Determination and Reduction of GPS Reference Station ... - CiteSeerX

Determination and Reduction of GPS Reference Station Multipath Using Multiple Receivers Captain J. Raquet and G. Lachapelle Department of Geomatics Engineering, The University of Calgary

BIOGRAPHY Captain Raquet is a Ph.D. student at The University of Calgary under sponsorship from the Air Force Institute of Technology. Prior to his current assignment, he worked on INS/GPS integration for flight reference purposes at Holloman Air Force Base, New Mexico. Captain Raquet received a B.S. in Astronautical Engineering from the U. S. Air Force Academy and an M.S. in Aeronautical/Astronautical Engineering from The Massachusetts Institute of Technology. Dr. G´erard Lachapelle is Professor and Head of the Department of Geomatics Engineering where he is responsible for teaching and research related to positioning, navigation, and hydrography. He has been involved with GPS developments and applications since 1980. ABSTRACT A new method for reducing code and carrier-phase multipath is tested which uses GPS receiver measurements from two or more receivers in order to obtain accurate estimates of code or carrier-phase multipath. This method generates a multipath estimate for each individual receiver/satellite pair on an epoch by epoch basis. One of the strengths of this method is that it uses double differencing from receivers in very close proximity to each other, so all correlated errors (including atmospheric errors) are significantly reduced. The effectiveness of this method is demonstrated in a kinematic field test involving one mobile receiver and four reference receivers. Single difference L 1 code positioning of the mobile receiver was performed at distances between

ION GPS-96, September 1996, Session B4

5 and 29 km. When the reference receiver measurements were corrected using the new method and three additional reference receivers, there was a 28–35% improvement in positioning accuracy at the mobile receiver. It is also demonstrated that this method can be used in conjunction with other multipath mitigation techniques (such as carrierphase smoothing). INTRODUCTION With the recent advancements in GPS receiver technology and differential GPS positioning methods, many of the errors sources in GPS code and carrier-phase measurements have been significantly reduced. As a result, GPS multipath has become a dominant error source for many high precision applications, and various methods for reducing multipath have been developed. The most basic method is to place the GPS antenna in a low-multipath environment, away from any potential reflectors and with a good ground plane or chokering (Tranquilla et. al. 1994). Another common method for reducing code multipath is to smooth the code measurements with the carrier-phase measurements (Hatch, 1982). Some have attempted to model the multipath environment around a fixed antenna using simulated or real data (Hajj 1990, Cohen 1992, Hardwick et. al. 1995). Others have used the signal to noise ratio in combination with the antenna gain pattern to estimate the carrier-phase multipath (Axelrad, et. al. 1996). A number of techniques involve signal processing methods internal to the GPS receiver (Townsend and Fenton 1994, Townsend et. al. 1995, Kumar and Lau 1996). Filtering techniques have also been used to estimate and correct for the multipath errors (Johnson and King, 1996).

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A new approach was given in (Raquet 1996) which uses multiple fixed receivers at known coordinates to estimate and reduce multipath (and noise) for each code or carrierphase measurement at each receiver, using a network adjustment methodology. Others have proposed using multiple receivers for error reduction, normally in the context of a Wide-Area Differential GPS (WADGPS) system for positioning using the code measurements (Kee et. al. 1992, Lapucha and Huff 1992, Ashkenazi and Hill 1992, Spradley 1993). The primary differences between the new network adjustment method and other multiple-reference methods are that





The new method corrects the reference receiver's measurements, as opposed to providing differential range corrections to be applied to the mobile receiver's measurements. From an implementation point of view, this means that this method can be used with existing code or carrier-phase differential positioning software that utilizes reference receiver raw measurements. After the network adjustment is completed, the corrected measurements are essentially more accurate versions of the original raw measurements. This distinction is especially important for network carrierphase ambiguity resolution, because all ambiguity resolution algorithms require the “raw” measurements from both the mobile and reference receivers. The new method corrects only the errors which are uncorrelated between each receiver. Any error which is seen equally by all receivers (such as a satellite clock error) will not be corrected. If the reference stations are close to each other (within several kilometers), the primary error sources that will be removed by the network adjustment are multipath (to the degree that it's uncorrelated) and noise.

