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Global Positioning Systems, Inertial Navigation, and Integration, Mohinder S. Grewal, Lawrence R. Weill, Angus P. Andrews Copyright # 2001 John Wiley & Sons, Inc. Print ISBN 0-471-35032-X Electronic ISBN 0-471-20071-9 9 Differential GPS 9.1 INTRODUCTION Differential GPS (DGPS) is a technique for reducing the error in GPS-derived positions by using additional data from a reference GPS receiver at a known position. The most common form of DGPS involves determining the combined effects of navigation message ephemeris and satellite clock errors [including the effects of selective availability (SA), if active] at a reference station and transmitting pseudorange corrections, in real time, to a user's receiver. The receiver applies the corrections in the process of determining its position [63]. This results in the following:  Some error sources are canceled completely: (a) selective availability and (b) satellite ephemeris and clock errors.  With other error sources, cancelation degrades with distance: (a) ionospheric delay error and (b) tropospheric delay error.  Still other error sources are not canceled at all: (a) multipath errors and (b) receiver errors. 265 266 9.2 9.2.1 DIFFERENTIAL GPS LADGPS, WADGPS, AND WAAS Description of Local-Area DGPS (LADGPS) LADGPS is a form of DGPS in which the user's GPS receiver receives real-time pseudorange and, possibly, carrier phase corrections from a reference receiver generally located within the line of sight. The corrections account for the combined effects of navigation message ephemeris and satellite clock errors (including the effects of SA) and, usually, atmospheric propagation delay errors at the reference station. With the assumption that these errors are also common to the measurements made by the user's receiver, the application of the corrections will result in more accurate coordinates [81]. 9.2.2 Description of Wide-Area DGPS (WADGPS) WADGPS is a form of DGPS in which the user's GPS receiver receives corrections determined from a network of reference stations distributed over a wide geographical area. Separate corrections are usually determined for speci®c error sources, such as satellite clock, ionospheric propagation delay, and ephemeris. The corrections are applied in the user's receiver or attached computer in computing the receiver's coordinates. The corrections are typically supplied in real time by way of a geostationary communications satellite or through a network of ground-based transmitters. Corrections may also be provided at a later date for post-processing collected data [81]. 9.2.3 Description of Wide Area Augmentation System (WAAS) WAAS enhances the GPS SPS and is available over a wide geographical area. The WAAS being developed by the Federal Aviation Administration, together with other agencies, will provide WADGPS corrections, additional ranging signals from geostationary (GEO) satellites, and integrity data on the GPS and GEO satellites [81]. The GEO Uplink Subsytem includes a closed-loop control algorithm and special signal generator hardware. These ensure that the downlink signal to the users is controlled adequately to be used as a ranging source to supplement the GPS satellites in view. The primary mission of WAAS is to provide a means for air navigation for all phases of ¯ight in the National Airspace System (NAS) from departure, en route, arrival, and through approach. GPS augmented by WAAS offers the capability for both nonprecision approach (NPA) and precision approach (PA) within a speci®c service volume. A secondary mission of the WAAS is to provide a WAAS network time (WNT) offset between the WNT and Coordinated Universal Time (UTC) for nonnavigation users. WAAS provides improved en route navigation and PA capability to WAAS certi®ed avionics. The safety critical WAAS system consists of the equipment and 9.2 LADGPS, WADGPS, AND WAAS 267 software necessary to augment the Department of Defense (DoD) provided GPS SPS. WAAS provides a signal in space (SIS) to WAAS certi®ed aircraft avionics using the WAAS for any FAA-approved phase of ¯ight. The SIS provides two services: (1) data on GPS and GEO satellites and (2) a ranging capability. The GPS satellite data is received and processed at widely dispersed wide-area reference Stations (WRSs), which are strategically located to provide coverage over the required WAAS service volume. Data is forwarded to wide-area master stations (WMSs), which process the data from multiple WRSs to determine the integrity, differential corrections, and residual errors for each monitored satellite and for each predetermined ionospheric grid point (IGP). Multiple WMSs are provided to eliminate single-point failures within the WAAS network. Information from all WMSs is sent to each GEO uplink subsystem (GUS) and uplinked along with the GEO navigation message to GEO satellites. The GEO satellites downlink this data to the