early evening that declines as the night progresses. It would appear that the electric fields from spread-F phenomena propagate to higher altitudes and higher latitudes than previously believed. At yet higher latitudes an entirely new phenomenon occurs that is closely associated with magnetic storms. The low latitude boundary of this phenomenon is not well understood but it appears to extend possibly as far south as the equator and possibly as far north as the polar cap. Various features of the phenomenon have different names such as storm-enhanced density (SED), sub-auroral ion drift (SAID) and subauroral polarization streams (SAPS). A grid of GPS stations measuring TEC across the U.S. revealed that these phenomena are connected and have even been associated with plasmaspheric tails on the magnetic equator (Foster et al., 2002). In all cases thus far, the intrusion of large ionospheric densities to midlatitudes has been associated with magnetic storms. Hence, we will call this ionospheric phenomenon ionospheric magnetic storms (IMS). An example of an ionospheric magnetic storm is shown in Fig. 14. This image was made using the Continuous Operating Reference Stations (CORS) chain of GPS receivers measuring TEC. Up to 400 stations participate in CORS, including several university and governmental organizations at federal and state levels with interests in geophysics, geodesy, meteorology, navigation, and resource management. The data are held online and are available for analysis. Typical features of an IMS can be seen in the TEC map presented in Fig. 14. Note that this is a

GPS TEC Map 30 Oct 2003 21:44 UT

TEC 70

Geodetic Latitude, Deg

70

60

60

50

50

40 40 30 30 20 20 10 10 200

220 240 260 280 300 Geodetic Longitude, Deg

320

0

0 Time of IMS

−50 −100

Dst (nT)

−150 −200 −250 −300 −350 −400 −450 0

10

20

30 40 50 60 70 80 90 100 Time (hrs from 28 Oct 2003)

Fig. 14. A TEC plume over western North America in the top panel and Dst showing the TEC plume coinciding with a magnetic storm onset in the lower panel.

The principal characteristics of an IMS are large densities extending from the equatorward latitudes

15

are an elevated value of TEC early in the event with values of 60-70 compared to typical values of 30-35 followed by a sudden decrease in TEC shortly after midnight on September 25. Following this decrease the TEC is structured with more typical daytime values. The sudden decrease is not a temporal event but rather occurs as the satellite IPP traverses a region of sharp TEC gradients. Concurrent with the sudden decrease and spatially coincident with the TEC gradient is a period of large amplitude scintillations. The S4 index for these scintillations reached a maximum value of 0.8, and similar TEC gradients and scintillations were observed from the signals of three other GPS satellites during this period.

over midlatitudes and into the auroral region or polar cap, visible as the swath across the map of TEC=70. Clearly the swath extends equatorward and, even though there are few stations in the arctic, it extends into the daytime auroral zone. Next the IMS has a sharp and greatly extended TEC gradient stretching from the southeast to the northwest over a distance of perhaps 5000 km. The VTEC value changes by a factor of two over the 100-200 km range along the gradient. The lower panel of Fig. 14 is a plot of Dst for the time period and includes the IMS in the upper panel. The time of the upper panel is marked in the lower panel and in the time of the IMS. Two magnetic storms occur. The first begins early on October 29 and then begins recovering early on October 30. Near the end of October 30 a second magnetic storm begins and this is when the IMS pictured in the upper panel occurs. IMS typically occur during the developmental phase of a magnetic storm when Dst is decreasing.

4

energy, eV

10 10

2 ions

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20 UT C (hours ) 23 MLat (deg N) 51.62

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P ower (dB)

6

3

Ds t , S ignal P ower and T E C on S eptember 25-26, 2001

T E C (T E C U)

electrons

500

Fig. 15. Dst in the top panel. The gray area in the top panel corresponds to the time interval in the lower two panels. GPS signal power and TEC are in the lower two panels.

