MATLAB GPS Software Toolbox User's Guide and Reference Manual

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  • GPS

    MATLAB GPS SOFTWARE TOOLBOX

    USER'S GUIDE AND REFERENCE MANUAL

    -- VERSION 3.01 --

    Copyright 1996-2001 by Lupash Consulting. All Rights Reserved Worldwide.

  • COPYRIGHT NOTICE

    Copyright 1996-2001 by Lupash (LL) Consulting. All Rights Reserved Worldwide.This software and related documentation are fully protected by the United Statescopyright law. No part of this software and publication may be copied or distributed,transmitted, transcribed, stored in a retrieval system, or translated into any human orcomputer language, in any form and by any means, electronic, mechanical, magnetic,manual, or otherwise, or disclosed to third parties without the express writtenpermission of Lupash (LL) Consulting, 2625 Monterey Pl., Fullerton, CA 92833.

    TRADEMARK ACKNOWLEDGEMENTS

    MATLAB is a registered trademark of The MathWorks, Inc.

    IBM Personal System/2, OS/2, and IBM PC/XT/AT/386/486 are trademarks of IBMCorporation.

    MS-DOS, Microsoft FORTRAN, Microsoft C/QuickC and Microsoft Pascal aretrademarks of Microsoft Corporation.

    Pentium is a registered trademark of Intel Corporation.

    DISCLAIMER OF WARRANTY

    We have made every effort to verify that GPS TOOLBOX software is working properly.However, the software and manual are sold "as is" and without warranties as toperformance or merchantability. LL Consulting shall have no liability or responsibility ofany kind, including special, indirect or consequential damages, arising out of or resultingfrom such software or the use or modification thereof. In no event shall LL Consulting beliable or responsible for any problems that arise from the use of the GPS TOOLBOXsoftware and manual. This statement shall be construed, interpreted, and governed by thelaws of the state of California.

  • Preface

    - Page iii -

    PREFACE

    Your Global Positioning System (GPS) engineering support software requirements can bemet efficiently, yet inexpensively, by using the MATLAB GPS Toolbox library ofGPS related m-file modules/programs developed by Lupash Consulting.

    This software allows you to perform a variety of mathematical, scientific, and engineeringcalculations related to the GPS applications quickly and easily, and it can help youincrease your productivity and improve your competitive position without effort -- at aprice you can afford.

    Known as GPS Toolbox, Lupash Consulting's library of GPS related m-files supports afull range of mathematical and engineering operations required by the implementation ofthe GPS applications. It uses MATLAB environment and is operational on IBM PersonalSystem 2, IBM PC/XT/AT/386/486/Pentium and compatibles.

    The current Version 3.x of GPS TOOLBOX library can interface with the entire range ofMathWorks toolboxes and by using MATLAB compilers you can generate highperformance C code from MATLAB m-files. GPS Toolbox gives you dozens of functionsfor specific GPS applications, providing an integrated set of tools to speed up yourdevelopment and optimize your designs.

    Manual Organization

    This User's Guide and Reference Manual documents the architecture, functional designand operational characteristics of GPS Toolbox.

    Section 1.0, Getting, Started provides you with general information about the package.

    Section 2.0, Architectural Overview and Functional Description, summarizes GPSToolbox architecture and functional setup. Functional Description provides you with astructured, top-down, hierarchical description of the functional modules. Also includedare the library design specifications and list of functions by topics (see Tables 2-1).

    Section 3.0, GPS Toolbox Examples, shows you how to use some m-file main programscontained in the GPS Toolbox into your applications; all programs are ready to be used,including input data sets. Furthermore, you can use the examples included herein asstarters for your own programs -- a quick and easy way to develop applications.

    Section 4.0, Detailed Specifications for GPS Toolbox m-file modules, gives you, for eachGPS Toolbox m-file/module function listed in alphabetical order, the complete sequenceof calling parameters, functional specifications, operating instructions and other technicaldetails that will help you benefit from this powerful engineering and scientific supportlibrary. Sections 5, Detailed Specifications for GPS Toolbox main programs, follows theformat used in section 4 for documentation of all main programs.

  • Preface

    - Page iv -

    Section 6.0 provides you with technical references. Appendix A includes a complete listof functions and input/output files in alphabetical order. Finally, a user registration formis included.

    Language Implementation and MATLAB environment

    MATLAB is a high performance interactive software environment for scientific andengineering computation and visualization. It is a complete integrated system, wellbeyond matrix laboratory, including graphics, programmable modules, a fastinterpreter, many analytical commands, and a possibility to generate high performance C-code from m-files by using a MATLAB compiler. In MATLAB environment problemsolutions are expressed almost exactly as they are written mathematically. In industrialsettings, MATLAB is used for research and to solve practical engineering andmathematically problems.

    MATLAB has been acclaimed for many of its features and, in particular, for its ability toallow engineers and scientists to implement algorithms efficiently. It is the environmentof choice for more than 200,000 technical professionals in industry and research aroundthe world.

    In order to preserve the clarity and readability of the m-files, we elected to translatealmost literally the software design algorithms into self-documented code. We tried to beconsistent both in the layout of the programs and in the selection of the variable names.Where necessary, comments are added to further increase the readability of the code. Inaddition, the m-files were written such that they can be easily translated into otherlanguages, thus extending usefulness to other programming environments.