users via the GPS SPS L-band ranging signal (L1 ) frequency with GPS-type modulation. Each ground-based station=subsystem communicates via a terrestrial communications subsystem (TCS). See Fig. 9.1. In addition to providing augmented GPS data to the users, WAAS veri®es its own integrity and takes any necessary action to ensure that the system meets the WAAS performance requirements. WAAS also has a system operation and maintenance function that provides status and related maintenance information to FAA airway facilities (AFs) NAS personnel. WAAS has a functional veri®cation system (FVS) that is used for early development test and evaluation (DT&E), re®nement of contractor site installation procedures, system-level testing, WAAS operational testing, and long-term support for WAAS. GEO subsystem GPS satellites User’s WAAS receiver GEO uplink subsystem Wide-area reference station-1 Wide-area master station Wide-area reference station-n Fig. 9.1 WAAS Top Level View 268 DIFFERENTIAL GPS Correction and Veri®cation (C&V) processes data from all WRSs to determine integrity, differential corrections, satellite orbits, and residual error bounds for each monitored satellite. It also determines ionospheric vertical delays and their residual error bounds at each of the IGPs. C&V schedules and formats WAAS messages and forwards them to the GUSs for broadcast to the GEO satellites. C&V's capabilities are as follows: 1. Control C&V Operations and Maintenance (COM) supports the transfer of ®les, performs remotely initiated software con®guration checks, and accepts requests to start and stop execution of the C&V application software. 2. Control C&V Modes (CMD) manage mode transitions in the C&V subsystem while the application software is running. 3. Monitor C&V (MCV) reports line replaceable unit (LRU) faults and con®guration status. In addition, it monitors software processes and provides performance data for the local C&V subsystems. 4. Process Input Data (PID) selects and monitors data from the wide-area reference equipment (WREs). Data that passes PID screening is repackaged for other C&V capabilities. PID performs clock and L1 GPS Precision Positioning Service L-band ranging signal (L2 ) receiver bias calculations, cycle slip detection, outlier detection, data smoothing, and data monitoring. In addition, PID calculates and applies the windup correction to the carrier phase, accumulates data to estimate the pseudorange to carrier phase bias, and computes the ionosphere corrected carrier phase and measured slant delay. 5. Satellite Orbit Determination (SOD) determines the GPS and GEO satellite orbits and clock offsets, WRE receiver clock offsets, and troposphere delay. 6. Ionosphere Correction Computation (ICC) determines the L1 IGP vertical delays, grid ionosphere vertical error (GIVE) for all de®ned IGPs, and L1 ±L2 interfrequency bias for each satellite transmitter and each WRS receiver. 7. Satellite Correction Processing (SCP) determines the fast and long-term satellite corrections, including the user differential range error (UDRE). It determines the WNT and the GEO and WNT clock steering commands [99]. 8. Independent Data Veri®cation (IDV) compares satellite corrections, GEO navigation data, and ionospheric corrections from two independent computational sources, and if the comparisons are within limits, one source is selected from which to build the WAAS messages. If the comparisons are not within limits, various responses may occur, depending on the data being compared, all the way from alarms being generated to the C&V being faulted. 9. Message Output Processing (MOP) transmits messages containing independently veri®ed results of C&V calculations to the GUS processing (GP) for broadcast. 10. C&V Playback (PLB) processes the playback data that has been recorded by the other C&V capabilities. 9.3 GEO UPLINK SUBSYSTEM (GUS) 269 11. Integrity Data Monitoring (IDM) checks both the broadcast and the to-bebroadcast UDREs and GIVEs to ensure that they are properly bounding their errors. In addition, it monitors and validates that the broadcast messages are sent correctly. It also performs the WAAS time-to-alarm validation [1, 99]. 9.2.3.1 WRS Algorithms Each WRS collects raw pseudorange (PR) and accumulated delta range (ADR) measurements from GPS and GEO satellites selected for tracking. Each WRS performs smoothing on the measurements and corrects for atmospheric effects, that is, ionospheric and tropospheric delays. These smoothed and atmospherically corrected measurements are provided to the WMS. 9.2.3.2 WMS Foreground (Fast) Algorithms The WMS foreground algorithms are applicable to real-time processing functions, speci®cally the computation of fast correction, determination of satellite integrity status and WAAS message formatting. This processing is done at a 1-HZ rate. 9.2.3.3 WMS Background (Slow) Algorithms The WMS background processing consists of algorithms that estimate slowly varying parameters. These algorithms consist of WRS clock error estimation, grid ionospeci®c delay computation, broadcast ephemeris computation, satellite orbit determination, satellite ephemeris error computation, and satellite visibility computation. 