0

−500

UT 0422 MLat 41.8

Fig. 15 shows an example of scintillations measured during an IMS. Different physical processes produce the scintillations than those shown in Fig. 5 but there are similar features. The upper panel shows Dst with a magnetic storm beginning near the end of September 25 and continuing into September 26. This is relatively moderate storm with Dst of about 100 compared to the previous example of Dst at nearly 400. Below the Dst plot in the upper panel of Fig. 15 are shown the signal amplitude (middle panel) and TEC (bottom panel) for a single GPS satellite as measured at Ithaca, NY. The important features

0423

0424

0425

0426

0427

45.2

48.6

51.9

55.1

58.3

Fig. 16. DMSP observations of electrons, ions, ionospheric drift velocity, and magnetic field perturbations. [Figure courtesy of Evgenii Mishin.]

Mishin and colleagues have investigated the highly structured ionosphere associated with scintillations using DMSP data. The DMSP satellites are in sun-synchronous polar orbits at an altitude of about 800 km. Fig. 16 shows a poleward pass during a magnetic storm. The primary feature can be seen in the third panel from

16

the estimate. Civilian receivers currently do not have convenient access to dual-frequency information but may have access in the next decade either through modernized GPS or Galileo. Hence, dual-frequency estimates are not an option. We showed earlier that, even on a quiet ionosphere day, estimation errors in the TEC model could be 20 TECU, producing 3.2 m of ranging error or 6-9 m of navigational error. On a day in which an ionospheric magnetic storm occurs these errors could easily exceed 100 TECU, corresponding to 32-48 m of navigational error. Additionally, the ionospheric models have no provision for spread-F bubbles or similar TEC structures and gradients. We are not aware of any studies comparing the GPS ionospheric model to the spread-F ionosphere, but since 50 TECU bubbles are common this yields 16-24 m navigational errors. The third technique relies on reference stations providing differential corrections. In principle this technique can be very accurate, even more accurate than the dual-frequency technique, if the reference and mobile station are observing the same ionosphere. For cases in which a grid of reference stations is used, such as WAAS, the accuracy depends on the ability of the grid and measurement model to estimate the ionospheric TEC. When there are sharp gradients the measurement model will fail. Knowing when the model fails to provide accurate TEC estimates is critical for system integrity. In Fig. 14 any measurement model not employing thousands of TEC reference receivers will fail but it also seems possible that a smaller set of stations can detect the gradient to provide system integrity. Defining and making these measurement models operational is an active area of interest for aviation. A similar set of problems exists for using differential techniques in regions where spread F is common. In this case the gradients may be more localized, making their detection more difficult. Even if the TEC is accurately estimated, tracking during scintillations is required for accurate and reliable navigation. We discussed this earlier in section IIC and we return to it again because this is potentially the most misunderstood consequence of ionospheric weather on GNSS systems. Scintillations are fluctuations in signal amplitudes that can reduce the signal amplitude below detection levels. When they cannot be detected, the tracking loops for following the signals cannot operate. When the tracking loops

the top, which shows cross-track convection or ionospheric flows as being large, structured, and highly variable (±1 km/s). These fluctuating convection fields are believed to be associated with the scintillations shown in Fig. 15 (Mishin et al., 2002). The upper two panels show increasing fluxes of energetic (1-20 keV) electron and ions during the poleward motion of the satellite. These flux gradients are indicative of the inner edge of the ring current and plasma sheet. The source of the fluctuating ionospheric flows is not known other than being associated with the inner edge of the developing ring current.