    Version 3.x of GPS TOOLBOX replaces the earlier Version 2.x and incorporates morethan 200 m-files (modules and programs) as well as reference input/output data files,which greatly expand the capabilities of its predecessor. All m-files are compatible withMATLAB version 4.0 or higher, and most of them are also compatible with version 3.5and Student Edition of MATLAB, exceptions are few main programs

    We are confident at this point that the old m-file functions are virtually bug-free, andhope that the newly added m-files (modules and main programs) follow the same pattern.Should we identify any problems, we will keep you updated through our TechnicalAssistance and Product Maintenance service. The source code is royalty free, i.e. the usercan incorporate this software in his/her particular application but is not permitted to resellthe software as is or with changes.

    Lawrence Lupash, Ph.D.Lupash (LL) Consulting2625 Monterey PlaceFullerton, CA 92833-2084USA

  • Table of contents

    - Page v-

    TABLE OF CONTENTS

    Preface ...................................................................................................................... iiiTable of contents ...................................................................................................... v

    1.0 Getting started ........................................................................................................1-11.1 Package............................................................................................................1-11.2 Installation. ......................................................................................................1-11.3 How to use the MATLAB GPS Toolbox ........................................................1-2

    2.0 Architectural overview and functional description ............................................2-12.1 Library architecture ..........................................................................................2-12.2 Functional highlights........................................................................................2-22.3 Functional description ......................................................................................2-3

    2.3.1 GPS related constants and conversion factors .......................................2-42.3.2 Angle transformations............................................................................2-42.3.3 Coordinate transformations ...................................................................2-4 (1) Point transformations ......................................................................2-4 (2) Matrix transformations....................................................................2-5 (3) Vector transformations....................................................................2-52.3.4 Specialized plotting programs ...............................................................2-52.3.5 Specialized statistics related functions ..................................................2-62.3.6 GPS time utilities...................................................................................2-62.3.7 Specialized GPS data processing functions ...........................................2-62.3.8 Trajectory and related utilities ...............................................................2-72.3.9 Satellite position computation ...............................................................2-72.310 Elevation and azimuth determination and satellite visibility................2-82.3.11 DOPs computation, satellite selection and related functions...............2-82.3.12 Special signal processing and Kalman filtering functions...................2-82.3.13 Pseudorange and deltarange determination and related functions .......2-92.3.14 Determination of users position and related functions .......................2-92.3.15 RAIM/FDE availability and integrity evaluation and related functions ...........................................................................................................2-10

    2.4 List of functions by topics ..............................................................................2-10

    3.0 GPS Toolbox Examples .........................................................................................3-13.1 Matrix coordinate transformation generation...................................................3-23.2 Generation of a first order Gauss-Markov process ..........................................3-43.3 Generation of a second order Gauss-Markov process......................................3-63.4 Covariance analysis by using the conventional and alternate conventional Kalman filter formulation................................................................................3-93.5 GPS time related utility transformations ........................................................3-103.6 Read Yuma format almanac file and generate two ASCII data only files......3-123.7 Read RINEX 2 navigation message and generate three data files..................3-133.8 Determination of the WGS-84 geoid height correction .................................3-14

  • Table of contents

    - Page vi

    3.9 Generation and plotting of the longitude-latitude WAAS grid ......................3-153.10 Determination of geodesic based on departure and destination points ........3-163.11 Determination of great circle dead reckoning trajectory ..............................3-193.12 Determination of acceleration from the input time/position/velocity data and execution of relevant trajectory plots ....................................................3-203.13 Determination of satellite position based on almanac/ephemeris data.........3-243.12 Determination of azimuth and elevation angles and execution of related plots ..............................................................................................................3-273.15 Determination of DOP quantities and execution of contour plots ...............3-323.16 Satellite selection based on minimum GDOP criteria..................................3-363.17 Determination of iono correction and execution of related graphs ..............3-383.18 Determination of tropospheric delay correction...........................................3-423.19 Determination of user clock errors...............................................................3-433.20 Determination of multipath error .................................................................3-443.21 Determination of user earth rotation error....................................................3-453.22 Computation of position fix through direct and iterative methods ..............3-463.23 Evaluation of weighted least square navigation solution .............................3-483.24 GPS RAIM integrity evaluation ...................................................................3-513.25 Determination of thresholds used in RAIM/FDE evaluations .....................3-533.26 RAIM fault detection availability determination .........................................3-563.27 RAIM fault exclusion availability determination.........................................3-613.28 GPS error budget determination...................................................................3-65

    4.0 Detailed specifications for GPS Toolbox m-file modules....................................4-14.01 CEP ................................................................................................................4-14.02 CHI2_DOF .....................................................................................................4-14.03 CONVCON ....................................................................................................4-14.04 DHMAX.........................................................................................................4-24.05 DOP1..............................................................................................................4-34.06 DOP2..............................................................................................................4-34.07 ELEVA...........................................................................................................4-34.08 ELEVAR ........................................................................................................4-44.09 ELEVAZ ........................................................................................................4-44.10 ELIMCOL ......................................................................................................4-54.11 ELIMROW.....................................................................................................4-54.12 FDNT .............................................................................................................4-54.13 FOM ...............................................................................