9.2.3.4 Independent Data Veri®cation and Validation Algorithms This includes a set of WRS and at least one WMS, which enable monitoring the integrity status of GPS and the determination of wide-area DGPS correction data. Each WRS has three dual frequency GPS receivers to provide parallel sets of measurement data. The presence of parallel data streams enables Independent Data Veri®cation and Validation (IDV&V) to be employed to ensure the integrity of GPS data and their corrections in the WAAS messages broadcast via one or more GEOs. With IDV&V active, the WMS applies the corrections computed from one stream to the data from the other stream to provide veri®cation of the corrections prior to transmission. The primary data stream is also used for the validation phase to check the active (already broadcast) correction and to monitor their SIS performance. These algorithms are continually being improved. The latest versions can be found in references [48, 96, 97, 137, 99] and [98, pp. 397±425]. 9.3 GEO UPLINK SUBSYSTEM (GUS) Corrections from the WMS are sent to the ground uplink subsystem (GUS) for uplink to the GEO. The GUS receives integrity and correction data and WAAS speci®c messages from the WMS, adds forward error correction (FEC) encoding, and transmits the messages via a C-band uplink to the GEO satellites for broadcast to the WAAS user. The GUS signal uses the GPS standard positioning service 270 DIFFERENTIAL GPS waveform (C=A-code, BPSK modulation); however, the data rate is higher (250 bps). The 250 bps of data are encoded with a one-half rate convolutional code, resulting in a 500-symbols=s transmission rate. Each symbol is modulated by the C=A-code, a 1:023  106 -chips=s pseudo random sequence to provide a spread-spectrum signal. This signal is then BPSK modulated by the GUS onto an IF carrier, upconverted to a C-band frequency, and uplinked to the GEO. It is the C=A-code modulation that provides the ranging capability if its phase is properly controlled. Control of the carrier frequency and phase is also required to eliminate uplink Doppler and to maintain coherence between code and carrier. The GUS monitors the C-band and L1 downlinks from the GEO to provide closed-loop control of the PRN code and L1 carrier coherency. WAAS short- and long-term code carrier coherence requirements are met. 9.3.1 Description of the GUS Algorithm The GUS control loop algorithm ``precorrects'' the code phase, carrier phase, and carrier frequency of the GEO uplink signal to maintain GEO broadcast code±carrier coherence. The uplink effects such as ionospheric code±carrier divergence, uplink Doppler, equipment delays, and frequency offsets must be corrected in the GUS control loop algorithm. Figure 9.2 provides an overview of the functional elements of the GUS control loop. The control loop contains algorithm elements (shaded boxes) and hardware elements that either provide inputs to the algorithm or are controlled or affected by outputs from the algorithm. The hardware elements include a WAAS GPS receiver, GEO satellite, and GUS signal generator. Downlink ionospheric delay is estimated in the ionospheric delay and rate estimator using pseudorange measurements from the WAAS GPS receiver on L1 and L2 (downconverted from the GEO C-band downlink at the GUS). This is a twostate Kalman ®lter that estimates the ionospheric delay and delay rate. At each measurement interval, a range measurement is taken and fed into the range, rate, and acceleration estimator. This measurement is the average between the reference pseudorange from the GUS signal generator PRsign and the received pseudorange from the L1 downlink as measured by the WAAS GPS Receiver PRgeo † and adjusted for estimated ionospheric delay PRiono †. The equation for the range measurement is then z ˆ 12 ‰ PRgeo PRiono † ‡ PRsign Š TCup TL1dwnS ; where TCup ˆ C-band uplink delay m† TL1dwnS ˆ L1 receiver delay of the GUS m† The GUS signal generator is initialized with a pseudorange value from satellite ephemeris data. This is the initial reference from which corrections are made. The range, rate and acceleration estimator is a three-state Kalman ®lter that drives the frequency and code control loops. 