DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination

DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Aircraft Velocity Determination Capt. J. Hebert and J. Keith 76th Test Squadron (CIGTF) Holloman AFB, NM S. Ryan, M. Szarmes, G. Lachapelle and M.E. Cannon Department of Geomatics Engineering The University of Calgary BIOGRAPHIES Capt. J. Hebert is a Development Engineer assigned to the 76th Test Squadron (CIGTF), Holloman Air Force Base, New Mexico. He is responsible for the development of airborne flight reference systems for guidance and navigation systems testing. He received a BS from Worcester Polytechnic Institute in 199 and a MSEE from the Air Force Institute of Technology in 199. Mr. J. Keith is a GPS Laboratory Engineer at the 76th Test Squadron (CIGTF), Holloman Air Force Base, New Mexico. He is responsible for the development of simulation test capabilities, and for laboratory testing of GPS integrations into USAF avionics suites. He received a Bachelors Degree from New Mexico State University in 1991. Sam Ryan holds a BEng (199) from Memorial University, St. John's, Newfoundland and is an Electronic Systems Engineer in the Marine Technical and Support Services Directorate of the Canadian Coast Guard. At present he is on educational leave to obtain his Masters in Geomatics Engineering at The University of Calgary. Michael Szarmes holds a B.Sc. in Surveying Engineering (199) and an M.Sc. in Geomatics Engineering (1997) both from The University of Calgary. He is currently employed at The University of Calgary as a research associate specialising in GPS positioning and navigation. Dr. Gérard 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 198. Dr. M.E. Cannon is a Professor in Geomatics Engineering at The University of Calgary. She has been involved with GPS research since 198 and has published numerous papers on static and kinematic GPS positioning. She is the author of several GPS-related software programs. ABSTRACT A Northern Telecom STR76 phase coherent differential GPS simulator is used to analyse the velocity accuracy achievable under aircraft dynamics using selected receiver technologies. The results of two C/A code L1 receiver types are presented herein, namely an Ashtech G-1 TM, and a NovAtel PowerPack OEM equipped with special Precise Velocity (PV) firmware which improves the receiver generated Doppler measurements. Simulated aircraft trajectories with velocities up to 1 m/s, accelerations up to m/s, and jerks up to m/s 3, are used. The code and carrier phase observables are processed in single difference mode with the velocity estimates based solely on the Doppler observables. The accuracy of receiver generated Doppler-derived velocities and that of integrated carrier phase-derived velocities are tested as a function of aircraft dynamics. INTRODUCTION GPS derived velocities are required for a number of applications, such as aircraft test and evaluation analysis, GPS/INS integration, and geophysical exploration. Depending on the receiver technology, dynamics, evaluation environment, and other factors, GPS can provide velocity estimates with 3D RMS up to mm/s under low dynamics (accelerations <.m/s ) (e.g. Cannon et al., [1997]). However, there are some unresolved problems when considering the strong correlation between the accuracy of the velocity estimates and high dynamics (accelerations >. m/s ). The objective of this analysis is to evaluate the accuracy of the velocity estimates for the Ashtech G1 and NovAtel PowerPack OEM (with special Precise Velocity (PV) firmware) receivers. In order to maintain a wellcontrolled test environment for analysis, the Northern Telecom STR76 Differential GPS Simulator System was used to generate the code and carrier phase signals. Velocities were generated using two types of Doppler measurements: (i) the receiver generated Doppler observable, and (ii) a carrier phase derived Doppler based on the receiver s carrier phase observable. GPS velocities Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 1/11

