NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS REAL-TIME POSITION DETERMINATIONS USING THE GPS T14100/GEOSTAR RECEIVER by Peter J. Rakowsky September 1984 Thesis Advisor: R. L. Hardy Approved for public release; distribution unlimited T222488 SECURITY CLASSIFICATION oc This PAGE (When Data Entered) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM I. REPORT NUMBER 2. GOVT ACCESSION NO. 3 RECIPIENT'S CATALOG M 'J M 8 E R 4. TITLE (and Subtitle) Real-Time Position Determinations Using the GPS TI4100/GEOSTAR Receiver 5. TYPE OF REPORT & PERIOD COVERED Master's Thesis September 1984 6. PERFORMING ORG. REPORT NUMBER 7. AuTHORfs; Peter J. Rakowsky 6. CONTRACT OR GRANT NUMBERS; 9. PERFORMING ORGANIZATION NAME AND AOORESS Naval Postgraduate School Monterey, California 93943 10. program element project, task- area a WORK UNIT NUMBERS II. CONTROLLING OFFICE NAME AND ADDRESS Naval Postgraduate School Monterey, California 93943 12. REPORT DATE September 19 8 4 13. NUMBER OF PAGES 80 14. MONITORING AGENCY NAME & ADDR ESSOl different from Controlling Office) 15. SECURITY CLASS. (o( this report) 15*. DECLASSIFICATION DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release, distribution unlimited 17. DISTRIBUTION STATEMENT (ol the abstract entered In Block 30. II different from Report) 18. SUPPLEMENTARY NOTES '9. KEY WORDS (Continue on reverse aide If necessary and Identify by block number) Global Positioning System, geodetic positioning, Satellite Locating System GEOSTAR Receiver, Real-Time Positioning 20 ABSTRACT (Continue on reverse aide If necessary and Identity by block number) The NAVSTAR Global Positioning System is a worldwide, all-weather, satellite positioning system capable of high accuracy real-time position determinations The Applied Research Laboratories (ARL:UT) , in conjunction with the Naval Surface Weapons Center (NSWC/DL) and other government agencies, conducted geodetic field tests of a government sponsored prototype receiver, the TI4100/GEOSTAR, in March 1984. Data were acquired from four satellites by three receivers, with antennas located at known stations, over approximately six-hour periods each day. DD 1 jan 73 1473 EDITION OF I NOV 65 IS OBSOLETE S N 0102- LF- 014- 6601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) SECURITY CLASSIFICATION OF THIS PAGE (Whtn Dmtm Enffd) ABSTRACT cont. Based on the real-time solutions acquired on March 1, 8, and 9, 1984, absolute point position determinations have an average discrepancy of 7.5 meters with a one sigma repeatability of less than a meter. Relative positions were determined to an average relative accuracy of 1:9,700 for distances of 14 to 26 kilometers. SN 0102- LF- 014-6601 SECURITY CLASSIFICATION OF THIS PAGE(T»7i«n Data Entarad) 2 Approved for public release; distribution unlimited, Real-Time Position Determinations Osing the GPS TI4 100/GEOSTAR Receiver by Peter J. Rakowsky :artographer, Defense Mapping Agenc B.S., University of Maryland, 1979 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN HYDROGRAPHIC SCIENCES from the NAVAL POSTGRADUATE SCHOOL September 1984 m ABSTRACT The NAVSTAR Global Positioning System is a worldwide, all-weather, satellite positioning system capable of high accuracy real-time position determinations. The Applied Research Laboratories (ARL:UT), in conjunction with the Naval Surface Weapons Center (NSWC/DL) ani othar government agencies, conducted geodetic field tests of a government sponsored prototype receiver, the II4100/GEOSTAR , in March 1984. Data were acquired from four satellites by three receivers, with antennas located at known stations, over approximately six-hour periods each day. Based on the real-time solutions acquired on March 1, 8, and 9, 1984, absolute point position determinations have an average discrepancy of 7.5 meters with a one sigma repeat- ability of less than a meter. Relative positions were determined to an average relative accuracy of 1:9,700 for distances of 14 to 26 kilometers. TABLE OF CONTENTS C I. INTRODUCTION 9 II- BACKGROUND 11 A. THE GLOBAL POSITIONING SYSTEM 11 B. TRANSMISSION SIGNALS 12 C. THE NAVIGATION MESSAGE 12 D. RECEIVER OPERATION 15 E. POSITION COMPUTATION 17 F. GEODETIC DATUMS . . 18 III. ANALYSIS METHODS 19 A. EXPERIMENT DESIGN 19 B. GPS USER TAPES 19 C. COORDINATE TRANSFORMATIONS 21 D. SATELLITE UPDATES 22 S. AVERAGING METHODS 22 F. COMPUTATIONS 23 G. GEODETIC COMPARISONS 2U IV. RESULTS AND DISCUSSION 26 A. GIVEN POSITIONS AND DISTANCES 2b B. SATELLITE UPDATE TIMES 29 C. BEHAVIOR OF THE REAL-TIME SOLUTIONS 29 1. WGS-72 Coordinate Discrepancies 29 2. WGS-72 Point Position Discrepancies ... 30 3. WGS-72 Side-length Discrepancies 30 D. AVERAGING RESULTS 47 1. Determination of the Method of Averaging 47 2. WGS-72 Results 55 E. GEODETIC COMPARISONS 58 1. Discrepancies of Point Position Determinations 58 2. Discrepancies of Point Positions for Entire Pvecording Sessions 60 3. Relative Position Comparisons 60 4. Relative Position Discrepancies 6 1 V. CONCLUSIONS AND RECOMMENDATIONS 64 APPENDIX A; GPS USER-TAPE READ-WRITE PROGRAM 66 APPENDIX B: PROGRAM TO COMPUTE REAL-TIME SOLUTION DISCREPANCIES 72 APPENDIX C: LIST OF ABBREVIATIONS 76 LIST OF REFERENCES 77 INITIAL DISTRIBUTION LIST 79 LIST OF TABLES I. Data Types of GPS User Tapes 20 II. Transformation Progcam Parameters 2 1 III. Station Names • 27 IV. NAD-27 Station Coordinates 27 V. NAD-27 Geodetic Distances and Azimuths 23 VI. WGS-72 Side-length Distances 23 VII. Satellite Update Times (Seconds) 29 VIII. Means and Sig&as 3eginning Dne Hour After Initial Solutions 56 IX. Means and Sigmas Beginning Two Hours After Initial Solutions 57 X. Geodetic and Horizontal Point Position Discrepancies 59 XI. Discrepancies of Observed Distances and Azimuths 61 XII. Discrepancies in Relative Position Determinations 63 LIST OF FIGURES 2.1 The TI4 100/GEOSTAR Receiver 16 4.1 WGS-72 Coordinate Discrepancies 31 4.2 WGS-72 Coordinate Discrepancies 32 4.3 WGS-72 Coordinate Discrepancies 33 4.4 WGS-72 Coordinate Discrepancies 34 4.5 WGS-72 Coordinate Discrepancies 35 4.6 WGS-72 Coordinate Discrepancies 36 4.7 WGS-72 Coordinate Discrepancies ........ 37 4.8 WGS-72 Coordinate Discrepancies 38 4.9 Discrepancies and Standard Errors 39 4.10 Discrepancies and Standard Errors 40 4.11 Discrepancies and Standard Errors 41 4.12 Discrepancies and Standard Errors 42 4.13 Discrepancies and Standard Errors 43 4.14 Discrepancies and Standard Errors 44 4.15 Discrepancies and Standard Errors 45 4.16 Discrepancies and Standard Errors 46 4.17 Point Position and Side-length Discrepancies . . 43 4.18 Point Position and Side-length Discrepancies . . 49 4.19 Point Position and Side-length Discrepancies . . 50 4.20 Point Position and Side-length Discrepancies . . 51 4.21 Point Position and Side-length Discrepancies . . 52 4.22 Point Position and Side-length Discrepancies . . 53 4.23 Point Position and Side-length Discrepancies . . 