IV. Summary A review of GPS, GNSS, and the ionosphere in one (page restricted) paper is, by necessity, limited. We have reviewed the operating principle of radio navigation and its implementation by GPS. We have also examined how GPS can be used as a remote sensing system for the ionosphere by measuring total electron content (TEC) and by measuring the drift of scintillation patterns with multiple receivers. In a few instances we have noted how ionospheric disturbances can affect the operation of GPS and GNSS systems. Here we will complete the review by examining the effects of ionospheric estimation, gradients, and scintillations on GPS reliability and integrity. To accurately correct for the ionospheric group delay or phase advance to the GPS navigation signal, three methods are used. The first is to employ an 8 parameter ionospheric model and to include the parameters in the navigation message. We showed how, on a quiet day, inaccuracies in the TEC estimate could easily be 20 TECU. The second method is to transmit the ranging signals on two frequencies sufficiently far apart that the dispersive effects of propagation through a plasma permit the total electron content to be estimated from the differential delay. The third method is to create reference receivers at known locations that measure the ranging error due to ionospheric delay (as well as ephemeris and clock errors) and then transmit those errors to mobile receivers. Once TEC is estimated (through a model) or measured directly (through dual-frequency systems) or indirectly (through differential systems), a ranging correction can be applied. One TEC unit of 1016 electrons per meter2 produces a 16 cm ranging error. The accuracy of the ranging correction depends on the accuracy of

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somewhat. The L2 civil long code will repeat once per 1.5 s and not contain data which will help track through shorter fades. However, at the smaller L2 frequency, fades will be deeper compared to L1 for the same ionospheric conditions. Long fades during resonance will continue to remain a challenge. GPS and GNSS have become part of our technical infrastructure and a public utility. A somewhat unintended consequence of GPS is the ability to image the ionosphere over continental size regions. This ability has revealed in fascinating detail the reaction of the midlatitude ionosphere to magnetic storms. Previous investigations with single ionosondes suggested that F-region densities might increase but did not reveal the large and structured regions of increased densities. At the same time, ionospheric structure will make accurate, highly reliable, and continuous navigation difficult. Spread F or ionospheric magnetic storms will increase errors because they create short-scale TEC gradients. Detecting these errors will be a focus for incorporating differential correction approaches to aviation navigation. GPS has created the most accurate and available navigation in existence. However, users always want more accuracy and availability. To reach the next level, the effects of the ionosphere and of ionospheric storms must be considered in designing practical systems.

stop operating, a variety of consequences are possible, depending on the details of the tracking loop implemented in the receiver. Unfortunately, most tracking loops are proprietary and without thorough evaluation, predicting their performance is difficult at best. When the tracking loop fails it must reacquire the signal. Some tracking loops assume that the signal properties will not change in time and thus wait for the signal to return while maintaining the code phase and Doppler. This assumption cannot continue forever, though, and if the signal does not return, a strategy of searching for code phase and Doppler must be implemented. There are smart and not so smart ways to do this, depending on information from the remaining satellites being tracked.

Acknowledgements The author thanks Anthea Coster, Ted Beach, Hyosub Kil, Eurico de Paula, and Mark Psiaki for their contributions to this paper. Work at Cornell University was supported by the Office of Naval Research under grant N00014-92-j-1822.

Fig. 17. Scintillations from Fig. 15 shown on an expanded time scale in the lower panel with loss of control loop tracking.

As an example of how a receiver might operate in a scintillating environment, we show signal amplitudes when tracking lock was lost during the event previously discussed in section IIE. In this case we have expanded in time the period of largest amplitude scintillations from Fig. 17 to see three periods of about 15 s each when tracking failed. This example is one in which the scintillation time scale is rapid, the order of a second. We noted earlier that when the receiver moves with the scintillation pattern resonance, longer fades are expected. With longer fades reacquisition becomes more difficult. The new signals created for modernized GPS and under consideration for Galileo will help

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Vacchione, J.D., Franke, S.J., and Yeh, K.C., 1987. A new analysis technique for estimating zonal irregularity drifts and variability in the equatorial F region using spaced receiver scintillation data, Radio Science 22, 745-756. Valladares, C.E., Sheehan, R., Basu, S., Kuenzler, H., and Espinoza, J., 1996. The multi-instrumented studies of equatorial thermosphere aeronomy scintillation system: Climatology of zonal drifts, Journal of Geophysical Research 101(12), 26,839-26,850. Vo, H.B., and Foster, J.C., 2001. A quantitative study of ionospheric density gradients at midlatitudes, Journal of Geophysical Research 106(A10), 21,555-21,563. Woodman, R.F., 1972. East-west ionospheric drifts at the magnetic equator, Space Research 12, 969-974. Yeh, K.C., and Liu, C.H., 1982. Radio wave scintillations in the ionosphere, Proceedings of the IEEE 70, 324-360.