were obtained using software developed at The University of Calgary. A significant amount of research into GPS derived velocities has been conducted over the past several years [May et al., 199; Cannon and Lachapelle, 199; Fenton and Townsend, 199; Hebert, 199; Evans et al., 1996; Cannon et al. 1997; Hebert, 1997; Szarmes et al. 1997]. In all cases, position and velocity accuracy were a function of the dynamics under which the receivers were tested. Depending upon the receiver tested and the Doppler measurement used to generate the velocity estimates, velocity accuracy exhibited direct correlation with the magnitude of either acceleration or jerk. The order of the phase lock loop (PLL) was found to be a contributing factor in establishing these correlations. If the Doppler observable is asynchronous to the measurement strobes this also affects the apparent correlation. The use of GPS Signal simulators for precise DGPS velocity determination and system evaluation is not wide spread. However, their applicability to consistent and reliable analysis has been seen in previous studies (e.g. Cannon et al. [1997]). The main advantage of signal simulators over other evaluation environments is the provision of cost-effective truth position, velocity and acceleration information under variable dynamics, both for the receiver positions and for the simulated satellite constellation. In addition to providing accurate and reliable truth information, signal simulators provide maximum flexibility in assigning repeatable trajectories, dynamics, error sources, signal characteristics, atmospheric conditions and multipath. A similar analysis to that reported herein was conducted by Cannon et al. [1997]. In that analysis, the Ashtech Z-1 receiver was compared with the NovAtel MiLLennium receiver for performance in both low dynamics (accelerations <. m/s ) and high dynamics (accelerations up to g s) using a differential GPS signal simulator system. Table 1 summarises the results obtained. It was determined that the best velocity results for low dynamics were obtained by applying a first-order central difference approximation to the carrier phase measurements and using these values as the carrier phasederived Doppler for velocity determination. 3D velocity RMS values of -3 mm/s under low dynamics were reported based on this technique. Both receivers exhibited larger errors (between. m/s and several m/s) under high dynamics. Direct correlation between velocity error and dynamics (either acceleration or jerk) was established. TABLE 1 Summary of results Based on Cannon et al. [1997] 3D RMS Velocity [low dynamics] RX generated Doppler 1st Order Φ derived Doppler MiLLennium Z-1 6.8 16.8.1.9 An analysis under real aircraft conditions was conducted by Szarmes et al. [1997]. The NovAtel MiLLennium and NovAtel PowerPack OEM with special PV firmware were compared in terms of the accuracy of the DGPS velocity estimates using both receiver generated and carrier phase derived Doppler measurements. Table summarises the results obtained. It was reported that for low dynamics (accelerations <. m/s ), the accuracy of the velocity estimates for the NovAtel PowerPack OEM with special precise velocity firmware were better than 3.8 mm/s and were at least comparable to the results of the NovAtel MiLLennium using the first order carrier phase derived velocities. TABLE Summary of results Based on Szarmes et al. [1997] 3D 68 Percentile Velocity Difference MiLL 1st Order Φ minus MiLL RX Gen. MiLL 1st Order Φ minus PV RX Gen. Aircraft Static Initialisation Aircraft Kinematic 6 3.6. TEST EQUIPMENT AND SOFTWARE The Central Inertial Guidance Test Facility (CIGTF) Northern Telecom STR76 Differential GPS Simulator System used for the simulations consists of two multichannel, GPS simulators capable of outputting L1 and L frequencies, C/A and P/Y-codes, and the full navigation message under a wide range of dynamic conditions. The system is suitable for both pseudorange and carrier phase analysis. The trajectories of land, sea, air and space vehicles can be programmed. Trajectory and signal characteristics, such as motion, attitude, SA/AS and signal strength can be applied. Various errors can be simulated, such as clock, multipath and ephemeris errors. Atmospheric conditions can also be simulated by applying a tropospheric model and one of two available ionospheric models. Body masking due to aircraft banking can also be simulated. Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 /11