54 I. IHTRQDOCTION The Naval Surface Weapons Center (NSWC) , with sponsor- ship by the Defense Mapping Agency (DMA) , has developed a system for geodetic positioning with the use of the NAVSTAR Global Positioning System (GPS) [Ref. 1]. A government sponsored prototype receiver, the II4100/G2OSTAE, was devel- oped by Texas Instruments through contract with Applied Research laboratories, The University of Texas at Austin (ARL:DT) [Ref. 2]. The receiver was tested by ARL:UT in conjunction with NSTCC and other government agencies over short and medium base lines in March 1984. The Defense Mapping Agency Hydrographic/Topographic Center (DMAHTC) has expressed interest in independent analyses of the data from these tests [Ref. 3]. Absolute point positioning, as it is used in this thesis, is the determination of a position with the use of one GPS receiver. Relative positioning is the determination of two positions relative to each other with the use of two receivers. The basic premise of real-time relative posi- tioning is that GPS observation errors are to a large extent systematic in the same general area at the same time. If such is the case, relative positioning by two receivers can locate positions relative to each other more accurately than absolute positioning alone. Accuracy standards for horizontal control require certain relative accuracies between directly connected adja- cent points. Third-order surveys are used for local hori- zontal control in hydrographic surveying and other local projects. Third-order, Class II standards require relative accuracies of at least 1:5,000 between directly connected adjacent points (e.g., 5 meters relative accaracy between stations separated by 25 kilometers). [Ref. 4] Geodetic positioning with GPS has advantages over conventional surveying methods. Visibility between sites and fair weather conditions are not required. Real-time positioning has a special application in the case where the position of a station is needed in a short amount of time and before the data can be post-processed. An analysis of the real-time solutions of the GEOSTAR short and medium base line tests will give an estimate as to what degree of accu- racy the system can achieve in real-time. 10 II. BACKGROUND A. THE GLOBAL POSITIONING SYSTEM The Global Positioning System is a worldwide, all- weather, satellite positioning system. GPS can be thought of as consisting of three components; the Space Segment, the Control SegmeQt, and the User Segment. The Spare Segment will consist of eighteen satellites (with three spares) in six orbit planes when fully operational in late 1988 or early 1989 [Ref. 5]. The satellites will orbit the Earth in twelve-hour periods at altitudes of approximately 20,000 kilometers. This constellation will provide four satellites in view at one time at elevations of greater than 20° above the horizon. [Ref. 6] The satellites' ground paths will be fixed. The time at which a particular satellite will be in view at a certain position will be about four minutes earlier each day due to the differences betweeu solar and sidereal time. [Ref. 7] The GPS satellites have on orbit weight of 950 pounds. Power is supplied by solar panels and nickel-cadmium batteries. The satellites are equipped with atomic clocks with stabilities on the order of 1 part in 1013. [Ref. 8] Perturbations in the satellite orbits are caused by the forces of attraction of astronomical bodies, gravitational irregularities of the earth, and solar radiation pressure. These perturbations are compensate! for by the Control Segment and frequency standard offsets. [ Ref. 7 ] The Control Segment consists of four monitor stations located at Alaska, Hawaii, Guam, and Vandenburg AFB; and a Master Control Station (MCS) and an Upload Station at Vandenburg AFB [Ref. 9]. The monitor stations track the 11 satellites then send the data to the MCS for processing to determine updated predictions of satellite and clock behavior. The updated predictions are transmitted to the satellites by the Upload Station. [Ref. 10] B. TRANSMISSION SIGNALS The GPS NAVSTAR satellites simultaneously transmit navi- gation information on 2 RF frequencies; the L1 frequency at 1575.4 MHz. and the L2 at 1227.6 MHz. Both freguencies are modulated with pseudo-random noise (PRN) codes. The Precise Positioning Service (PPS) , formerly called the "P-code", is modulated on both freguencies and the Standard Positioning Service (SPS) , formerly called the "C/A-code", is available only on the L1 frequency. PRN codes, different for each satellite, serve the purpose of uniquely identifying the particular satellite and provide a means of determining the signal transit time by measuring the phase shift necessary for the receiver to match codes. [Ref. 11 and 12] The SPS is a relatively short code of 1023 bits. The code repeats itself every millisecond at a bit rate of 1.023 Mbps. Due to the short duration time of the SPS, the code is relatively easy to match and lock on to. The PPS has a 7-day code duration and 10 times the bit rate, making the PPS code relatively difficult to match with the receiver's internally generated code. The PPS offers the advantage of a finer resolution of the phase shift necessary to match codes, thus a greater measurement accuracy of signal transit time. [ Ref. 11] C. THE NAVIGATION MESSAGE The GPS Navigation Message is modulated on both the L1 and L2 frequencies and contains information necessary to compute the user's position. The information is in the form 12 of a 50 tps. data stream common to both the PPS and SPS. The data frame is 1500 bits long and consists of 5 subframes of 6 seconds (300 bits) each. The Navigation Message provides information such as satellite e^hemerides, system time, satellite clock behavior, and transmitter status. [Ref. 13] Subframes are divided into ten 30-bit words. The first two words of each subframe contain system time and time synchronization information for transfer from the SPS to the PPS in the form of hand-over words (HOW) and telemetry words (TLM) . The remaining 8 words contain user navigation data generated by the Control Segment. [Ref. 13] Data Block 1 occupies words 2 through 10 in subframe one. It contains frequency standard corrections, an associ- ated age of data word, and ionospheric delay corrections for single frequency receivers. The clock correction parameters are used to determine the satellite's clock offset from GPS time by the following equations: t = t - At (2.1) sv sv At = a ♦ a. (t - t ) + a. (t - t ) 2 (2.2) sv 0 1 oc 2 x oc where t is the GPS time in seconds measured from the begin- ning of the GPS week (approximately Saturday/Sunday midnight GMT), t is the satellite's PRN code phase time at the time ' sv r of message transmission, t is Data Block 1 reference time J ' oc (seconds), and aQ, a-,, and a2 are Data Block 1 clock correc- tion parameters (coefficients of a second order polynomial) . Note that t may be approximated by t in equation 2.2. [Ref. 13] The age of data word (AODC) is the time between Data Block 1 reference time and the time since the last measure- ment used in computing the clock correction parameters 13 [Eef. 13]. Test data in this thesis ware obtained using both the L1 and L2 frequencies, therefore, the ionospheric delay parameters for single frequency receivers contained in Data Block 1 are not used (see Van Diarendonck, et al, 1978) . Data Elock 2 contains ephemeris information in subfraaes 2 and 3. This