WDL-TR2184 f5 NOVEMBER 1963 GPU PRICE $ CFSTI PRICE(S) $ Hard copy (HC) Microfiche (MF> ^ • H653 July 65 PROGRAMMER'S MANUAL for Interplanetary Error Propagation Program K66-15732 (ACCESSION NUMBER) (NASA CR OR TMX OR AD NUMBER) CONTRACT NAS 5-3342 prepared for National Aeronautics and Space Administration joddard Space Flight Center ^reenbelt, Maryland PHILCO WDL DIVISION PALO ALTO. CALIFORNIA WDL-TR2184 15 November 1963 PROGRAMMER'S MANUAL FOR INTERPLANETARY ERROR PROPAGATION PROGRAM Prepared by PHILCO CORPORATION A Subsidiary of Ford MoCor Company WDL Division Palo Alto, California CONTRACT NAS 5-3342 Prepared for NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GODDARD SPACE FLIGHT CENTER Greenbelt, Maryland PHILCQ WDL DIVISION ABSTRACT WDL-TR2184 UNCLASSIFIED PROGRAMMER'S MANUAL FOR INTERPLANETARY ERROR PROPAGATION PROGRAM 420 pages 15 November 1963 NAS 5-3342 This report discusses the subroutines that are used in the Interplanetary Error Propagation Program. A narrative des- cription and card listing are provided for each subroutine; flow diagrams are included, if applicable. A listing of assigned locations in common is also presented. THIS UNCLASSIFIED ABSTRACT IS DESIGNED FOR RETENTION IN A STANDARD 3-BY-5 CARD-SIZE FILE, IF DESIRED WHERE THE ABSTRACT COVERS MORE THAN ONE SIDE OF THE CARD, THE ENTIRE RECTANGLE MAY BE CUT OUT AND FOLDED AT THE DOTTED CENTER LINE (IF THE ABSTRACT IS CLASSIFIED, HOWEVER, IT MUST NOT BE REMOVED FROM THE DOCUMENT IN WHICH IT IS INCLUDED ) PHILCQ WDL DIVISION WDL-TR2184 FOREWORD This report is submitted to the National Aeronautics and Space Administration, Goddard Space Flight Center, in fulfilling the require- ments of Contract NAS 5-3342. The documentation provided by Philco WDL in support of the Interplane- tary Error Propagation Program consists of the following three volumes: • WDL-TR2184, "Programmer's Manual for Interplanetary Error Propagation Program" • WDL-TR2185S "User's Manual for Interplanetary Error Propagation Program" 9 Guidance and Control System Engineering Department Technical Report No. 48" The application of State Space Methods to Navigation Problems," by Stanley F. Schmidt These volumes discusse the theory of the Schmidt-Kalman filter used in the program for data smoothing, the manner in which the program is used, and subroutine description and listing. -iii- 'HILCQ WDL DIVISION Page intentionally left blank WDL-TR2184 TABLE OF CONTENTS Section Page 1 INTRODUCTION 1-1 1. 1 General . 1-1 ... 1-1 Main Chains MAIN(Chain 1) M-3 MAIN(Chain 2) M-13 MAIN(Chain 3) M-19 Subroutine Listing ARKTAN S-3 ARKTNS S-5 ASINH S-7 BODY S-9 BVEC S-15 CHNGP S-23 COMPHQ S-27 CONST! S-41 CONVPI S-51 CORRTP S-63 CROSS S-67 (CSH)S S-69 DE6FN S-71 DOT S-117 EARTR S-119 ECLIP S-145 ENCKE S-147 ERP S-151 ERPT S-153 FINP S-155 FNORM S-173 -v- »HILCQ WDL DIVISION WDL-TR2184 TABLE OF CONTENTS (Cont'd) Section Paee Subroutine Listing (Cont'd) GHA S-175 GOTOB S-179 GOTOR S-197 GUID S-203 HOUR S-217 HPHT S-221 INPUT S-223 INTR.INTRI S-231 INV3 S-245 INVAO S-249 LOADO S-251 LOADT S-253 MASS S-255 MATRX S-259 MATSUB S-261 MNA S-267 MNAND S-273 MONBTR S-277 MULT S-285 NUTAIT S-287 OBLN S-295 ONBTR S-303 ORTC S-307 OUTC S-311 OUTDAT S-321 OUTP S-325 PTRAN S-338 RETRO S-341 ROTATE S-347 ROTEQ S-349 RVIN S-355 -vi- PHILCQ WDL DIVISION WDL-TR2184 TABLE OF CONTENTS (Cont'd) Section Subroutine Listing (Cont'd) RVOUT S-361 SDEC S-365 SETN S-369 SHIFTP S-371 STEPC S-375 TIMEC S-391 TIMED S-395 TRAC S-397 TRANSH S-403 LIST OF TABLES Number Page 1-1 List of Assigned Quantities in Common "C" Array T . 