Other advantages of the network adjustment method are as follows: 1. It can be used to reduce both code and carrier-phase multipath (and measurement noise). 2. It is performed on an epoch by epoch basis, so there are no assumptions about error dynamics and there is no required initialization time. 3. Multipath and noise errors are isolated and assigned to specific measurements. This can provide insight into the cause of the multipath at a reference receiver site. 4. It can be performed in real-time. All that is required to do this is to combine the data from each of the reference receivers together in real-time, which is generally not difficult because the reference receivers are at fixed locations on the ground. ION GPS-96, September 1996, Session B4

5. It is computationally efficient, involving a single multiplication of a measurement vector by a matrix which is uniquely a function of the number of receivers and the number of visible satellites. 6. It can be used with measurements from any GPS receiver that outputs raw measurements. 7. It can be used in combination with other multipath reduction methods. It was shown in a previous test that this network adjustment method improved code positioning accuracy between receivers in a small network in which all receivers were within 1 km of each other. The same methodology was also applied to reduce carrier-phase multipath, which resulted in a significant reduction in the time required to accurately determine the carrier-phase integer ambiguities (Raquet 1996). In this paper, the network adjustment method is applied to a more realistic differential positioning scenario which involves a moving vehicle (van) at distances between 5 and 29 km from the reference station. The adjustment is performed using both carrier-phase smoothed code measurements and pure code measurements, and the results are compared. NETWORK ADJUSTMENT METHOD A brief description of the network adjustment method for code measurements is given below. See (Raquet 1996) for a more detailed description, including the application to carrier-phase measurements. With the network adjustment method, a least-squares condition adjustment is applied at each measurement epoch, resulting in corrections for every measurement. The condition is that all of the double differences of the adjusted measurements minus the calculated ranges is zero (which would be true if there were no uncorrelated errors). The calculated ranges (the vector ) are the distances between the receivers' known positions and the positions of the satellites, as calculated from the ephemeris data.

R

If all of the code measurements from each receiver to each satellite are placed into the vector  , then the corrections to these measurements is calculated by

^ = ;CBT [BC BT ];1r
 ; 




(1)

where r is a vector of all independent double differenced measurement minus range values (r  ; ),  is the variance-covariance matrix of the errors in the pseudorange measurements  , and


(


) : B = @ (r@
  

R) C

(2)

2

KINEMATIC TEST SCENARIO

Percent Reduction in Standard Deviation 10

Reference Receivers

9 50%

Number of Satellites

8 7

45%

6

40%

5 35%

4

30% 20%

3

25%

15%

2

2

3

4 5 6 Number of Receivers

7

8

Figure 1: Reduction in the (Multipath and Noise) Error Standard Deviation After Applying Network Adjustment Corrections The equation

^ ^ =  +  :

(3)

^

is then used to calculated the corrected measurements  . A contour plot showing the effectiveness of this method as a function of the number of receivers and the number of satellites is given in Figure 1. This plot shows the percentage reduction in the standard deviation of the multipath and noise errors obtained by applying the network adjustment. It is evident that the more receivers and satellites, the better the results. Note that with just two receivers, however, there can be a 25% reduction when there are 7–8 visible satellites. This plot assumes that, over all time, the multipath error distributions are Gaussian, that they are identical between all receivers and all satellites, and that they are uncorrelated. While these assumptions may not be true in every situation, they are reasonable for obtaining a rough estimate of how well the method could work. Experience with actual field data has been consistent with the values shown in the plot.

C

Note that the off-diagonal terms of the matrix  is able to account for any correlation that does exist between the errors in the pseudorange measurements. For the results presented below, all of the measurements were assumed to be uncorrelated and of uniform variance, so the identity matrix was used for  . Using a more accurate  to account for different multipath conditions and crosscorrelations at each site would improve the results that follow.

