- COVER
- TITLE PAGE
- PREFACE
- ACKNOWLEDGMENTS
- CHAPTER 1: INTRODUCTION
- CHAPTER 2: OBSERVATIONS AND THEIR ANALYSIS
- 2.1 INTRODUCTION
- 2.2 SAMPLE VERSUS POPULATION
- 2.3 RANGE AND MEDIAN
- 2.4 GRAPHICAL REPRESENTATION OF DATA
- 2.5 NUMERICAL METHODS OF DESCRIBING DATA
- 2.6 MEASURES OF CENTRAL TENDENCY
- 2.7 ADDITIONAL DEFINITIONS
- 2.8 ALTERNATIVE FORMULA FOR DETERMINING VARIANCE
- 2.9 NUMERICAL EXAMPLES
- 2.10 ROOT MEAN SQUARE ERROR AND MAPPING STANDARDS
- 2.11 DERIVATION OF THE SAMPLE VARIANCE (BESSEL'S CORRECTION)
- 2.12 SOFTWARE
- PROBLEMS
- PRACTICAL EXERCISES
- CHAPTER 3: RANDOM ERROR THEORY
- CHAPTER 4: CONFIDENCE INTERVALS
- 4.1 INTRODUCTION
- 4.2 DISTRIBUTIONS USED IN SAMPLING THEORY
- 4.3 CONFIDENCE INTERVAL FOR THE MEAN: T STATISTIC
- 4.4 TESTING THE VALIDITY OF THE CONFIDENCE INTERVAL
- 4.5 SELECTING A SAMPLE SIZE
- 4.6 CONFIDENCE INTERVAL FOR A POPULATION VARIANCE
- 4.7 CONFIDENCE INTERVAL FOR THE RATIO OF TWO POPULATION VARIANCES
- 4.8 SOFTWARE
- PROBLEMS
- NOTES
- CHAPTER 5: STATISTICAL TESTING
- CHAPTER 6: PROPAGATION OF RANDOM ERRORS IN INDIRECTLY MEASURED QUANTITIES
- CHAPTER 7: ERROR PROPAGATION IN ANGLE AND DISTANCE OBSERVATIONS
- 7.1 INTRODUCTION
- 7.2 ERROR SOURCES IN HORIZONTAL ANGLES
- 7.3 READING ERRORS
- 7.4 POINTING ERRORS
- 7.5 ESTIMATED POINTING AND READING ERRORS WITH TOTAL STATIONS
- 7.6 TARGET-CENTERING ERRORS
- 7.7 INSTRUMENT CENTERING ERRORS
- 7.8 EFFECTS OF LEVELING ERRORS IN ANGLE OBSERVATIONS
- 7.9 NUMERICAL EXAMPLE OF COMBINED ERROR PROPAGATION IN A SINGLE HORIZONTAL ANGLE
- 7.10 USING ESTIMATED ERRORS TO CHECK ANGULAR MISCLOSURE IN A TRAVERSE
- 7.11 ERRORS IN ASTRONOMICAL OBSERVATIONS FOR AZIMUTH
- 7.12 ERRORS IN ELECTRONIC DISTANCE OBSERVATIONS
- 7.13 CENTERING ERRORS WHEN USING RANGE POLES
- 7.14 SOFTWARE
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTES
- CHAPTER 8: ERROR PROPAGATION IN TRAVERSE SURVEYS
- 8.1 INTRODUCTION
- 8.2 DERIVATION OF ESTIMATED ERROR IN LATITUDE AND DEPARTURE
- 8.3 DERIVATION OF ESTIMATED STANDARD ERRORS IN COURSE AZIMUTHS
- 8.4 COMPUTING AND ANALYZING POLYGON TRAVERSE MISCLOSURE ERRORS
- 8.5 COMPUTING AND ANALYZING LINK TRAVERSE MISCLOSURE ERRORS
- 8.6 SOFTWARE
- 8.7 CONCLUSIONS
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTES
- CHAPTER 9: ERROR PROPAGATION IN ELEVATION DETERMINATION
- CHAPTER 10: WEIGHTS OF OBSERVATIONS
- CHAPTER 11: PRINCIPLES OF LEAST SQUARES
- 11.1 INTRODUCTION
- 11.2 FUNDAMENTAL PRINCIPLE OF LEAST SQUARES
- 11.3 THE FUNDAMENTAL PRINCIPLE OF WEIGHTED LEAST SQUARES
- 11.4 THE STOCHASTIC MODEL
- 11.5 FUNCTIONAL MODEL
- 11.6 OBSERVATION EQUATIONS
- 11.7 SYSTEMATIC FORMULATION OF THE NORMAL EQUATIONS