data includes associated age of lata words (AODE) which represent the time difference between Data Elock 2 reference time and the time of the last measurement used in the estimation of the ephemeris parameters. The ephemeris data includes conventional Keplerian-t ype parame- ters, secular drift terms, and harmonic coefficients used to cocrect for perturbations in the Keplerian orbit. [Eef. 13] The satellite's position is calculated by Van Dierendonck • s algorithm [Eef. 13] with the addition of a secular drift term to correct for perturbations in the inclination of the satellite's orbit [Ref. 14]. The Message Block appears in the third through the tenth 30-bit words of subframe 4 of the Navigation Message. This space is reserved for alphanumeric messages provided to the user by the Control Segment. Space exists for 23 eight-bit ASCII characters. [Eef. 13] Almanac information appears in Data Block 3 in the fifth subframe. Data Block 3 consists of 25 subframes allowing for almanacs of up to 24 satellites (with one dummy subframe) . Twenty-five navigation messages must be received to acquire the complete data set of Data Block 3. Extra subframes can be used to repeat the almanacs for certain satellites. Satellite almanacs provide the user with less precise position and clock correction information. Almanacs aid the user in satellite selection and simplify the acqui- sition of signals. Almanacs include ephemeris parameters, clock correction parameters, satellite identification, and satellite health terms. [Ref. 13] 14 D. RECEIVER OPERATIC!) The GEOSTAR GPS receiver is a government sponsored version of the TI4100 commercial receiver (Fig. 2.1). The GEOSTAR is a single channel, multiplex receiver capable of tracking four satellites on the L1 and L2 PPS. The control and display unit (CDU) is a hand-held input/output device with two 16-character alphanumeric displays. The antenna assembly consists of a conical omnidirectional antenna with a preamp that allows remote operation of the receiver. Two 100-foot cables connect the antenna assembly to the receiver. One cable is used to input DC power to the preamp and output the amplified RF signals. The other cable is used for a built-in test signal injection from the receiver. [Ref. 15] A typical GEOSTAR geodetic surveying unit consists of a 2-man team, a station wagon or van, and the GEOSTAR field set. The field set contains the receiver, CDJ, the antenna assembly, a cassette tape recorder, a tripod with a leveling bracket, two 12-volt automobile batteries, an EFRATOM FRK-H rubidium oscillator, a weather station with sensors, cables, transportation cases, tools, manuals, and spare parts. The field set is easily contained and transported in the rear of the vehicle. The antenna assembly is mounted on a standard surveyor's tripod with a leveling bracket then leveled and plumbed over the mark to be surveyed. A reference mark on the base of the antenna assembly is oriented to north using a hand compass. The height of the L2 phase center mark at the base of the antenna assembly above the survey point is measured ani recorded. The antenna assembly, the power supply, the cassette recorder, the weather station, and the rubidium oscillator are then connected to the receiver with the appropriate cables. Scratch tapes are inserted in the cassette recorder for the power-up procedure. 15 Figure 2.1 The TI4 100/SEOSTAR Receiver 16 The system is turned on and the receiver and cassette recorder self-tests are initiated. When the self-tests are successfully completed, the GESAP. bootstrap tape is inserted in Drive 1. The program is loaded and blank tapes are inserted in the two tape drives. The operator is then prompted by the CDU for input information including an esti- mate of the user's position, weather data, satellites to be tracked, and Doppler aiding values for each satellite. The system then operates unattended except for the replacement of cassette tapes as required and the periodic manual input of weather data (if the automatic weather station is not used) . E. POSITION C0HP0TATION The satellite's position and the time of signal trans- mission are computed with the broadcast ephemeris and the clock correction parameters included in the Navigation Message. The time between the transmission and the recep- tion of the satellite signal multiplied by the speed of iignt is the pseudorange. Pseudoranges used to calculate the real-time solutions are corrected for atmospheric delays in the GSOSTAR Receiver [fief. 17]. Ionospheric refraction is nearly inversely proportional to the square of the frequency. By receiving both the L1 and the L2 frequencies, the ionospheric delay is calculated by comparison. [ Ref- 16] Iropospheric delay is calculated by a model based on temperature, pressure, humidity, and the elevation of the satellite above the horizon [Eef. 17]. Knowing the positions of four satellites and the ranges to the user, the user's position is calcu- lated by a least squares method. 17 F. GEODETIC DATOMS The GEOSTAR real-time solutions are referenced in DoD World Geodetic System 1972 (WGS-72) Cartesian coordinates. WGS-72 is an earth-centered, earth-fixed, glooal, geodetic datum adopted by DMA in March 1974 [Eef. 18]- The reference surface is an ellipsoid that test approximates the shape of the earth's geoid. The ellipsoid is normally defined by the length of the semimajor axis and the flattening. Latitude ranges between -90° and 90° with north posi- tive. Longitude is measured positive east from 0° to just less than 360° from the WGS-72 reference meridian at 0".54 east of the Greenwich Meridian. The Cartesian X-axis is formed by the intersection of the reference meridian plane and the plane of the equator. The Y-axis is 90° east of the X-axis in the plane of the equator. The Z-axis is in the direction of the earth's mean rotation axis based on the average terrestrial pole of 1900-05. [fief. 19] The North American Datum 1927 (NAD-27) is a regional datum based on the Clarke 1866 Ellipsoid with the origin at Meades' Ranch, Kansas. The Clarke 1366 Ellipsoid minimizes tne deflection of the vertical and geoidal undulations in the continental United States. The National Ocean Survey (NOS) , the National Geodetic Survey (NGS) , and the United States Geological Survey (USGS) use NAD-27 coordinates in most survey operations. The transformation from NAD-27 to WGS-72 reference systems creates offsets of the order of 5 meters [fief. 2]. It is assumed that this error is removed when the reverse transformation is made; but the error source will still exist in the analysis of the WGS-72 point position discrepancies. 