1-3 1-2 List of Assigned Quantities in Common "S" Array 1-6 1-3 List of Assigned Quantities in Common "1C" Array 1-12 1-4 List of Assigned Quantities in Common "T" Array 1-15 -vii- PHILCQ WDL DIVISION Page Intentionally Left Blank WDL-TR2184 PROGRAM SUBROUTINE LISTING ARKTNS Single Precision Arctangent ARKTAN Double Precision Arctangent ASINH(X) Function Evaluation BODY Calculates Accelerations Due to Perturbing Bodies BVEC Calculates B Vector CHNGP Determines when to Shift Body Center COMPHQ Computations for ONBTR and MONBTR Subroutines CONST1 Array of Input Constants CONVPI Converts Input Covariance Matrix to 1950 CORRTP Updates P Matrix CROSS Cross Product (CSH)S Fortran II Card Image Input Subroutine DE6FN Fapclmtegfation ,SubroGtine' u DOT Function Forming Dot Product EARTR Updates Covariance Matrix for Earth Based Tracking KCLIP Transforms Coordinates through Transformations ENCKE Calculates Perturbation due to Deviation from CONIC ERP Prints Out Ephemeris Error ERPT Prints Out Time of Ephemeris Error FINP Data Input Subroutine FNORM Norm of A Vector GHA Greenwich Hour Angle GOTOB Main Subroutine for Integration of Trajectories GOTOR Iterates to Solve Keplers Equation GUID Performs Guidance Calculations HOUR Reads Printer Clock HPHT Performs Matrix Multiplication H*P*HT INPUT Converts Inputs to Equinox of 1950 Reference INTR FAP Ephemeris Subroutine INV3 Inverts Up to a 6 By 6 Matrix INVAO Forms Inverse of Transistion Matrix LOADO Obtains Transition Matrix From T Array -ix- WDL DBVBSION WDL-TR2184 LOADT Puts Unit ICS On Perturbation Equations MASS Arranges Gravitational Constants of Bodies Considered MATRX Multiplies A*B=C or A*B*AT=C Max Dimension (10.10) MATSUB Error Propagation Logic Subroutine MNA Transformation to Selenocenic.. Coordinates MNAND Transformation for Selenocenic Velocities MONBTR Updates Covariance Matrix for Moon Beacons MULT Multiplies Two 3 by 3 Matrices NUTAIT Calculates Nutation Matrix OBLN Calculates Acceleration Due to Oblateness ONBTR Updates Covariance Matrix for Onboard Tracking ORTC Outputs Orbital Parameters OUTC Outputs Trajectory OUTDAT Outputs Calendar Date OUTP Outputs RMS Values of Orbital Parameters PTRAN Transforms P Matrix RETRO Performs Retro Fire ROTATE Calculates Transformation for Rotation About an Axis ROTEQ Calculates Matrix from Equinox 1950 to Mean Equinox of Date RVIN Transforms Coordinates From Spherical to Cartesian RVOUT Transforms Coordinates from Cartesian to Spherical SDEC Second Derivative Subroutine SETN Set Read and Write Tape Numbers SHIFTP Shifts Body Center STEPC Move Along Conic in Time TIMEC Converts Calendar Date to Days from 1950 TIMED Converts Days Hours Min Sec to Seconds TRAC Tracking Station -Coordinates TRANSH Transforms H Matrix From Date to 1950 -x- PHILCO WDL DIVISION WDL-TR2184 PROGRAMMER'S MANUAL FOR INTERPLANETARY ERROR PROPAGATION PROGRAM WDL DIVISION WDL-TR2184 SECTION 1 INTRODUCTION 1.1 GENERAL This manual contains subroutine descriptions, logic, and FORTRAN listings for the Interplanetary Error Propagation Program. Listings of the quantities which are in the four common storage arrays (T,S,C, and 1C) are also included. 