- 11.8 TABULAR FORMATION OF THE NORMAL EQUATIONS
- 11.9 USING MATRICES TO FORM THE NORMAL EQUATIONS
- 11.10 LEAST SQUARES SOLUTION OF NONLINEAR SYSTEMS
- 11.11 LEAST SQUARES FIT OF POINTS TO A LINE OR CURVE
- 11.12 CALIBRATION OF AN EDM INSTRUMENT
- 11.13 LEAST SQUARES ADJUSTMENT USING CONDITIONAL EQUATIONS
- 11.14 THE PREVIOUS EXAMPLE USING OBSERVATION EQUATIONS
- 11.15 SOFTWARE
- PROBLEMS
- NOTES
- CHAPTER 12: ADJUSTMENT OF LEVEL NETS
- CHAPTER 13: PRECISIONS OF INDIRECTLY DETERMINED QUANTITIES
- CHAPTER 14: ADJUSTMENT OF HORIZONTAL SURVEYS: TRILATERATION
- 14.1 INTRODUCTION
- 14.2 DISTANCE OBSERVATION EQUATION
- 14.3 TRILATERATION ADJUSTMENT EXAMPLE
- 14.4 FORMULATION OF A GENERALIZED COEFFICIENT MATRIX FOR A MORE COMPLEX NETWORK
- 14.5 COMPUTER SOLUTION OF A TRILATERATED QUADRILATERAL
- 14.6 ITERATION TERMINATION
- 14.7 SOFTWARE
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTES
- CHAPTER 15: ADJUSTMENT OF HORIZONTAL SURVEYS: TRIANGULATION
- CHAPTER 16: ADJUSTMENT OF HORIZONTAL SURVEYS: TRAVERSES AND HORIZONTAL NETWORKS
- CHAPTER 17: ADJUSTMENT OF GNSS NETWORKS
- 17.1 INTRODUCTION
- 17.2 GNSS OBSERVATIONS
- 17.3 GNSS ERRORS AND THE NEED FOR ADJUSTMENT
- 17.4 REFERENCE COORDINATE SYSTEMS FOR GNSS OBSERVATIONS
- 17.5 CONVERTING BETWEEN THE TERRESTRIAL AND GEODETIC COORDINATE SYSTEMS
- 17.6 APPLICATION OF LEAST SQUARES IN PROCESSING GNSS DATA
- 17.7 NETWORK PREADJUSTMENT DATA ANALYSIS
- 17.8 LEAST SQUARES ADJUSTMENT OF GNSS NETWORKS
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTES
- CHAPTER 18: COORDINATE TRANSFORMATIONS
- 18.1 INTRODUCTION
- 18.2 THE TWO-DIMENSIONAL CONFORMAL COORDINATE
- 18.3 EQUATION DEVELOPMENT
- 18.4 APPLICATION OF LEAST SQUARES
- 18.5 TWO-DIMENSIONAL AFFINE COORDINATE TRANSFORMATION
- 18.6 THE TWO-DIMENSIONAL PROJECTIVE COORDINATE TRANSFORMATION
- 18.7 THREE-DIMENSIONAL CONFORMAL COORDINATE TRANSFORMATION
- 18.8 STATISTICALLY VALID PARAMETERS
- PROBLEMS
- PROGRAMMING PROBLEMS
- CHAPTER 19: ERROR ELLIPSE
- 19.1 INTRODUCTION
- 19.2 COMPUTATION OF ELLIPSE ORIENTATION AND SEMIAXES
- 19.3 EXAMPLE PROBLEM OF STANDARD ERROR ELLIPSE CALCULATIONS
- 19.4 ANOTHER EXAMPLE PROBLEM
- 19.5 THE ERROR ELLIPSE CONFIDENCE LEVEL
- 19.6 ERROR ELLIPSE ADVANTAGES
- 19.7 OTHER MEASURES OF STATION UNCERTAINTY
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTES
- CHAPTER 20: CONSTRAINT EQUATIONS
- 20.1 INTRODUCTION
- 20.2 ADJUSTMENT OF CONTROL STATION COORDINATES
- 20.3 HOLDING CONTROL STATION COORDINATES AND DIRECTIONS OF LINES FIXED IN A TRILATERATION ADJUSTMENT
- 20.4 HELMERT'S METHOD
- 20.5 REDUNDANCIES IN A CONSTRAINED ADJUSTMENT