18 III. A HAL YS IS METHODS A. EXPEBIMENT DESIGN Relative position field testing of the GEOSTAR Receiver was performed in central Texas in February and March 1984. Three receivers, each with an antenna located over a different known position, were operated continuously over approximately the same period of satellite visibility. Four satellites, with PRN codes 6, 8, 9, and 11, were tracked in these tests. The period of data gathering was coordinated with the time period in which all four satellites were in view at the same time. The real-time positions of the antennas were recorded every 12 seconds over approximately a six-hour period each day. The data were recorded on cassette tape then transferred to 9-track tape by AHL:[JT. B. GPS USER TAPES The recorded data and the associated position coordi- nates used in the analysis were obtained from NSVIC/DL. The GPS User Tapes are a standardized format, 9-track magnetic tape. The tapes are unlabelled, ASCII coded, 1600 bpi, with 80 characters per physical record and 1 record per block. The first file on the tapes consists of header comment records. This file assists the user in identifying the tape and includes information such as the date and site of the data acguisition. Data files begin with an 80-character control record (Lata Item List) which identifies the types of lata that follow. The first location of all records is reserved for a control character. The Data Item List control, record has an asterisk •*' in the first position followed by an integer in 19 the next three positions which specifies the numcer of times to repeat the sequence of the Data I tea List. The remaining 76 characters contain up to 19, 4-digit data type identi- fiers which specify the type of data that is to follow the control record. Control records are read with a (A1, 13, 1914) format. Data information are one or more records in length and divided into groupings called data items (Tab. I) [Bef. 19]. TABLE I Data Types of GPS Jser Tapes item Identifier Data Type 000 1-0999 Exchange conversion program information 1000-1999 Constant equipment related data 2000-2999 Campaign identifying data 3000-3999 Infrequent measurement data 4000-4999 Space vehicle related data 5000-5999 Heather data 6000-6999 Real-time solution data 7000-7999 Measurement data 8000-8999 Post analysis data The data type identifiers of the Data Item List specify the order and the format of how the data is to be read. Data used in the analysis were read from the user exchange tapes using a slight modification of the sample input program contained in reference 19 (App. A) . Eeal-time solution information (data type 6010) was read from the tapes and written to mass storage and retained. Other information such as measurement data types (data type 920), real-time solution configuration (data type 1150), and 20 antenna location (data type 2210) were read manually from the first page of the printouts of the tapes. C. COORDINATE TRANSFORMATIONS The coordinates of the stations used in the field testing were given in NAD-27 geodetic coordinates. The real-time solution output of the GEOSTAfi Receiver are in w'GS-72 Cartesian coordinates. To make comparisons of the given positions to the observed positions, the given posi- tions were transformed to WGS-72 Cartesian coordinates. The transformation was done using the Abridged Molondensky formulas contained in the NGS's conversion program (D035-41) for the HP-41CV programmable calculator. The program prompts the user for the values of the origin shift between coordinate systems. The X, I, and Z origin shifts for transforming from NAD-27 to WGS-72 are -22, 157, and 176 meters, respectively [Ref. 20]- These values differ from the origin shift values supplied with the transformation program by NGS. The NGS values are -12.547, 155.804, and 175.369, for the X, Y, and Z origin shifts, respectively. The program generates semimajor axis and inverse flattening parameters of both reference systems (Tab. II) . TABLE II Transformation Program Parameters Ellipsoid a (meters) Vf Clarke 1866 6,378,206.4 294.9786982 WGS 72 6,378,135.0 298.2600000 21 D. SATELLITE UPDATES The ephemeris elements and clock model updates occurred at identical times according to the data recorded in field tests. An approximation of the update times is calcu- lated by subtracting the Age of Data (AODE) from the ephem- eris reference time (t ), i.e., oe update time = t - AODE (3.1) oe The update times changed by -496, 1052, or 1552 seconds when the computation of equation 3. 1 was performed for each satellite with subsequent occurrences of the broadcast ephemeris on the recording. The change is due to packing of bits in the transmissions of the AODE values. An approxima- tion of the update times is made, within a few minutes, by using the first AODE values that cnange to smaller numbers (on the order of 1 to 2 hours) from previously recorded large values (on the order of 24 hours) . [Ref. 14] E. AVERAGING METHODS Relative position determinations were made using real- time solutions from two different stations at the same GPS time tags. Computer programs were written to read the real- time solutions from mass storage and compute the discrepan- cies between the observed and the given WGS-72 coordinates of pairs of stations at common GPS times. The beginning and ending times of data acquisition varied among the three receivers operated during the same time period; thus, the effect of comparing solutions at the same time tags resulted in the elimination of some of the real-time solutions from the analysis. In effect, the tape with the earlier starting time was spooled forward to correspond to the starting time of the first real-time solution recorded by the receiver 22 that began operation at a slightly later time. Similarly, the time of the last solution common to both receivers is the last solution recorded by the receiver that ended opera- tion first. A mean position was determined in two different ways to show the effect of the ephemeris and clock updates on the real-time solutions and to eliminate real-time solutions with large discrepancies from the averaging. In general, relatively large discrepancies are evident in roughly the first hour of receiver operation. The real-time solution discrepancies of pairs of stations were averaged beginning with the values one hour after and two hours after the first solution time common to both receivers. In these tests, beginning the averaging one hour after the initial solutions corresponds to averaging the solutions that were recorded a short time before or after the update times and through the remainder of the recording session. Beginning the averaging two hours after the initial solutions corresponds to using only those values that were recorded much after the updates and through the remainder of the session. Real-time solu- tions are treated as independent observations in the statis- tical analysis. F. COMPUTATIONS The distances between stations (d) , in the H3S-72 refer- ence system, are computed by equation 3.2 where X ]_ ,Y1# and Z -, are the WGS-72 Cartesian coordinates of one of the stations, and X , Y , and Z are the coordinates of the other station of the side. The side-lengths are calculated = V(Xi " X2) 2 + (Yl " Y2)2 + (Zl " Z2)2 (3-2) 23 for both the given coordinates and the mean values of the GEOSTAE real-time solution coordinates. The discrepancies between the two are computed by subtracting the given distances from the observe! distances. Discrepancies are used in the averaging to save computer time and to reduce round-off error. The absolute value of the point position discrepancies are computed by eguation 3.3 where the subscripts o and g represent the observed and given values, respectively. 