C

ION GPS-96, September 1996, Session B4

C

A total of four reference receivers were used for this test as shown in Figure 2. Receiver 1 was a NovAtel MilleniumTM all-in-view dual frequency receiver with an L1 /L2 antenna with chokering. It was mounted on a concrete pillar N4 on the roof of the four story Engineering building at The University of Calgary. The other three receivers were NovAtel 3515R GPSCardTM12 channel L1 only receivers. The antenna for Receiver 2 was a NovAtel model 501 dome antenna (with no choke ring or ground plane), mounted on pillar N1 on the Engineering building, approximately 9 m from receiver 1. Receivers 3 and 4 both had NovAtel model 501 dome antennas with chokerings, and they were mounted at the University of Calgary weather station which is 620 m west of the engineering building. Receiver 3 was placed on a tripod on the roof of the single story weather building, and receiver 4 was placed on a tripod on the ground about 9 m from the building and 11 m from receiver 3. Data from all of the reference receivers was collected at a 1 Hz rate. The positions of each of the reference receivers is shown on the inset of Figure 2. The positions of receivers 2, 3, and 4 were calculated relative to receiver 1 by using the carrier-phase integer ambiguity resolved positions generated by FLYKINTM(Lachapelle et. al. 1992). The average position over one hour was taken to be the true positions for these receivers. Using this method, the relative positions between the reference receivers is estimated to be accurate to 1–2 cm. This level of accuracy is sufficient for adjustment and analysis of the code measurements, which have an approximate accuracy of 0.1–1 m, depending upon the actual multipath conditions at the site. Based upon past experience and the fact that there are a few potential reflecting surfaces on the roof of the Engineering building, it could be characterized as a moderate multipath environment. The same is true of the receivers at the weather station. Mobile Receiver A NovAtel Millenium dual frequency receiver was used in the test van (a Plymouth Grand Voyager). It was attached to an L1 /L2 antenna with chokering, mounted 25 cm above the roof of the van. Raw measurement data was collected through the RS-232 port onto a laptop computer at a 1 Hz rate. Figure 2 shows the route that was taken by the van. The thick line represents the sections in which there was a valid double difference carrier-phase position solution with correctly resolved integer ambiguities. This truth data was obtained by running an enhanced version of the

3

15

10

Ref 4

Ref 1

Ref 3

Ref 2

0

−0.3 −0.6

5

−0.3 0 East Dist (km)

Static Pt 1

0 Static Pt 2

−5

−10 −30

Van route Truth data available

Radial Distance From Reference Station 1 (km)

0.3 North Dist (km)

North Distance from Reference Station 1 (km)

20

30

25

Van route Truth data available

20

15

10

5

0 244800 14:00

246600 14:30

248400 250200 252000 15:00 15:30 16:00 GPS Week Seconds/Local Time

253800 16:30

−25 −20 −15 −10 −5 0 East Distance from Reference Station 1 (km)

Figure 2: Kinematic Test Layout

FLYKINTMsoftware filter in both the forward and backward directions, and a series of quality checks was performed on the results to make sure that they were reliable. The estimated accuracy of the truth data is 2–3 cm (with residuals of only a few millimeters). The areas where there is no truth data represents regions where there were numerous satellite obstructions, such as bridges, overhead signs, and trees on the side of the road. The distance between reference station 1 and the test van is shown in Figure 3. Once again, the thick line represents epochs where valid truth data is available. Note that the first hour and a half was static (Static Pt 1), followed by nearly continuous dynamics until another static period at 14:20 local time (Static Pt 2). The test was performed on September 3rd, 1996. Using a cutoff angle of 10 degrees, there was an average of 6.6 usable satellites over the period of test, with a PDOP generally less than 2.4 (with occasional spikes to 3.5). KINEMATIC TEST ANALYSIS For the analysis that follows, the position of the mobile receiver was calculated by code single difference differential positioning using the C3NAVTM software package (Cannon et. al. 1992) in a number of different modes using single frequency L1 data. The accuracy of these code based solutions was then evaluated by comparing them with the truth data. Figure 4 shows three representative example error plots. Each of them shows the north error component in the single difference code mobile solution when reference receiver 1 was used with no network adjustment performed. ION GPS-96, September 1996, Session B4