- 20.6 ENFORCING CONSTRAINTS THROUGH WEIGHTING
- PROBLEMS
- PRACTICAL PROBLEMS
- CHAPTER 21: BLUNDER DETECTION IN HORIZONTAL NETWORKS
- 21.1 INTRODUCTION
- 21.2 A PRIORI METHODS FOR DETECTING BLUNDERS IN OBSERVATIONS
- 21.3 A POSTERIORI BLUNDER DETECTION
- 21.4 DEVELOPMENT OF THE COVARIANCE MATRIX FOR THE RESIDUALS
- 21.5 DETECTION OF OUTLIERS IN OBSERVATIONS: DATA SNOOPING
- 21.6 DETECTION OF OUTLIERS IN OBSERVATIONS: THE TAU CRITERION
- 21.7 TECHNIQUES USED IN ADJUSTING CONTROL
- 21.8 A DATA SET WITH BLUNDERS
- 21.9 SOME FURTHER CONSIDERATIONS
- 21.10 SURVEY DESIGN
- 21.11 SOFTWARE
- PROBLEMS
- PRACTICAL PROBLEMS
- NOTES
- CHAPTER 22: THE GENERAL LEAST SQUARES METHOD AND ITS APPLICATION TO CURVE FITTING AND COORDINATE TRANSFORMATIONS
- 22.1 INTRODUCTION TO GENERAL LEAST SQUARES
- 22.2 GENERAL LEAST SQUARES EQUATIONS FOR FITTING A STRAIGHT LINE
- 22.3 GENERAL LEAST SQUARES SOLUTION
- 22.4 TWO-DIMENSIONAL COORDINATE TRANSFORMATION BY GENERAL LEAST SQUARES
- 22.5 THREE-DIMENSIONAL CONFORMAL COORDINATE TRANSFORMATION BY GENERAL LEAST SQUARES
- PROBLEMS
- PROGRAMMING PROBLEMS
- CHAPTER 23: THREE-DIMENSIONAL GEODETIC NETWORK ADJUSTMENT
- CHAPTER 24: COMBINING GNSS AND TERRESTRIAL OBSERVATIONS
- CHAPTER 25: ANALYSIS OF ADJUSTMENTS
- CHAPTER 26: COMPUTER OPTIMIZATION
- 26.1 INTRODUCTION
- 26.2 STORAGE OPTIMIZATION
- 26.3 DIRECT FORMATION OF THE NORMAL EQUATIONS
- 26.4 CHOLESKY DECOMPOSITION
- 26.5 FORWARD AND BACK SOLUTIONS
- 26.6 USING THE CHOLESKY FACTOR TO FIND THE INVERSE OF THE NORMAL MATRIX
- 26.7 SPARENESS AND OPTIMIZATION OF THE NORMAL MATRIX
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTES
- APPENDIX A: INTRODUCTION TO MATRICES
- A.1 INTRODUCTION
- A.2 DEFINITION OF A MATRIX
- A.3 SIZE OR DIMENSIONS OF A MATRIX
- A.4 TYPES OF MATRICES
- A.5 MATRIX EQUALITY
- A.6 ADDITION OR SUBTRACTION OF MATRICES
- A.7 SCALAR MULTIPLICATION OF A MATRIX
- A.8 MATRIX MULTIPLICATION
- A.9 COMPUTER ALGORITHMS FOR MATRIX OPERATIONS
- A.10 USE OF THE MATRIX SOFTWARE
- PROBLEMS
- PROGRAMMING PROBLEMS
- NOTE
- APPENDIX B: SOLUTION OF EQUATIONS BY MATRIX METHODS
- APPENDIX C: NONLINEAR EQUATIONS AND TAYLOR'S THEOREM
- APPENDIX D: THE NORMAL ERROR DISTRIBUTION CURVE AND OTHER STATISTICAL TABLES
- APPENDIX E: CONFIDENCE INTERVALS FOR THE MEAN
- APPENDIX F: MAP PROJECTION COORDINATE SYSTEMS
- APPENDIX G: COMPANION WEBSITE
- APPENDIX H: ANSWERS TO SELECTED PROBLEMS
- BIBLIOGRAPHY
- INDEX
- END USER LICENSE AGREEMENT
ADJUSTMENT COMPUTATIONS
Spatial Data Analysis
Sixth Edition
CHARLES D. GHILANI, PhD
Professor Emeritus of Engineering
The Pennsylvania State University
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