5 = V(Xo * v2 + (Yo - v2 + (zo - v2 <3-3> The standard error of a single observation was calcu- lated as a measure of the precision of the real-time solu- tions. The means and standard errors of a single, 12-second real-time solution were calculated for the coordinate discrepancies and the point position discrepancies. Comparisons are made for the two averaging methods (Sect. Ill E) - The mean WGS-72 Cartesian coordinate discrepancies were used to compute the final observed positions. The observed positions are computed by subtracting the discrep- ancies from the given coordinates. G. GEODETIC COMPARISONS Geodetic accuracy standards for horizontal control reguire certain relative accuracies between directly connected adjacent points. The distances between points are computed along the ellipsoid - the geodesic. To compare the accuracies of the observed positions with the standards for geodetic control, the WGS-72 Cartesian coordinates of the observed positions are transformed to NAD-27 geodetic coor- dinates. The transformations were done using a modification of NGS's D035 program for the HP-41CV programmable 24 calculator. The modified version uses the same parameters as those contained in the original program (Tab. II) . The geodetic inverse computation is used to calculate the geodetic distance and azimuths between two known points. The inverses between given positions and between observed positions were computed and compared. To simulate the positioning of an unknown station, one station of a side is held fixed and the other station is located using the direct computation. The coordinates of the known position and the distance and azimuth to the unknown position are the input variables and the coordinates of the unknown station are computed. The distance and azimuth calculated by the inverse computation of the observed point positions are used in this calculation. The direct and inverse computations were done on the IBM 3033 based on Puissant's Coast and Geodetic Survey Formula [fief. 21 ]. The standard errors of the discrepancies of the geodetic position determinations for entire recording sessions are calculated as an approximation of the repeatability. To do so, the two point position discrepancies of each station on days 61 and 63 must first be averaged to determine a single value for the station. 25 IV. RESULTS AND DISCUSSION A. GIVEH POSITIONS AND DISTANCES Data in this report are from relative position tests of March 1, 8, and 9, 1984. Three receivers were operated simultaneously over a period of approximately six hours. The antennas of the March 1st tests were located over a second-order position and two of its reference marks. The triangle has side- lengths of approximately 30 meters. The tests of March 8th and 9th were conducted at first-order survey points separated by distances of 14 to 25 kilometers. The data of the tests at one of the positions on March 9th was not available at the time of this writing. The data gathered on March 1st will be defined as the short base line tests and the 14 to 25 kilometer testing will be termed medium base line tests. Tables III and IV give the names and the NAD-27 coordinates of the stations and Table V gives the distances and azimuths in each triangle. Distances and azimuths were calculated using the inverse computation (Sect. Ill G) . The NAD-27 coordinates of the given positions were transformed to WGS-72 Cartesian coordinates using a NGS transformation program (D035-41). The ellipsoidal heights are corrected for the heights of the antennas above the station marks prior to the transformations. The heights of the antennas above the stations (data type 2113) were read manually from the first page of the printouts of the tapes. The distances between the points in W3S-72 Cartesian coordi- nates were calculated using equation 3.2 (Tab. VI). The computed side distances foe the FGS-72 Cartesian coordinate system are in all cases greater than or equal to 26 ths computed geodetic distances. In the medium base line tests, the differences vera found to increase by -0035 TABLE III Station Names J.D. Number Name Abbreviation 61 85019 ARL 10563 D3A J HE 35020 ARL 10563 R3 1 DMA RM1 35021 ARL 10563 EH 2 DMA RK2 68,69 35022 BE ZERO BZERG 35027 PILOT FCNOI 1935 PILOT * 35028 BALD KNOB 1935 BNOB * Station not used in March 9th analysis TABLE 17 NAD-27 Station Coordinates St at ion Il2£th Latitude West Loa^itude Ht- (m JMR 300 22' 56". 74285 970 43' 35". 97558 235.5 RM1 30 o 22i 57". 54452 970 43' 36". 31041 235. 7 FM2 30O 22' 57". 06234 970 43' 35". 01009 235.6 BZERO 30° 23' 16". 31238 970 43' 42'*. 05790 238. 4 PILOT 30° 09' 30". 93387 970 42' 28". 08922 215.9 EN 0B 30O 20' 07". 61000 970 35' 30". 84700 204. 4 percent of ths length of the line. Differences of .911, .748, and .534 meters were computed for the side-lengths of approximately 25.5, 22.6, and 14.3 kilometers, respectively. These differences occur because the Cartesian distances are computed between each point; the geodetic distances are computed from the projections of the points on the ellipsoid 27 which does not account for the ellipsoidal heights. The distances between BZERO and PILOT are aqual to the nearest TABLE V NAD-27 Geodetic Distances and Azimuths Side Distance (m. ) Az im uth JMR - RH1 26.255 340° 05' 34". 72573 JMR - RM2 27.591 690 Q6' 37". 54898 EM1 - RE2 37.759 113° 09' 19". 14446 BZERO - PILOT 25,492.277 175° 32' 48". 25379 RZERO - BNOB 14,346.955 113° 51' 26". 80840 BNOB - PILOT 22,556.303 209° 40' 09". 53915 TABLE VI WGS-72 Side-length Distances Distance (m. ) 26.255 27.593 37.759 J.D. Sic ie 61 JMR - RM1 JMR - RM2 RH1 - RM2 68 BZEPO - PILO BZERO - BNOB BNOB - - PILOT 25, 493. 188 14, 347.439 22, 557.051 69 BZERO - PILOT 25,493.188 a millimeter for tests run on days 63 and 59 even though the heights of the antennas above the stations were different on both days. 28 B. SATELLITE UPDATE TIMES The ephemeris and clock update tiaes occurred approxi- mately one hour after the start of data acquisition in these tests. There are approximately 25 to 30 recordings of the broadcast ephemeris (data type 4113) during the six-hour recording periods. The update times were computed (egn. 3.1) using the AODE values that changed from large numbers to much smaller numbers in subsequent recordings of the broadcast ephemeris (Tab. VII). Satellites with PRN codes 9 and 11 were updated approximately one-half hour after the updates of codes 6 and 8 on days 61 and 69. According to the recorded ilata, all four satellites were updated at approximately the same time on day 68. TABLE 711 Satellite Update Times (Seconds) J.D. PPN codes t oe 378,000 A3DE toe - AODE 61 6,8 6, 144 371, 856 9,11 378,000 4, 096 373,904 68 6,3,9, 11 378,000 6,144 371,856 69 'I1 460,300 4,096 456, 704 9,11 464,400 6, 144 458,256 C. BEHAVIOR OF THE REAL-TIME SOLUTIONS 1 * ££S-72 Coordinate Disc repancie s The real-time solutions were read from the GPS User Tapes and retained. The solutions of pairs of stations, with time tags of real-time solutions common to both, were 29 used in the analysis. The discrepancies between the observed coordinates and the given WGS-72 coordinates (observed - given) were computed and plotted over time (Figs. 4-1 - 4.8) . The vertical arrows in the figures indicate the times of satellite updates (Tab. VII) . The tick marks on the horizontal (time) axis represent one hour. In general, the X, Y, and Z coordinate discrepancies begin with large values in the initial solutions and then become smaller and more consistent after satellite updates and over time. There is a significant improvement in the discrepancies of the observed coordinates near the time of the update of PEN codes 6 and 8 at station J/IR and near the update of codes 9 and 11 at station F.M1 on day 61 (Figs. 4.1 and 4.2). The precision of the discrepancies in each coordinate increase at all three stations on day 6 1, a snort time after the update of codes 9 and 11. The discrepancies at stations BZEEO and PILOT on day 68 decrease approximately one hour after the initial solutions (Figs. 4.4 and 4.5) . 