Two sets of GPS receivers were used for each of the tests conducted: the Ashtech G1 and NovAtel PowerPack OEM with PV firmware S6-3.. Each receiver is a high performance receiver capable of outputting raw code and carrier phase measurements. Each receiver utilises a 3rd-order PLL which performs well under highly dynamic conditions. The Ashtech G1 is a 1 channel L1 C/A code high performance (Edge and Strobe Correlators ) receiver. The Doppler observable is averaged from the PLL using the last. s phase measurements. This means that for the 1 Hz data rate chosen for these tests, there will be a. s time offset between the Doppler and the phase measurements. The NovAtel PowerPack OEM unit is based on the GPSCard series and is a 1 channel single frequency receiver. For the purpose of the velocity analysis for these tests, special Precise Velocity (PV) firmware S6-3. developed by NovAtel (Fenton and Townsend, [199]) was used. The main feature of this firmware revision is the Hz phase measurement nd-order curve fitting process providing more precise carrier phase, Doppler and phase acceleration measurements at 1 Hz. The Doppler and acceleration are the first and second derivative of the curve fitted phase. The curve fit is done over the ±. s from the data point. The result is highly accurate measurements output with just over a. s latency. A flag is set in the measurement log if the curve fit fails a statistical test. This is significant when considering higher dynamics. When the curve fit fails the observation is not used in computing the velocity estimate. The software used to derive velocity estimates for the analysis was C 3 NAV. C 3 NAV was developed at The University of Calgary and utilises a combined code and carrier phase processor (carrier-smoothed code generation) for navigation purposes. It provides an epochby-epoch single difference solution where rover velocities are based solely on Doppler measurements. In addition to utilising the receiver generated Doppler measurements in the analysis, carrier phase-derived Doppler measurements were obtained by applying the first order central difference approximation on the carrier phase as follows: f ( x) f ( x+ h) f ( x h). (1) h This approach is however limited to the logging data rate of the receiver. Hence, it is not possible to recover the dynamics which occur below this rate. A single frequency phase velocity trend cycle slip detection algorithm was applied to ensure consistency between the phase measurements and the derived Doppler. SIMULATION DESCRIPTION The simulation was set up to last 6 minutes. Data was logged a 1 Hz. There was no SA/AS, no satellite clock errors, no ephemeris errors, no multipath, no tropospheric or ionospheric models and no signal masking applied. The dynamics of the trajectory were set to simulate the dynamics a real fighter aircraft would undergo during a combat mission. The trajectory chosen is shown in Figure 1. The extent of the trajectory is 37 km E/W and 6 km N/S. The base reference station was held fixed at the starting point of the trajectory, and the maximum interantenna distance between aircraft and fixed reference of less than 19 km. Latitude (km) 7 6 3 1 Start & Reference Station 1 3 Longitude (km) Fig. 1 - Simulated aircraft trajectory. Figure shows the latitude, longitude and height components of the trajectory. The height above the fixed reference remained constant during the flight at 1 m. Figure 3 shows the dynamics (velocity, acceleration and jerk) experienced by the remote receiver during the simulation. For the test, there was an initial 1 minute static initialisation prior to aircraft movement. Maximum constant velocities of 1 m/s were simulated. In all, there were loops of the trajectory, each loop exhibiting increasing magnitudes of acceleration (from m/s to m/s in m/s increments per turn). Jerk also increased at a rate of. m/s 3 per turn to a maximum of m/s 3. Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 3/11

Lat. (Deg) Long. (Deg) Alt (m) Velocity (m/s) Accel (m/s ) Jerk (m/s 3 ) 3.9 3.93 3.91 3.89-1.9-16 -16.1-16. -16.3 16 1 1116 1: Latitude Longitude Altitude 118 11 11 1: 1: : Fig. - Simulated aircraft trajectory components. 1 1 6 3 1 1116 1: Absolute Velocity Absolute Acceleration Absolute Jerk 118 11 11 1: 1: : Fig. 3 - Simulated aircraft trajectory dynamics. The Northern Telecom STR76 Differential GPS Simulator System outputs truth position, velocity and acceleration data output at 1 Hz. From the acceleration truth, jerk was computed for each epoch. Figure shows a typical trend for acceleration and jerk experienced during the turns. For this 1 g turn, as with the other turns, there is a sharp north jerk at the start and end of the turn. Acceleration (m/s ) Jerk (m/s 3 ) 1 - -1 - - -6 1193 1::3 Accelerations for the 1 g Turn North Acceleration East Acceleration Jerks for the 1 g Turn North Jerk East Jerk 1196 1199 1:3: 1:3:3 Fig. - N/E