Figure 3: Relative Distance Between Reference Receiver 1 and the Test Van

The top plot was generated using pure code from the reference and mobile receivers. For the middle plot, the reference receiver code measurements were smoothed by the carrier-phase measurements, but the mobile receiver measurements were still pure code. For the bottom plot, both the mobile and reference receivers were smoothed by the code measurements. This carrier-phase smoothing was done using the algorithm implemented in C3NAVTM . These plots show that the noise is reduced by the carrier-phase smoothing, but there is not an appreciable improvement in overall accuracy due to some large time-correlated errors that look like multipath. Figure 5 shows a set of plots that were generated in the same manner as those in Figure 4, except that the reference receiver data was corrected using the network adjustment method. (The mobile receiver measurements were identical for both figures). Note that there is a significant accuracy improvement over the non-adjusted values shown in Figure 4, because the network adjustment was able to remove a significant portion of the reference receiver's multipath. Now that the multipath has been reduced, the reduction in noise resulting from carrier-phase smoothing caused a further improvement in overall accuracy. When the reference data was both carrier-smoothed and adjusted by the network adjustment, the order in which the two procedures were performed was not significant. Both procedures yielded an incremental improvement in accuracy. This clearly demonstrates the feasibility of using the network adjustment method in combination with other error reduction methods. The network adjustment method will incrementally reduce multipath and noise if used in combination with any other error reduction method 4

North Error (m)

Pure Code Solution (No Carrier Smoothing

2 0 −2

Mean = 0.59, Std Dev = 0.85, RMS = 1.03

−4

North Error (m)

Reference Receiver Carrier Smoothed

4 2 0 −2

Mean = 0.58, Std Dev = 0.70, RMS = 0.91

−4

Both Receivers Carrier Smoothed

4

North Error (m)

North Error (m) North Error (m) North Error (m)

4

2 0 −2

−4 244800 14:00

Mean = 0.64, Std Dev = 0.65, RMS = 0.91

246600 14:30

248400 250200 252000 15:00 15:30 16:00 GPS Week Seconds/Local Time

253800 16:30

4

Pure Code Solution (No Carrier Smoothing

2 0 −2

Mean = 0.24, Std Dev = 0.47, RMS = 0.53

−4 Reference Receiver Carrier Smoothed

4 2 0 −2

Mean = 0.25, Std Dev = 0.38, RMS = 0.45

−4

Both Receivers Carrier Smoothed

4 2 0 −2

−4 244800 14:00

Mean = 0.27, Std Dev = 0.30, RMS = 0.40

246600 14:30

248400 250200 252000 15:00 15:30 16:00 GPS Week Seconds/Local Time

253800 16:30

Figure 4: Single Difference Code North Positioning Error of Van Using Reference Receiver 1 (Unadjusted)

Figure 5: Single Difference Code North Positioning Error of Van Using Reference Receiver 1 With Reference Network Adjustment

which does not introduce correlations between measurements from different receivers or between measurements within a single receiver. Even if there are correlations introduced by other methods, the network adjustment method will still be effective as long as those correlations are accounted for appropriately in the covariance matrix of equation 1.

perform single difference code positioning between each of the reference receivers (separately) and the mobile receiver. The position errors at the mobile receiver were calculated relative to the truth data, and the root mean square (RMS) error was calculated separately for the north, east, and vertical directions (RMSeast , RMSnorth , and RMSvert ). Additionally, a 3-Dimensional RMS (RMS3-D ) was calculated as

Statistical Results The results given above demonstrate the ability of the network adjustment algorithm to reduce reference station multipath, but Figures 4 and 5 only show results in a single axis for only one of the reference receivers. In order to quantify the results in a more general sense, statistical results have been tabulated for every possible combination of reference receivers. Note that for all test runs represented in this paper and the discussion that follows, network adjustments are performed between multiple reference receivers, but positioning is always performed by single differencing between the mobile receiver and one reference receiver (which may or may not have been corrected by a network adjustment).

RMS 3-D =

n
P i=1 i ;

rP

n

(4)




where n is the number of points in the sample, and P i is the 3-dimensional magnitude of the position error. This represents a probability of 60.8% that the magnitude of the error is less than the 3-D RMS value, assuming zero mean errors in the north, east, and vertical directions, and assuming the the standard deviations of the errors in the three directions are identical. If they are not identical, then the probability increases (to values around 63–64% for the distributions present in this test).