2- WGS-72 Point Position Discrepancies The absolute values of the point position discrepan- cies of pairs of stations with common time tags were computed (eon. 3.3) for five-minute time segments and plotted with the standard errors oyer time (Figs. 4.9 - 4.16). In general, the point position discrepancies and the standard errors decrease after satellite updates and over time. Except for the general trend, there is no obvious correlation of the accuracies (discrepancies) and the preci- sion of the five-minute time segments at all stations on the same day. 3 • WGS-72 Side-length Discrepancies Relatively high accuracy side-length determinations are evident at certain times; however, the times of these 30 on I- 9 uj 2 >- ° u °" o o-| 7 en u QS- q o'_ l o 6 in I o _ I q 6 J.D. 61, 1984 SHORT BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES 369.0; i STATION JMR a X COORDINATE « r COORDINATE * Z COORDINATE ULJL""' VullMO- °. U o- Ld u Q o _ I o_ J.D. 61, 1984 SHORT BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES STATION RM1 X COORDINATE r COORDINATE Z COORDINATE 369.00 1 — 372.60 1 1 1 1 376.20 379.80 . 383.40 387.00 GPS TIME (SEC) 390.60 *103 Figure 4.2 WGS-72 Coordinate Discrepancies 32 J.D. 61, 1984 SHORT BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES STATION RM2 X COORDINATE Y COORDINATE Z COORDINATE 376.20 379.80 383.4-0 GPS TIME (SEC) 387.00 390.60 *103 Figure 4.3 WGS-72 Coordinate Discrepancies 33 J.D. 68, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES STATION BZERO X COORDINATE COORDINATE 369.00 372.60 ~~\ 1 1 1 1 376.20 379.80 383.40 387.00 390.60 GPS TIME (SEC) *103 Figure 4.4 WGS-72 Coordinate Discrepancies 34 r J.D. 68, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES STATION PILOT X COORDINATE Y COORDINATE Z COORDINATE 369.30 372.60 376.20 379.80 383.40 387.00 390.60 GPS TIME (SEC) *103 Figure 4.5 WGS-72 Coordinate Discrepancies 35 J.D. 68, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES q ^~s d 00 rN en •- S uj 2' >- U UJ (J (/} Q o d_ I o d_ in o. ID I O STATION BNOB X COORDINATE T COORDINATE Z COORDINATE 369.00 372.60 376.20 379.80 383.40 GPS TIME (SEC) 387.00 I 390.60 *103 Figure 4.6 HGS-72 Coordinate Discrepancies 36 J.D. 69, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES STATION BZERO X COORDINATE \ COORDINATE I COORDINATE Figure 4.7 WGS-72 Coordinate Discrepancies 37 J.D. 69, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES STATION PILOT X COORDINATE 45^.00 457.60 461.20 464.80 468.40 472.00 475.60 GPS TIME (SEC) *103 Figure 4.8 HGS-72 Coordinate Discrepancies 38 STATION JMR J.D. 61,1984 SHORT BASELINE TESTS 5 MINUTE SEGMENTS 4r& A A £i?- A -J; & A jj .Ji ■ ****** LEGEND DISCREPANC ~SIGMA ~ 369.00 372.60 376.20 379.80 383.40 GPS TIME (SEC) 387.00 390.60 *103 Figure 4.9 Discrepancies and Standard Errors 39 STATION RM1 J.D. 61,1984 SHORT BASELINE TESTS 5 MINUTE SEGMENTS 369.00 372.60 -1 ' 1 1 ■ 1 376.20 379.80 383.40 387.00 390.60 GPS TIME (SEC) *103 Figure 4.10 Discrepancies and Standard Errors 40 STATION RM2 J.D. 61,1984 SHORT BASELINE TESTS 5 MINUTE SEGMENTS 369.00 372.60 376.20 379.80 383.40 GPS TIME (SEC) 387.00 390.60 *103 Figure 4.11 Discrepancies and Standard Errors 41 STATION BZERO J.D. 68,1984 MEDIUM BASELINE TESTS 5 MINUTE SEGMENTS tr^A&i*ji*rftiL*n'iiii6fla6flft'&(i) +rt3 tlnh ± A t»A 1*1 ft 1* A At*-A A 6 *r& LEGEND DISCREPANC 1 SIGMA 369.00 372.60 Figure 4.12 Discrepancies and Standard Errors 42 "O- wo_ 00 LJ h- O- O- O- Ju!iftit[iliJmiLi!ii!li!. '"* STATION PILOT J.D. 68,1984 MEDIUM BASELINE TESTS 5 MINUTE SEGMENTS LEGEND a DISCREPANCY • 1 SIGMA 369.00 372.60 376.20 379.80 383.40 GPS TIME (SEC) 387.00 390.60 *103 Figure 4.13 Discrepancies and Standard Errors 43 "O- "o_ 00 LJ h- UJ o_ o_ o. STATION BNOB J.D. 68,1984 MEDIUM BASELINE TESTS 5 MINUTE SEGMENTS a a il dniifl a LEGEND DISCREPANCY 369.00 372.60 376.20 379.80 383.40 GPS TIME (SEC) 387.00 1 390.60 *io3 Figure 4.14 Discrepancies and Standard Errors 44 STATION BZERO J.D. 69,1984 MEDIUM BASELINE TESTS 5 MINUTE SEGMENTS LEGEND a DISCREPANCY "" SIGMA 453.600 457.200 l ; r 464.401 468.001 460.801 GPS TIME (SEC) 471.602 475.202 *io3 Figure 4.15 Discrepancies and Standard Errors 45 STATION PILOT J.D. 69,1984 MEDIUM BASELINE TESTS 5 MINUTE SEGMENTS aa»a aaa^ LEGEND DISCREPANC CIGMA 453.600 457.200 460.801 464.401 468.001 GPS TIME (SEC) 471.602 475.202 *103 Figure «J.16 Discrepancies and Standard Errors 46 solutions are not consistent at all stations luring the same day (Figs. 4.17 - 4.23). The discrepancies in the lengths of sides JME-RM2 and RM1-RM2 are relatively small near time tag 382632; however, the side- length discrepancy of JMR-RM1 at approximately the same time is relatively larger than other determinations of that side on day 6 1. The side- length discrepancies of JHR-RM2 and RM1-RM2 are -.044 and .037 meters at time tags 382632 and 382600, respectively. The discrepancy of JHF.-RM1 at time tag 382600 is .955 meters; whereas, the discrepancy is .476 meters at time tag 386400. Therefore, the most accurate side-length determina- tions do not necessarily occur at approximately the same time for all three sides. The cost accurate side-length determinations do not necessarily occur when the magnitudes of the point position discrepancy vectors of two stations are nearly the same because of differences in the directions of the discrepan- cies. The side-length discrepancies determined on day 68 for the side BZEEO-BNOB illustrate this point (Fig. 4.21). The point position discrepancies for stations BZERO and BNOB are 10.889 and 10.816 meters at time tag 377808 and the side-length discrepancy is -.151 meters. At time tag 384408, the side-length discrepancy is -.036 meters and the magnitudes of the point position discrepancies are 9.295 and 14.053 meters. The side-length discrepancy is smaller at the later time tag even though the difference in the magni- tudes of the point position discrepancies are greater at that time. D. AVERAGING RESULTS 1 • Determination of the Method of Averaging Two averaging schemes were used to arrive at mean position discrepancies (Sect. Ill E) . The means and 47 J.D. 61, 1984 SHORT BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES LEGEND STATION J MR 369.00 372.60 376.20 379.80 383.40 GPS TIME (SEC) 