acceleration and jerk for 1 g turn. SIMULATION RESULTS This section presents the results of the analysis conducted. It is divided into two subsections: (i) results obtained during static and constant velocity sections of the trajectory, and (ii) detailed analysis of the results obtained during periods of high dynamics (i.e. at the high g turns). STATIC AND CONSTANT VELOCITY NovAtel PowerPack OEM Figures and 6 show the velocity errors resulting during the 1 min static initialisation and the constant velocity sections of the trajectory. It is apparent that the level of noise is consistent for both static and constant velocities. There are excursions from the mean noticeable at various epochs during constant velocity sections (see Figure 6 at epochs 1137 and 113). These excursions correspond to the high dynamic sections of the trajectory. When the receiver performs the curve fit, it tests if the fit passes. The results of this curve fit test are reported in a measurement flag. By reviewing the flag, it has been determined that the test often fails at periods of high dynamics. This results in an apparent loss of satellites as shown in Figure 6. Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 /11

. -. -. -. -. -. - 1119 1: Static Initialization - North Velocity Error Static Initialization - East Velocity Error Static Initialization - Down Velocity Error 118 116 11 1:8 1:11 1:1 Fig. - Velocity error during static initialisation (NovAtel PowerPack OEM RX Generated Doppler). # Sats. -. -. -. -. -. - 1 8 6 1119 1: Constant Velocity - North Velocity Error Constant Velocity - East Velocity Error Constant Velocity - Down Velocity Error Number of Satellites 1131 113 1: 1: Fig. 6 - Velocity error during constant velocity (NovAtel PowerPack OEM RX Generated Doppler). However, although this explains the discontinuities, it does not explain the resulting bias immediately following the discontinuities. These biases correspond to the number of satellites available in the simulated constellation, as shown in Figure 6. The question remains as to why there remains a shift in the velocity from the truth due to a constellation change and a change of geometry. The first order carrier phase (Φ) derived Doppler was not analysed for this receiver because the receiver generated Doppler is itself derived from the carrier phase observations through the ±. s curve fitting process. Ashtech G1 Figure 7 shows the velocity errors resulting during the constant velocity sections of the trajectory using the receiver generated Doppler. It is clear that there is a bias introduced in the measurements. The sign of the bias is a function of the direction of travel. This bias is similar to a bias which is introduced when the Doppler measurement is not synchronous to the carrier phase measurements from which they may be derived. A similar trend was reported in Cannon et al. [1996] where derived Doppler measurements were offset. s from their original epoch, resulting in the same type of bias seen in Figure 7. The bias is not evident during static tests. Recall that there is a time offset introduced in the G1 between the Doppler and the phase measurements due to the manner in which the Doppler is computed. By applying a time shifted value of. s obtained from 1-1 - 1-1 - - 11 1:1 Constant Velocity - North Velocity Error Constant Velocity - East Velocity Error Constant Velocity - Down Velocity Error 1136 118 1:3 1: Fig. 7 - Velocity error during constant velocity (Ashtech G1 RX Generated Doppler). Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 /11

the correlations outlined in the following section (as well as considering the. s time offset), the resulting velocity errors shown in Figure 8 are as expected with no bias as seen in Figure 7. 1-1 - 1-1 - - 11 1:13 Constant Velocity - North Velocity Error Constant Velocity - East Velocity Error Constant Velocity - Down Velocity Error 1136 118 1:33 1:3 Fig. 8 - Velocity error during constant velocity (Ashtech G1 shifted RX Generated Doppler).. -. -. -. -. -. - 11 1:13 North Velocity Error - Constant Velocity East Velocity Error - Constant Velocity Down Velocity Error - Constant Velocity 1136 118 1:33 1:3 Fig. 9 - Velocity error during constant velocity (Ashtech G1 1 st Order Φ). Figure 9 shows the accuracy of the velocity estimates when using the first order carrier phase derived Doppler measurements. Again, as with the shifted receiver generated Doppler, there is no apparent bias in the velocity estimates. As expected the noise of the 1st order carrier phase velocities is significantly lower than that of the receiver generated Doppler velocities, due to increasing the averaging time from. s for the receiver generated Doppler to. s for the 1 st order carrier phase approximation. Summary of Results Table 3 presents the summary of statistics for the constant velocity sections of the trajectory for each receiver based on the various receiver generated and carrier phase derived Doppler measurements. TABLE 3 Summary of Statistics Static and Constant Velocity RMS Velocity PV G1 TM RX Gen RX Gen RX Gen Offset 1 st Order Φ North.6.3 3.7.9 East.9. 