First, any measurement that was not common to all four of the reference receivers was rejected, so that at each epoch, every reference receiver had measurements from the same set of satellites. This assures a fair comparison between reference receivers. After performing this equalization, there was an average of 6.6 satellites visible at each epoch.

There were a total of four test runs using only one reference receiver (one for each receiver), and the four RMS statistics were calculated and recorded separately for each run. Then, to determine average or “typical” values over all reference receivers, the RMS values from the four runs were averaged to obtain mean RMS values for the east, north, vertical, and 3-D position errors. These mean RMS values could be interpreted as the expected value of the RMS position error (east, north, vertical, and 3-D) when only one reference receiver is used.

Next, completely unadjusted measurements were used to

Next, twelve more runs were performed in which the ref-

ION GPS-96, September 1996, Session B4

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1.4 East North Vertical 3−D

1.3 1.2 Mean RMS Position Error (m)

Table 1: All Runs Using Two Reference Receivers In Network Adjustment Reference Receiver Reference Receivers Used For SingleUsed For Network Difference Positioning Adjustment 1 1 and 2 2 1 and 2 1 1 and 3 3 1 and 3 1 and 4 1 4 1 and 4 2 2 and 3 3 2 and 3 2 2 and 4 4 2 and 4 3 3 and 4 4 3 and 4

1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

1 2 3 4 Number of Reference Receivers Used in Adjustment

Figure 6: Summary of Positioning Accuracy Using Unsmoothed Code Measurements erence receiver's measurements were adjusted by using the network adjustment method along with one additional receiver (for a total of two receivers). Table 1 shows the twelve runs which were performed using two receivers in the network adjustment (but only one receiver as a reference for the single difference code position solution). These represent every possible combination involving only two receivers. The same mean RMS statistics were calculated for all of these runs as for the single reference receiver case. This complete process was repeated two more times using all possible combinations with three reference receivers used in the adjustment (a total of 12 runs), and with all four reference receivers used in the adjustment (a total of 4 runs).

again, except that this time all of the raw reference receiver code measurements were carrier-smoothed prior to any other processing. The pure (unsmoothed) code measurements were used for the mobile receiver. The mean RMS values for this case are shown in Figure 7. This plot shows an overall 28% reduction in the 3-D RMS error when using the network adjustment with four receivers. Finally, the process was performed a third time, only this time carrier-phase smoothing of the code was performed with both the reference receivers and the mobile receivers, with the results shown in Figure 8. In this case, there was a 35% reduction in the 3-D RMS error when using the network adjustment with four receivers.

The results for all of these cases are given in Figure 6. Each line represents a different axis (east, north, vertical, and 3D). The lines represent the average RMS errors as a function of the number of receivers used in the network adjustment. A value of 1 on the x-axis means that no network adjustment was performed. This plot shows an overall 30% reduction in the 3-D RMS error when four reference receivers are used rather than just one. The RMS values in Figure 6 for 1 reference receiver (the left-most values) represent standards code single difference positioning. A similar ground-based test scenario was performed in (Cannon 1992), resulting in single difference RMS errors of 0.56 m, 0.82 m, and 0.99 m for east, north, and vertical errors, respectively. These are very similar to the values of 0.49 m, 0.73 m, and 0.99 m shown in Figure 6. This comparison provides a good quality check for the baseline (nonadjusted) results.

As before, a quality check can be accomplished by comparing the baseline (unadjusted) results with independent results from the test described in (Cannon 1992). In that test, the RMS error in the east, north, and vertical directions when using carrier-phase smoothing were 0.35 m, 0.52 m, and 0.68 m, respectively. These compare well with the results of 0.38 m, 0.54 m, and 0.61 m shown on the left-most side of Figure 8.