1.2 GENERAL DESCRIPTION OF METHOD OF ORBIT DETERMINATION USED IN PROGRAM The classical approach to the determination of an orbit from tracking data is the maximum likelihood, least-squares technique. This program uses a different approach to this problem. The relationships between the observed tracking data and the initial conditions (or an equivalent set of parameters) which determine the orbit are highly nonlinear. Therefore, it is assumed that a preliminary estimate of the initial conditions and, therefore, the orbit, is known. The equations are then linearized about this "nominal" orbit and an adjustment to the nominal orbit found from the differences between the observed tracking data and the predicted tracking data based on the nominal orbit. In the least-squares technique, the data is pro- cessed in parallel in the sense that the normal equations are summed over all the available tracking data before a modification to the nominal orbit is determined. The Schmidt-Kalman technique differs from the classical least-squares approach in two ways: first, the estimate used is based upon the mini- mization of a risk function different from that used in the least-squares approach and, second, the data is processed serially instead of in parallel. The Schmidt-Kalman technique depends upon a linearization of the relations between the orbit parameters and the observed tracking data. Therefore, it assumes some nominal trajectory and an associated error estimate (covariance matrix) for the nominal trajectory. 1-1 PHILCQ WDL DIVISION WDL-TR2184 CrNF-RAL TLOW PIIAOPAM Or OVf-RAI.l. ERROR PROPAGATION PROGRAM Mft.t, n MM i r ' " ' i ARE 1 1 ".',';',' IS TIMS A UIDANCE YES CALL CALL I Jl 1 ~ * ^ i --» „,,..,, • '-' ^ ' GOTOB |~~*! CHAIN 2 ~| ' TO oE I "/"* cOMPUTEO 1 | NO NO 4 1 1 | , GOTOB INTE- GRATES TRAJECTORY TO TARGET TO OUTAIN GUIDANCE MATRIX MAIN CHAIN I MAIN CHAIN 3 r -i r 1 1 t.FI 1)1' 1 1 ^ ; ROf.HAM CALL , CALL CALI 1 | FOR ERROR O'AIN 3 1 1 GOTOB CHAIN 1 | I PROrAGATlON HUN 1 1 L_ II _ | MATSUB GOT OR i r~ "*" ~i r~ | READ PROPAGATE GOTOB 1 COVARI'iNCE DATA MATRICES CARDS IN TIME J SET UP MATSU- R CALL INT, SEQUENCE CALL AND TYPE EARTR MEASUREMENTS REfNG MADE CALL ONPTR CONTROL INTEORAT'ON 1 — -• TACKACE TO PERMIT CAI 1 CAI 1. OF MAT'jim ,. CAI 1 c-uin CALL MAT '",11 >? — ' | i 1 Figure 1-1 1-2 PHILCO NA/DL DIVISION WDL-TR2184 The serial processing of the tracking data and associated updating of the nominal orbit occurs as follows: At the start of the time period for which tracking data are to be processed and an improved estimate of the orbit is to be obtained, it is assumed that an estimate of the orbit (a set of state variables) and an error estimate exist. Both of these estimates are updated to an instant of time when tracking data are available.