3..8 Up 1.8 1.6 8.. 3D.1 13.9 9..3 From Table 3, it is evident that 3D velocity accuracies under constant velocities are of the order of.1 mm/s for the PV receiver, and.3 mm/s for the G1. The 1st order carrier phase derived velocities for the G1 are equivalent to those of the PV receiver generated Doppler, and are an improvement over the receiver generated shifted Doppler velocities by a factor of four (). These results are as expected due to the longer averaging time for the first order carrier phase approximation ( s). Note the higher error in the east component in the PV receiver compared with the north component. This is due to the bias which occurred at the later stages of the test in the east component, as shown in Figure 6. HIGH DYNAMICS NovAtel PowerPack OEM Figures 1 and 11 show the velocity errors resulting during two high dynamic sections of the trajectory (the 1 g turn and 3 g turn respectively) and the direct positive correlation with jerk. Not shown in the figures are the Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 6/11

outliers which occur at the maximum level of jerk in the north component. The trend, however, is clearly evident. Note also the consistent number of epochs for which a differential velocity estimate could be obtained. Thus, there was a relatively minor number of epochs for which the phase curve fit failed. 3 1-1 - -3 3 1-1 - -3 11939 1::39 North Velocity Error and Jerk (1. g Turn) East Velocity Error and Jerk (1. g Turn) 1199 11979 1::9 1:3:19 Fig. 1 - Velocity error vs. jerk for 1 g turn (NovAtel PowerPack OEM RX Generated Doppler). Figure 11 again shows the clear correlation between velocity error and the magnitude of jerk. Also evident is the increasing number of missed epochs for which velocity estimates are available. For the remaining higher g turns, there is corresponding increase in the number of missed epochs due directly to the failure of the curve fit test (as opposed to a loss of lock). Figure 1 shows the velocity errors plotted as a function of jerk for each of the north and east components. From the figure, there is a near linear relationship between velocity error and jerk which exists at all levels of jerk. There is no correlation with acceleration. - - - North Velocity Error vs North Jerk East Velocity Error vs East Jerk 1-1 - 1-1 North Velocity Error and Jerk (3. g Turn) East Velocity Error and Jerk (3. g Turn) - -1-1 - 1 1 Jerk m/s 3 Fig. 1 - Velocity error vs. jerk for all turns (NovAtel PowerPack OEM RX Generated Doppler). From Figure 1, the following relationship can be derived for the NovAtel PowerPack OEM with precise velocity software: δv(t) =. * J(t) () where δv(t) is the velocity error in m/s and J(t) is the magnitude of jerk in m/s 3. Ashtech G1 - Receiver Generated Doppler - 116 1::6 1111 1116 111 1::11 1::16 1::1 Fig. 11 - Velocity error vs. jerk for 3 g turn (NovAtel PowerPack OEM RX Generated Doppler). Figures 13 and 1 show the velocity errors resulting during two high dynamic sections of the trajectory (the 1 g turn and 3 g turn respectively) and the direct correlation with acceleration. Also note the magnitude of the velocity error is relatively large. Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 7/11