387.00 390.60 *103 Figure a. 17 Point Position and Side-length Discrepancies 48 J.D. 61, 1984 SHORT BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES o^ oo h- Ld >"9- u & Ld q: u 00 Q L_ O LJ D _J $ D " _l O CO CD < O- LEGEND a STATION JMR STATION RM2 SIDE-LENGTH 369.00 372.60 376.20 379.80 GPS TIME (SEC) — I 1 387.00 390.60 *103 Figure 4.18 Point Position and Side-length Discrepancies U9 J.D. 61, 1984 SHORT BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES LEGEND * STATION RM' TATIQN RM: 369.00 372.60 GPS TIME (SEC) | 390.60 *io3 Figure 4.19 Point Position and Side-length Discrepancies 50 o. ly i_j h- Ld u & Ld OH u (/) Q O Ld D _l h- _l O oo m < c_ J.D. 68, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES LEGEND STATION BZERO 369.00 372.60 1 1 1 1 1 376.20 379.80 383.40 387.00 390.60 GPS TIME (SEC) *103 Figure 4.20 Point Position and Side-length Discrepancies 51 J.D. 68, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES LEGEND STATION BZERQ 369.00 372.60 376.20 379.80 383.40 / 387.00 390.60 GPS TIME (SEC) I / *103 Figure 4.21 Point Position and Side-length Discrepancies 52 J.D. 68, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES LEGEND STATION PILOT STATION BNOB 369.00 372.60 376.20 379.80 t383.40 GPS TIME (SEC) 387.00 390.60 *103 Figure 4.22 Point Position and Side-length Discrepancies 53 o. m en Ld h- >-2- U z LlJ en u oo Q O LJ D _l h- D _l O CO CD < O- o. J.D. 69, 1984 MEDIUM BASE LINE TESTS SAMPLING INTERVAL = 5 MINUTES LEGEND • STATION BZERO 454.00 45160 461.20 464.80 468.40 GPS TIME (SEC) 472.00 475.60 *10 Figure 4.23 Point Position and Side-length Discrepancies 54 standard errors of discrepancies were computed for the X, Y, and Z coordinates and the absolute values of the total point position discrepancies (Tabs. VIII and IX). The standard errors of the point position discrepan- cies for the solutions that were averaged beginning two hours after the initial solutions are, in general, smaller than those that were determined using all solutions begin- ning one hour after the initial solutions. The average standard error of the absolute value of the point position discrepancies for all pairs of determinations is 2.302 meters using the former averaging method, compared to 1.422 meters using the latter averaging method. Much of the difference between these two standard errors can be attrib- uted to the relatively large point position discrepancies computed for stations BZEP.O and PILOT on day 69 between the first and second hours after the initial solutions (Figs. 4.15 and 4.16). Neglecting stations BZERO and PILOT on day 69, the average of all standard errors of the point position discrepancies are 1.657 meters and 1.333 meters for the two different averaging methods. The elimination of the real-time solutions recorded between one hour and two hours after the start of data acquisition results in smaller standard errors of the point position discrepancies in the averaging process. The remainder of the analysis uses the mean coordinates deter- mined by the averaging method in which only the real-time solutions recorded two hours after the initial solutions are used (Tab. IX) . 2 • WGS-72 Results The Y coordinate discrepancies are larger than the discrepancies of X and Z coordinates at all stations with the exception of those at station BZERO on day 69. The mean observed X coordinates are consistently different from the 55 TABLE VIII Means and Sigmas Beginning One Hour After Initial Solutions X mean Y mean Z mean Point Sample J. D . Station Sigma X Sigma Y Sigma Z Posi ti on Si ze 61 J MR RM1 6.677 -12.696 3.196 14.834 1.242 1.558 1.232 1.244 5.178 -13.512 5.371 15.495 0.688 1.927 0.635 1.667 1518 JMR RM2 7.502 3.356 205 574 11.648 4.593 12. 186 5.639 2.426 3.296 4.739 4.619 15.372 2.178 16.274 2. 197 1564 RM1 RM2 162 700 588 165 13. 623 1.900 13.548 1.375 5.405 0.682 794 707 15.600 1.632 16.019 1.512 1450 BZERO PILOT 806 725 5.653 0.571 7.578 0.8 18 7.877 1. 107 623 226 090 240 10.006 0.761 9.860 1.029 1536 BZEEO BNOB 5. 972 0.987 6.060 1.625 ■7. 337 1.452 •9. 125 5.337 015 734 563 919 10.185 0.966 13.348 2.872 1407 PILOT BNOB 5.708 0.59 1 5.822 1.241 •7. 916 1. 178 •9.777 4. 527 0.992 1 .293 0.053 5.324 9.924 1.086 13. 126 2.74 5 1342 69 BZERO PILOT 6.629 1.379 613 050 -1.833 4. 421 -1.030 11.727 441 758 0.208 9. 289 9.46 4 3.607 14.200 8.729 1664 Units are meters 56 TABLE IX Means and Sigmas Beginning Two Hours After Initial Solutions X mean Y mean Z mean Point Sample J.D. Station Sigma X Sigma Y Sigma Z Position Size 61 68 69 JRtf 6.288 -12.569 3.67!+ 14.537 0.561 1.571 0.730 1.269 RM1 5.414 -12.937 5.333 15.045 1218 0.492 1.657 0.689 1.492 JHR 6.291 -12.874 3.642 14.844 0.551 1.482 0.770 1.149 EM2 5.315 -14.004 6.573 16.454 1264 0.810 0.369 1.846 1.056 F.M1 5.407 -13.043 5.374 15.150 0.505 1.645 0.688 1.469 RM2 5.367 -14.069 6.950 16.650 1150 0.818 0.293 1.481 0.889 BZERO 5.513 -7.769 -2.074 9.780 0.411 0.755 0.530 0.652 PILOT * 5.432 -7.862 1.585 9.736 1236 0.317 1.193 0.764 1.072 BZERO 5.600 -7.793 -2.267 9.903 0.578 0.795 0.739 0.753 BNOB 5.476 -11.461 1.997 13.298 1107 0.697 2.637 3.454 2.802 PILOT 5.461 -7.910 1.552 9'.795 0.337 1.293 0.827 1.157 BNOB 5.480 -11.712 2.414 13.432 1042 0.715 2.510 3.114 2.787 BZERO 6.262 -3.504 -3.053 8.197 0.169 1.523 2.073 0.501 PILOT 5.717 -6.001 3.690 10.657 1364 0.940 4.678 4.085 2.860 Units are meters, 57 given X coordinates Ly approximately 5 to 6 meters at all stations on all days of data acquisition having an average standard error of .564 meters for all determinations. The Z coordinate has smaller discrepancies at all stations on days 68 and 69 compared to the other coordinates. The average standard errors of the Y and Z coordinate discrepancies for all determinations are 1.600 and 1.560 meters, respectively (Tab. IX). The mean point position discrepancies in the fc'GS-72 Cartesian coordinate system range between 16.650 meters at station EM2 on day 6 1 and 8.197 meters at station 3ZESO on day 69. The average of all the mean point position discrep- ancy determinations is 12.685 meters. The standard errors of the mean point position discrepancies range between .501 meters at station BZERO on day 69 and 2.802 meters at station BNOB on day 68, with an average value of 1.383 meters for all determinations (Tab. IX) . E. G'EODETIC COMPARISONS The observed WGS-72 coordinates of each station are computed by subtracting the observed discrepancies from the given coordinates. The observed W3S-72 Cartesian coordi- nates are then transformed to NAD-27 geodetic coordinates using a modified version of NGS's D035-41 transformation program. 