Further Reading Aarons, J., 1982. Global morphology of ionospheric scintillations, Proceedings of the IEEE 70, 360-378. Aarons, J., 1993. The longitudinal morphology of equatorial F-layer irregularities relevant to their occurrence, Space Science Review 63(3-4), 209-243. Aarons, J., 1997. 50 years of radio-scintillation observations, IEEE Antennas and Propagation Magazine 39(6), 7-12. Aarons, J., Mullen, J.P., Whitney, H.E., and MacKenzie, E.M., 1980. The dynamics of equatorial irregularity patch formation, motion, and decay, Journal of Geophysical Research 85(1), 139-149. Aarons, J., Klobuchar, J.A., Whitney, H.E., Austen, J., Johnson, A.L., and Rino, C.L., 1983. Gigahertz scintillations associated with equatorial patches, Radio Science 18, 421-434. Aarons, J., Mendillo, M., and Yantosca, R., 1996. GPS phase fluctuations in the equatorial region, Proceedings of the 1996 Ionospheric Effects Symposium, Alexandria, VA. Aarons, J., Mendillo, M., and Yantosca, R., 1997. GPS phase fluctuations in the equatorial region during sunspot minimum, Radio Science 32(4), 1535-1550. Abdu, M.A., Sobral, J.H.A., Batista, I.S., Rios, V.H., and Medina, C. 1998. Equatorial spread-F occurrence statistics in the American longitudes: Diurnal, seasonal and solar cycle variations, Advances in Space Research 22(6), 851-854. Basu, Sa., and Basu, Su., 1981. Equatorial scintillations - A review, Journal of Atmospheric and Terrestrial Physics 43(5-6), 473-489. Basu, Sa., McClure, J.P., Basu, Su., Hanson, W.B., and Aarons, J., 1980. Coordinated study of equatorial scintillations and in situ and radar observations of nighttime F region irregularities, Journal of Geophysical Research 85, 5119-5130. Basu, Sa., Basu, Su., Kudeki, E., Zengingonul, H.P., Bioni, M.A., and Meriwether, J.W., 1991. Zonal irregularity drifts and neutral winds measured near the magnetic equator in Peru, Journal of Atmospheric and Terrestrial Physics 53, 743-755. Basu, Su., Aarons, J., McClure, J.P., La Hoz, C., Bushby, A., and Woodman, R.F., 1977. Preliminary comparisons of VHF radar maps of F-region irregularities with