. -. -. -. - 11939 1::39 North Velocity Error and Accel. (1. g Turn) East Velocity Error and Accel. (1. g Turn) 1199 11979 1::9 1:3:19 Fig. 13 - Velocity error vs. jerk for 1 g turn (Ashtech G1 RX Generated Doppler). 1 1 - -1-1 1 1 - -1-1 - North Velocity Error vs North Acceleration East Velocity Error vs East Acceleration - -3 - -1 1 3 Acceleration m/s Fig. 1 - Velocity error vs. acceleration for all turns (Ashtech G1 RX Generated Doppler). 1 North Velocity Error and Accel. (3. g Turn) From Figure 1, the following relationship can be derived for the Ashtech G1 using the receiver generated Doppler: - -1 1 East Velocity Error and Accel. (3. g Turn) δv(t) = -.6 * A(t) (3) where δv(t) is the velocity error in m/s and A(t) is the magnitude of acceleration in m/s. Ashtech G1 - Shifted Receiver Generated Doppler - -1 116 1::6 1111 1116 111 1::11 1::16 1::1 Fig. 1 - Velocity error vs. jerk for 3 g turn (Ashtech G1 RX Generated Doppler). Figure 1 shows the velocity errors plotted as a function of acceleration for each of the north and east components. From the figure, there is a near linear relationship between velocity error and acceleration which exists at all levels of acceleration. It is possible to remove the correlation with acceleration by shifting the Doppler observations, as was done in the static and constant velocity section. In essence, the -.6 functional coefficient given in equation 3 must be in units of seconds, which confirms that the receiver generated Doppler has a time bias of. s. By computing a new value for the Doppler measurement (shifted by. s), the correlation with acceleration for the high dynamics sections of the trajectory, just as with the constant velocity sections, should be dramatically reduced. Figures 16 and 17 show the results when effectively shifting the Doppler measurement by. s. It is evident now that there is no longer a correlation with acceleration, but, just as with the NovAtel, there remains a correlation with jerk. Although the noise of the measurement is more than the NovAtel, the magnitudes of the velocity error are Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 8/11

the same (i.e. by shifting the Doppler measurement, this has effectively reduced the trend of the velocity errors from metres to millimetres. 3 1-1 - -3 3 1-1 - -3 11939 1::39 North Velocity Error and Jerk (1. g Turn) East Velocity Error and Jerk (1. g Turn) 1199 11979 1::9 1:3:19 Fig. 16 - Velocity error vs. jerk for 1 g turn (Ashtech G1 shifted RX Generated Doppler). Figure 18 shows the velocity errors plotted as a function of jerk for each of the north and east components. From the figure, there is now a near linear relationship between velocity error and jerk for low values of jerk. For higher values while there is still a correlation it is not as strong. There is no longer any remaining correlation with acceleration. - - - - -1 North Velocity Error vs North Jerk East Velocity Error vs East Jerk -1-1 1 Jerk m/s 3 1-1 - North Velocity Error and Jerk (3. g Turn) East Velocity Error and Jerk (3. g Turn) Fig. 18 - Velocity error vs. jerk for all turns (Ashtech G1 shifted RX Generated Doppler). From Figure 18, the following relationship can be derived for the Ashtech G1 using the shifted receiver generated Doppler: δv(t) = -.17 * J(t) () where δv(t) is the velocity error in m/s and J(t) is the magnitude of jerk in m/s 3. 1-1 - 116 1::6 1111 1116 111 1::11 1::16 1::1 Fig. 17 - Velocity error vs. jerk for 3 g turn (Ashtech G1 shifted RX Generated Doppler). Ashtech G1-1st Order Φ Approximation Figures 19 and show the velocity errors based on the 1st order carrier phase approximations. Due to the averaging interval over which the Doppler is computed ( s), the higher dynamics are not adequately represented resulting in larger maximum velocity errors. Figure 1 shows the velocity errors plotted as a function of jerk for each of the north and east components. From the figure, there is now a near linear relationship between velocity error and jerk for all values of jerk. While the Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 9/11

correlation is linear the functional coefficient is an order of magnitude greater than the correlation for the shifted receiver generated Doppler case. North Velocity Error vs North Jerk North Velocity Error and Jerk (1. g Turn) 1 1 - -1-1 1 1 - -1-1 11939 1::39 1 1 - -1-1 1 1 - -1 East Velocity Error and Jerk (1. g Turn) 1199 11979 1::9 1:3:19 Fig. 19 - Velocity error vs. jerk for 1 g turn (Ashtech G1 1st Order Φ). -1 116 1::6 North Velocity Error and Jerk (3. g Turn) East Velocity Error and Jerk (3. g Turn) 1111 1116 111 1::11 1::16 1::1 Fig. - Velocity error vs. jerk for 3 g turn (Ashtech G1 1st Order Φ). - - - - -1 East Velocity Error vs East Jerk -1-1 1 Jerk m/s3 Fig. 1 - Velocity error vs. jerk for all turns (Ashtech G1 1st Order Φ). From Figure 1, the following relationship can be derived for the Ashtech G1 using the 1st order carrier phase derived velocity estimates: δv(t) =.18 * J(t) () where δv(t) is the velocity error in m/s and J(t) is the magnitude of jerk in m/s 3. Summary of Results Table presents the summary of statistics for high dynamic sections of the trajectory for each receiver based on the various receiver generated and carrier phase derived Doppler measurements. TABLE Maximum Velocity Errors High Dynamics Maximum Velocity Component Error PV (mm/s) G1 TM (m/s) RX Gen RX Gen RX Gen Offset 1 st Order Φ 1 g N.3..6 1. E.7...1 g N 17.8.8.7.6 E 8.1.9.. 3 g N 176. 7.3 1. 3. E 18.1 7.3. 1.1 Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 1/11