1 • £iscrep_ancies of Point Position Determinations The point position discrepancies of all pairs of determinations are computed for the NAD-27 coordinates (Tab. X) . Azimuths are measured from north. The average point position discrepancy is -.08336 seconds of latitude, -.26088 seconds of longitude, and +9.391 meters in ellipsoid height. The horizontal position discrepancies of the observed point 58 >^ n' W a -CI 0) U Ql •H O w ns o Oi ^, X • ■p SI W C3 — * ►J •H % CQ O -PI «: Oi HI EH ^ • rtl en 4J G~. e out o >-J Ul N nil •H t Ul SM-|| 0 OI = uu >d T3I a • CI «J -POI (TJUI U H^CUI -H cot 4-> • ^^ ' (V s; n3 O a> o (01 4JI IQl Ql =T m ro «— ir. CN =r v£> o r- o o r— CN ^~ VO cn =f <~5 m >-o O in CN o m en O ro O in =*• m CO 00 ro CTl CM f- on m v£> r- 3- r- o m o 3 en CTi o CO CN o CO o o CN O cn © o cn o CN O m cn r*» m cn v£> =T n vO vO vo r- r» ^ ro CN =t CN CN CN CO r^ CO r- r- r- CO CN O O CO =* CN vO CN CTi CN m CO CN ;* =* ro =r in »- CN r- ro o >sO io CO p»« VO o cn l£) CTi vo> vo r- CN CN CN CN CN CN r- vo ro CN r» CN r>- T— \D CTi r- cl- r- cn rn T— en CN co a- CTi m =r CN o o o o o O CO cn cn r^ «— =t CTi CN VC ^o r-» T— CN m =r =* ro rr r— r- cr r- r~ rn CN p- o m T— ^~ J- CN in in co m ao CN O CN o O 3- cn in m o o en CN o CO o Q cn o P*» o 00 o o >*o o en O 3" co cr m co o CN in r^ co r~- CO VO CO m rn ^O en =j- =1- m o vO CO CN T— en en co *~ en vO 3- ^o St o va o + 4- + •+• + + o ro r^ 3- r» CO o ^o CN en o rn =t o p^ en cm r— 3- ■ at 3- m =r \0 CN CN CN CN CN CN r^ r— CO CO r~- en rn r~ en =t m CO CN o r>» CO CN o r» r-~ r~ T— r- r- T~ o *" *~ o r- m r- 3" CO lD i— cn r^ CM r- o O CN CO CN CO =r o CO r- co \o en ve- in ro cn ro r*~ ro MD cn m r- 00 O t— in rf CN CN cr> ^o o IH o EH O Eh Q3 o « 04 O CQ 05 O s r- ec r\] r- CN W J w n hJ O W .-J ca SZ S3 S s: S tSJ (H ISJ 2 H s CS3 M ^ cc ^3 (K oa cc CO SO CQ Oj CQ CQ Ch tQ en CQ C-* 59 positions for ail determinations range between 6.4 98 meters at station PILOT on day 69 and 8.530 maters at station BZERO on day 68. The average distance discrepancy along the ellipsoid is 7.596 meters. The azimuths from the given positions to the observed positions range between 129° 41' 53". 04469 at station BZEPO on day 58 and 84° 48' 17". 17131 at station PILOT on day 69. The observed positions have an average azimuth of 109° 25' 56". 5699 from the given positions. 2 • Discrepancies of Point Positions for Entire Recording Sessions There are two determinations of point position discrepancies on days 61 and 68 as a result of comparing pairs of stations in the computations. An estimate of the repeatability of an entire recording session can be calcu- lated by first averaging the two point position discrepan- cies for each station then computing tne standard error of the eight determinations. The average discrepancies of entire recording sessions are -.07980 seconds of latitude and -.25903 seconds of longitude with standard errors of .03976 and .01764 seconds, respectively. The average height discrepancy is 8.658 meters above the station with a standard error of 4.748 meters. The average horizontal distance discrepancy is 7.538 meters with a standard error of .714 meters. 3- Relative Position Comparisons The distances and azimuths between pairs of stations are computed for both the given coordinates and the observed coordinates by the inverse computation. The differences of twD are computed by subtracting ths given distances and azimuths from the observed values (Tab. XI) . Six of the seven observed side-lengths are shorter than the distances 60 TABLE XI Discrepancies of Observed Distances and Azimuths J.D. Side Dist.(m.) Azimuth 61 JRM-RM1 1.397 -44' 44". 2009 JMR-RM2 -0.006 -4° 17' 40". 3464 RM1-RM2 -0.231 -1° 14' 30". 5102 58 59 BZERO-PILOT -3.128 -1". 24259 BZERO-BNOB -0.428 -26". 09039 BNOB-PILOT -0.774 9". 49565 BZERO-PILOT -4.556 -1". 05927 computed from the given coordinates. In the short base line tests, the differences in azimuth are of the order of degrees compared to differences of the order of seconds of arc in the medium base line tests. In general, the azimuth differences decrease as the side-length differences increase in both the short base line and medium base line tests. ** • £§l§.t i v e Position Discrepancies Relative positioning is used to determine an unknown position relative to the position of a known station. The direct computation calculates the coordinates ot a position given the coordinates of a known position and the distance and azimuth to the unknown position. The distance and azimuth between pairs of observed positions are used in the calculation. Stations JMR and RH1 are taken as fixed in the short base line tests and the positions of RM1 and RH2 are calculated. Stations BZERO and BNOB are used to locate stations BNOB and PILOT in the medium base line tests. The 61 discrepancies of the calculated positions are computed in terms of latitude, longitude, elevation, distance, azimuth, and relative accuracy between stations (Tab. XII). The elsvation discrepancies are determined by computing the difference of the height discrepancies between pairs of point position solutions. Relative position determinations differ from the given positions by an average of 1.452 meters in the short base line tests and 2.712 meters in in the medium base line tests. The relative accuracies between stations range between 1:13 for the side JMR-RM1 on day 61 and 1:17,413 for the side BNOB-PILOT on day 68. The average relative accu- racy of the medium base line tests is 1:9,712. Station PILOT was determined to relative accuracies of 1:8,139 and 1:5,593 with respect to station ENDB on subsequent days. The data acquired in the short base line tests provide useful information in the absolute position anal- yses; however, this scenario is not a practical application of relative position determinations. It is not justifiable to measure distances of the order of thirty meters with such expensive equipment when the distances can be measured accu- rately with steel tape or other inexpensive equipment. 62 W a o ■H _ rd >-. c o •H c J3I a (d 4->l M cu 31 a> QJ Sl ■p M •Hi a> u Nl Q w •H d • • H -u £1 H (0 a *-* H o o • X a, N 4J| •H C0I W 01 U •HI - > O Ql 03 •H EC < 4J E-t «1 _ „ ^H" # 0) el OS • a 4J| •H ffil W 0) • ■H DW O - OI a O Ul (d ^a \ en r- «— co > ul oo en =r ct> Ul flpj «-«-^r oo r» «- in rHUI 0)UI a:<:i r- n m CN O CO oo =r r" •" ■=r r™ «" T— o CN LO o «- oo en n" o r- LO r— r*» on =»■ ■ • • CN cc r— CN =r 00 *» K m CN t— r* (N «~ ■" o o o it on m *— o r* CN CN *~ O r» 00 :* U3 =t cr o CO CC en r- «— on en =r r~ >^3 % V * r- 00 r-» *~ «- ^ «- in OO ^£> en m r- rn CO =3- en LO O =r T"" T— i t t CTi r- oo J* LD in „ „ m r*- en c rn *~ & o o o i— en m CO ^o o *" T- CN CN =T m oo ^3 en r— CO CN «- CN o CN 00 in m CO o in co oo o o «~ «- in r-> o cm in >>o r-» oo >«o m m co .-3 ml co «— r» *- en. oo r- • *- ' CO v£> CN O If, CO J- Z OOO *- O O r- • • t t f t • »— co en H H En • O CQ O • O CN Q >-l O h-1 Q h-1 S3 * \-\ -Z. of Texas aF~AusTTn, S"usfin, Texas, pp. TT/5-1192, 26 January 1979. 10. Parkinson, B. W., "The Global Positioning System {NAVSTAR)," Bulletin Geodesigue, vol. 53, pp. 89-108, 19 79. 11. Spilker, J. J. Jr., "GPS Signal Structure and Characteristics," Navigation, vol. 25, No. 2, pp. 121-146, Summer 1978T 77 12. Montgomery, B. 0., "NAVSTAR 3?S - A Giant Step for Navigation and Positioning," Sea Technology, vol. 25, No. 3, pp. 22-23, March 1984. 13. Van Dierendonck, A. J. , et al, "The GPS Navigation Message," Navigation, vol. 25, pp. 147-165, Summer 1978. 14. Denoyer, B. J. , telephone conversation, Defense Mapping Agency Hydrographic/Topographic Canter, Washington, D.C., 3 August 1984. 15. Ward, P., An Advanced NAVSTAR GPS Geodetic Receiver, paper presented" a£ T*h~ir