The entire process described above was repeated once

A rough calculation can be performed to see if the results

ION GPS-96, September 1996, Session B4

It is encouraging to note that the network adjustment method works equally well with or without carrier-phase smoothing. This would imply that the network adjustment method can be effectively applied in conjunction with other multipath reduction techniques that do not introduce significant correlations into the measurements. Comparison With Theoretical Results

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1.4

1.4 East North Vertical 3−D

Mean RMS Position Error (m)

1.2 1.1

1.2

1 0.9 0.8 0.7 0.6 0.5

1.1 1 0.9 0.8 0.7 0.6 0.5

0.4

0.4

0.3

0.3

0.2

0.2

1 2 3 4 Number of Reference Receivers Used in Adjustment

Figure 7: Summary of Positioning Accuracy, Reference Receivers Carrier-Smoothed, Mobile Receiver Unsmoothed from the field test match the theoretical results shown in Figure 1. First, we will assume that, without the reference adjustment the standard deviations of the multipath and noise at the mobile receiver (mob ) and the reference receiver (ref ) are

mob = 0:75s m ref = s m,

(5) (6)

where s is a scaling constant. The lower standard deviation for the mobile receiver is justifiable due to the commonly known fact that multipath tends to be reduced by motion. The total positioning error (pos ) is then approximated by q

2 2 = 1:25(PDOP)s pos = PDOP mob + ref

(7)

If we use the network adjustment with 4 receivers and 6.6 satellites in view (which was the average over the period of this test), Figure 1 shows that there should be approximately a 40% reduction in the multipath and noise errors. So the adjusted standard deviation at the reference receiver : s. The total positioning error, is now sigmarefadj when the reference receiver has been adjusted, is now

= 06

q

2 2 posadj = PDOP mob + ref = 0:96(PDOP)s adj

(8)

Finally, the estimated percent reduction in total positioning error obtained by applying the network adjustment at the reference receiver is

pos ; posadj (PDOP)s(1:25 ; 0:96) = (PDOP)s1:25 = 23% pos

(9)

This is only slightly lower than the values of 28–35% obtained from the data collected in the kinematic test as ION GPS-96, September 1996, Session B4

East North Vertical 3−D

1.3 Mean RMS Position Error (m)

1.3

1 2 3 4 Number of Reference Receivers Used in Adjustment

Figure 8: Summary of Positioning Accuracy, Mobile and Reference Receivers Carrier-Smoothed

shown above, indicating that the field data and the theory match fairly well. It should be noted that the estimated percent reduction as calculated above is very sensitive to the : results in an estimvalue of mob . A value of mob ated position reduction of 40%, which is higher than the results from the kinematic test.

=07

FUTURE WORK Field tests have already been conducted in which L 1 /L2 receivers were placed at greater distances, and the condition adjustment method will be used as a basis for network carrier-phase ambiguity resolution over long distances (relative to the normal limitations of ambiguity resolution techniques). This may involve populating many of the offdiagonal terms of the measurement covariance matrices  and  in a manner similar to that performed in least squares collocation, to account for correlation due to residual unmodeled atmospheric errors. Aspects relating to network differential code positioning will also be examined.

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Other work involves applying different types of constraints in the condition adjustment. The constraints presented in this paper are based on the fact that the 3-dimensional vectors between the receivers are known. Another constraint could be a fixed distance (magnitude) between two or more antennas on a mobile platform, such as a car, ship, or aircraft. It may be possible to reduce the multipath and noise errors in these cases, even if the exact 3-dimensional vectors between the antennas are not known (e.g. Lachapelle et. al. 1994). 7

CONCLUSIONS By performing the reference network adjustment to measurements from multiple reference receivers, the multipath and measurement noise errors were isolated and reduced. Applying the corrections to the reference receiver resulted in a 28%–30% reduction of the 3-D RMS error in the single difference code position solution for a mobile vehicle. This improvement in accuracy was observed whether or not carrier-phase smoothing was applied, exemplifying the ability to use the network adjustment method in conjunction with other multipath mitigation techniques. The network adjustment method provides a convenient way to combine the data from multiple reference receivers into individual measurement corrections, permitting a single receiver to be used as a reference without sacrificing the accuracy benefits of using a network of reference receivers. ACKNOWLEDGEMENTS The authors wish to acknowledge the contributions of other students and staff at The University of Calgary, namely Jamie Henriksen, Jim Stephen, Mike Szarmes, and Rick Smith for their assistance in the execution of the field test, and Shawn Weisenburger for his enhancements to the FLYKINTMsoftware. REFERENCES Ashkenazi, V., Hill, C, (1992), “Wide Area Differential GPS: A Performance Study,” in Proceedings of the Fifth International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GPS-92), Albuquerque, NM, pp. 589–598. Axelrad, P., Comp, C. J., MacDoran, P. A. (1996), “SNRBased Multipath Error Correction for GPS Differential Phase,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 32, No. 2, pp. 650–659. Cannon, M. E., Lachapelle, G. (1992), “Analysis of a High Performance C/A Code GPS Receiver in Kinematic Mode.” NAVIGATION, Journal of the Institute of Navigation, Vol. 39, No. 3, pp. 285–299. Cohen, C. E. (1992), Attitude Determination Using GPS, Ph.D. Dissertation, Department of Aeronautics and Astronautics, Stanford University.