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scintillations in the equatorial region, Journal of Atmospheric and Terrestrial Physics 39, 1251-1261. Beach, T.L., and Kintner, P.M., 1999. Simultaneous Global Position System observations of equatorial scintillations and total electron content fluctuations, Journal of Geophysical Research 104(10), 22,553-22,565. Beach, T.L., and Kintner, P.M., 2001. Development and use of a GPS ionospheric scintillation monitor, IEEE Transactions on Geoscience and Remote Sensing 39(5), 918-928. Bishop, G., S. Basu, S., Holland, E., and Secan, J., 1994. Impacts of ionospheric fading on GPS navigation integrity, Proceedings of ION GPS-94, Institute of Navigation, 577-585. Coley, W.R., and Heelis, R.A., 1989. Low-latitude zonal and vertical ion drifts seen by DE 2, Journal of Geophysical Research 94, 6751-6761. DasGupta, A., Basu, Sa., Aarons, J., Klobuchar, J.A., Basu, Su.,and Bushby, A., 1983. VHF amplitude scintillations and associated electron content depletions as observed at Arequipa, Peru, Journal of Atmospheric and Terrestrial Physics 45(1), 15-26. Doherty, P.H., Delay, S.H., Valladares, C.E., and Klobuchar, J., 2000. Ionospheric scintillation effects in the equatorial and auroral regions, Proceedings of ION GPS2000, Institute of Navigation, 662-671. Farley, D.T., Balsley, B.B., Woodman, R.F., and McClure, J.P., 1970. Equatorial spread F: Implications of VHF radar observations, Journal of Geophysical Research 75(34), 7199-7216. Hysell, D.L., 1999. Imaging coherent backscatter radar studies of equatorial spread F, Journal of Atmospheric and Terrestrial Physics 61(9) 701-716. Kelley, M.C., Haerendel, G., Kappler, H., Valenzuela, A., Balsley, B.B., Carter, D.A., Ecklund, W.L., Carlson, C.W., Hausler, B., and Torbert, R., 1976. Evidence for a Rayleigh-Taylor type instability and upwelling of depleted density regions during equatorial spread F, Geophysical Research Letters 3(8), 448-450. Kintner, P.M., Kil, H., Beach, T.L., and de Paula, E.R., 2001. Fading timescales associated with GPS signals and potential consequences Radio Science 36(4), 731-743. McClure, J.P., Hanson, W.B., and Hoffman, J.H., 1977. Plasma bubbles and irregularities in the equatorial ionosphere, Journal of Geophysical Research 82, 2650.

Mendillo, M., and Baumgardner, J., 1982. Airglow characteristics of equatorial plasma depletions, Journal of Geophysical Research 87, 7641-7652. Mendillo, M., Baumgardner, J., Colerico, M., and Nottingham, D., 1997. Imaging science contributions to equatorial aeronomy: Initial results from the MISETA program, Journal of Atmospheric and Solar-Terrestrial Physics 59(13), 1587-1599. Musman, S., Jahn, J.-M., LaBelle, J., and Swartz, W.E., 1997. Imaging spread-F structures using GPS observations at Alcântara, Brazil, Geophysical Research Letters 24(13), 1703-1706. Pi, X., Mannucci, A.J., Lindqwister, U.J., and Ho, C.M., 1997. Monitoring of global ionospheric irregularities using the worldwide GPS network, Geophysical Research Letters 24, 2283. Sobral, J.H.A., and Abdu, M.A., 1991. Solar activity effects on equatorial plasma bubble zonal velocity and its latitude gradient as measured by airglow scanning photometers, Journal of Atmospheric and Terrestrial Physics 53(8), 729-742. Sobral, J.H.A., Abdu, M.A., Yamashita, S., Gonzalez, W.D., de Gonzalez, A.C., Batista, I.S., Zamlutti, C.J., and Tsurutani, B.T., 2001. Responses of the low-latitude ionosphere to very intense geomagnetic storms, Journal of Atmospheric and Solar-Terrestrial Physics 63(9), 965974. Strauss, P.R., Anderson, P.C., and Danahar, J.E., 2002. GPS occultation sensor observations of ionospheric scintillation, Geophysical Research Letters, submitted. Tinsley, B.A., Rohrbaugh, R.P., Hanson, W.B., and Broadfoot, A.L., 1997. Images of transequatorial Fregion bubbles in 630- and 777-nm emissions compared with satellite measurements, Journal of Geophysical Research 102(2), 2057-2077. Vats, H.O., Sharma, S., Oza, R., Iyer, K.N., Chandra, H., Sawant, H.S., and. Deshpande, M.R., 2001. Interplanetary and terrestrial observations of an Earthdirected coronal mass ejection, Radio Science 36(6), 1769-1773. Woodman, R.F., and La Hoz, C., 1976. Radar observations of F region irregularities, Journal of Geophysical Research 81(31), 5447-5466.

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