Table presents the summary of the correlations for high dynamics for each receiver based on the various receiver generated and carrier phase derived Doppler measurements presented in the previous sections. Doppler Used PV RX Generated G1 RX Generated G1 Shifted RX Generated G1 1st Order Φ CONCLUSIONS TABLE Summary of Correlations Correlation dv(t) =. * J(t) dv(t) = -.6 * A(t) dv(t) = -.17 * J(t) dv(t) =.18 * J(t) Under constant velocities the NovAtel PowerPack OEM (PV firmware) provides velocities which are on the order of.1 mm/s (3D RMS). These results are consistent with those obtained from actual flight tests where at low dynamics (accelerations <. m/s ), velocity accuracies were better than 3.8 mm/s [Szarmes et al., 1997]. The Ashtech G1 utilising the first order carrier phase derived velocities provide equivalent accuracy (.3 mm/s 3D RMS) to that of the NovAtel PowerPack OEM. Depending on the Doppler measurement used to derive the velocities, there are correlations with the dynamics of the aircraft. The NovAtel PowerPack OEM receiver generated Doppler velocity errors exhibited correlations with jerk. The Ashtech G1 receiver generated Doppler velocity errors are correlated directly with acceleration due to the. s bias in the Doppler measurements. Applying the time offset to these receiver generated Doppler measurements effectively removes the correlation with acceleration and the underlying correlation with jerk becomes evident. Similarly, with the 1st order carrier phase approximation is used, there remains only a correlation with jerk. These remaining correlations with jerk are likely due to either (i) the order of the PLL and the inability of the receiver to correctly track through the dynamics, or (ii) the order of the interpolation used to derive the Doppler (whether within the receiver firmware or applied postmission) and the time interval over which the interpolation is computed. Third order PLLs can track under constant levels of jerk, but will show erroneous results under changing magnitudes of jerk. REFERENCES Cannon, M.E. and G. Lachapelle, 199. 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. 8-99 (Fall). Cannon M.E., G. Lachapelle and M. Szarmes, 1996. Development of a Position and Velocity Determination System Based on GPS Carrier Phase. Contract report submitted to 76TS/TGGMR, Holloman AFB, NM (December). Cannon, M.E., G. Lachapelle, M. Szarmes, J. Hebert, J. Keith and S. Jokerst, 1997. DGPS Kinematic Carrier Phase Signal Simulation Analysis for Precise Velocity and Position Determination. Proceedings of the ION NTM 97, Santa Monica, CA (January). Evans, A.G., et al., 1996. An Evaluation of Precise Kinematic On-The-Fly Relative Positioning for a Rocket Sled Test. Proceedings of the ION nd Annual Meeting, Cambridge, Massachusetts (June). Fenton, P. and B. Townsend, 199. NovAtel Communications Ltd. - What s New? Proceedings of KIS9, Department of Geomatics Engineering, The University of Calgary, Banff (August 3 - September ), pp. -9. Hebert, J.M., 199. Velocity Determination for an Inverted Pseudolite Navigation Reference System. MS Degree Thesis, AFIT/GE/ENG/9D-6. School of Engineering, Air Force Institute of Technology (AU), WPAFB, OH, (December). Hebert, J., 1997. High Accuracy GPS Velocity Using the Carrier Phase Observable. Proceedings of KIS97, Department of Geomatics Engineering, The University of Calgary, Banff (June). May, M., K. Nguyen, and B. Tanju, 199. On GPS Velocity. Proceedings of the ION 6th Annual Meeting, Atlantic City, NJ (June). Szarmes, M., S. Ryan, G. Lachapelle, and P. Fenton 1997. DGPS High Accuracy Aircraft Velocity Determination Using Doppler Measurements. Proceedings of KIS97, Department of Geomatics Engineering, The University of Calgary, Banff (June). Due to the strong correlations shown by the receivers with jerk, it is possible to significantly reduce the velocity errors during high g s by modelling the dynamics. Hebert et al., Proceedings of the ION Annual Meeting, Albuquerque, NM, 3 June - July 1997 11/11