and Multipath Errors for an Aircraft GPS Antenna,” in Proceedings of the Eighth International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GPS-95), Palm Springs, CA, pp. 491–498. Hatch, R. (1982), “The Synergism of GPS Code and Carrier Measurements,” in Proceedings of Third International Geodetic Symposium on Satellite Doppler Positioning, Washington, D.C., pp. 1213–1232. Johnson, G., King, D., “Low Cost Multipath Mitigation in a Single Frequency Environment for a DGPS Station,” in Proceedings of the 1996 National Technical Meeting of the Institute of Navigation, Santa Monica, CA. Kee, C., Parkinson, B., “Algorithms and Implementations of Wide Area Differential GPS,” in Proceedings of the Fifth International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GPS-92), Albuquerque, NM, pp. 565–572. Kumar, R. and Lau, K. (1996), “Deconvolution Approach to Carrier and Code Multipath Error Elimination in High Precision GPS,” in Proceedings of the 1996 National Technical Meeting of the Institute of Navigation, Santa Monica, CA. Lachapelle, G., Cannon, M. E., Lu, G. (1992), “Ambiguity Resolution On the Fly–A Comparison of P Code and High Performance C/A Code Receiver Technologies,” in Proceedings of the Fifth International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GPS-92), Albuquerque, NM, pp. 1025–1032. Lachapelle, G., Sun, H., Cannon, M. E., Lu, G. (1994), “Precise Aircraft-to-Aircraft Positioning Using a Multiple Receiver Configuration,” Canadian Aeronautics and Space Journal, Vol. 40, No. 2, pp. 74–78. Lapucha, D., Huff, M, “Multi-Site Real-Time DGPS System Using Starfix Link; Operational Results,” in Proceedings of the Fifth International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GPS92), Albuquerque, NM, pp. 581–588. Raquet, J. (1996), “Multiple Reference GPS Receiver Multipath Mitigation Technique,” in Proceedings of the 52nd Annual Meeting of the Institute of Navigation, Cambridge, MA, pp. 681–690.

Hajj, G. A. (1990), “The Multipath Simulator: A Tool Toward Controlling Multipath,” in Proceedings of the 2nd Symposium on GPS Applications in Space, Hanscom AFB, MA, pp. 229–243.

Spradley, L., “Performing Precise, Seamless Hydrographic Surveys over Extended Areas Through Use of Integrated DGPS Reference Networks,” in Proceedings of the 1993 National Technical Meeting of the Institute of Navigation, San Francisco, CA, pp. 233–240.

Hardwick, C. D., Liu, J. (1995), “Characterization of Phase

Townsend, B. and Fenton, P. (1994), “A Practical Approach

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to the Reduction of Pseudorange Multipath Errors in a L1 GPS Receiver,” in Proceedings of the 7th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS-94), Salt Lake City, UT, pp. 143– 148. Townsend, B., Fenton, P., Van Dierendonck, K. (1995), “Performance Evaluation of the Multipath Estimating Delay Lock Loop,” NAVIGATION, Journal of The Institute of Navigation, Vol. 42, No. 3, pp. 503–514. Tranquilla, J. M., Carr J. P., Al-Rizzo, H. M. (1994), “Analysis of a Choke Ring Groundplane for Multipath Control in Global Positioning System (GPS) Applications,” IEEE Transactions on Antennas and Propagation, Vol. 42, No. 7, pp. 905–911.

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