9.3 GEO UPLINK SUBSYSTEM (GUS) 271 Iono delay rate estimator PRL1 Ð PRL2 (cdwn) Iono delay estimator PRiono Range measurement Pseudo range PR WAAS GPS receiver GEO Range, rate residual PR SIGN WAAS pseudo range L1 and cdwn GEO satellite Σ Control GUS signal generator Cup Range, rate acceleration estimator Control bit Initialization from ephemeris L1 doppler frequency L1 carrier phase Code control loop Frequency control loop Iono delay estimate Range & rate estimates PRiono Iono delay estimate GUS control loop algorithim Fig. 9.2 GUS control loop block diagram. The code control loop is a second-order control system. The error signal for this control system is the difference between the WAAS pseudorange (Prsign † and the estimated pseudorange from the Kalman ®lter. The loop output is the code rate adjustments to the GUS signal generator. The frequency control loop has two modes. First, it adjusts the signal generator frequency to compensate for uplink Doppler effects. This is accomplished using a ®rst-order control system. The error signal input is the difference between the L1 Doppler frequency from the WAAS GPS receiver and the estimated range rate (converted to a Doppler frequency) from the Kalman ®lter. Once the frequency error is below a threshold value, the carrier phase is controlled. This is accomplished using a second-order control system. The error signal input to this system is the difference between the L1 carrier phase and a carrier phase estimate based on the Kalman ®lter output. This estimated range is converted to carrier cycles using the range estimate at the time carrier phase control starts as a reference. Fine adjustments are made to the signal generator carrier frequency to maintain phase coherence [35, 47±49, 94]. 9.3.2 In-Orbit Tests Two separate series of in-orbit tests (IOTs) were conducted, one at the COMSAT GPS Earth Station (GES) in Santa Paula, California with Paci®c Ocean Region (POR) and Atlantic Ocean Region-West (AOR-W) I-3 satellites and the other at the COMSAT GES in Clarksburg, Maryland, using AOR-W. The IOTs were conducted 272 DIFFERENTIAL GPS AOR-W POR Frequency reference Signal generator C-band upconverter IF HPA Frequency reference Measurement data Processor/ controller • prototype algorithm software L1-omni antenna Frequency reference L1 dwn WAAS GPS receiver L2 Cup C-band to L2 downconverter Cdwn Frequency reference FTS atomic clock WAAS phase 1 equipment Fig. 9.3 IOT test GUS setup. to validate a prototype version of the GUS control loop algorithm. Data was collected to verify the ionospheric estimation and code±carrier coherence performance capability of the control loop and the short±term carrier frequency stability of the I-3 satellites with a prototype ground station. The test results were also used to validate the GUS control loop simulation. Figure 9.3 illustrates the IOT setup at a high level. Prototype ground station hardware and software were used to assess algorithm performance at two different ground stations with two different Inmarsat-3 satellites. 9.3.3 Ionospheric Delay Estimation The GUS control loop estimates the ionospheric delay contribution of the GEO Cband uplink to maintain code±carrier coherence of the broadcast SIS. Figures 9.4± 9.6 provide the delay estimates for POR using the Santa Paula GES and AOR-W using both the Santa Paula and Clarksburg GES. Each plot shows the estimated ionospheric delay (output of the two-state Kalman ®lter) versus the calculated delay using the L1 and C pseudorange data from a WAAS GPS receiver. Calculated delay is noisier and varying about 1 m=s, whereas the estimated delay by the Kalman ®lter is right in middle of the measured delay, as shown in Figures 9.4±9.6. Delay measurements were calculated using the equation Ionospheric delay ˆ PRL1 1 PRC tau L1 ‡ tau C ‰L1 freqŠ2 =‰C freqŠ2 9.3 GEO UPLINK SUBSYSTEM (GUS) 273 Fig. 9.4 Measured and estimated ionospheric delay, POR, Santa Paula. where PRL1 ˆ L1 pseudorange m† PRC ˆ C pseudorange m† tau L1 ˆ L1 downlink delay m† tau C ˆ C downlink delay m† L1 freq ˆ L1 frequency; ˆ 1575:42 MHz Cfreq ˆ C frequency; ˆ 3630:42 MHz The ionosphere during the IOTs was fairly benign with no high levels of solar activity observed. Table 9.1 provides the ionospheric delay statistics (in meters) Fig. 9.5 Measured and estimated ionospheric delay, AOR-W, Santa Paula. 274 DIFFERENTIAL GPS Fig. 9.6 Measured and estimated ionospheric delay, Clarksburg. between the output of the ionospheric Kalman ®lter in the control loop, and the calculated delay from the WAAS GPS receiver's L1 and L2 pseudoranges. The statistics show that the loop's ionospheric delay estimation is very close (low RMS) to the ionospheric delay calculated using the measured pseudorange from the WAAS GPS receiver. 9.3.4 Code±Carrier Frequency Coherence The GEO's broadcast code±carrier frequency coherence requirement is speci®ed in the WAAS System Speci®cation and Appendix A of reference [106]. It states: The lack of coherence between the broadcast carrier phase and the code phase shall be limited. The short term fractional frequency difference between the code phase rate and the carrier frequency will be less than 5  10 11 : That is, fcode 1:023 MHz fcarrier < 5  10 1575:42 MHz 11 TABLE 9.1 Observed RMS WAAS Ionospheric Correction Errors In-Orbit Test Santa Paula GES, Oct. 10, 1997, POR Santa Paula GES, Dec. 1, 1997, AOR-W Clarksburg GES, Mar. 20, 1998, AOR-W RMS Error (m) 0.20 0.45 0.34