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END USER LICENSE AGREEMENT
by Charles D. Ghilani
Adjustment Computations, 6th Edition
COVER
TITLE PAGE
PREFACE
ACKNOWLEDGMENTS
CHAPTER 1: INTRODUCTION
1.1 INTRODUCTION
1.2 DIRECT AND INDIRECT MEASUREMENTS
1.3 MEASUREMENT ERROR SOURCES
1.4 DEFINITIONS
1.5 PRECISION VERSUS ACCURACY
1.6 REDUNDANT OBSERVATIONS IN SURVEYING AND THEIR ADJUSTMENT
1.7 ADVANTAGES OF LEAST SQUARES ADJUSTMENT
1.8 OVERVIEW OF THE BOOK
PROBLEMS
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
3.1 INTRODUCTION
3.2 THEORY OF PROBABILITY
3.3 PROPERTIES OF THE NORMAL DISTRIBUTION CURVE
3.4 STANDARD NORMAL DISTRIBUTION FUNCTION
3.5 PROBABILITY OF THE STANDARD ERROR
3.6 USES FOR PERCENT ERRORS
3.7 PRACTICAL EXAMPLES
PROBLEMS
PROGRAMMING PROBLEMS
NOTE
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
5.1 HYPOTHESIS TESTING
5.2 SYSTEMATIC DEVELOPMENT OF A TEST
5.3 TEST OF HYPOTHESIS FOR THE POPULATION MEAN
5.4 TEST OF HYPOTHESIS FOR THE POPULATION VARIANCE
5.5 TEST OF HYPOTHESIS FOR THE RATIO OF TWO POPULATION VARIANCES
5.6 SOFTWARE
PROBLEMS
NOTES
CHAPTER 6: PROPAGATION OF RANDOM ERRORS IN INDIRECTLY MEASURED QUANTITIES
6.1 BASIC ERROR PROPAGATION EQUATION
6.2 FREQUENTLY ENCOUNTERED SPECIFIC FUNCTIONS
6.3 NUMERICAL EXAMPLES
6.4 SOFTWARE
6.5 CONCLUSIONS
PROBLEMS
PRACTICAL EXERCISES
NOTE
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
9.1 INTRODUCTION
9.2 SYSTEMATIC ERRORS IN DIFFERENTIAL LEVELING
9.3 RANDOM ERRORS IN DIFFERENTIAL LEVELING
9.4 ERROR PROPAGATION IN TRIGONOMETRIC LEVELING
PROBLEMS
PROGRAMMING PROBLEMS
CHAPTER 10: WEIGHTS OF OBSERVATIONS
10.1 INTRODUCTION
10.2 WEIGHTED MEAN
10.3 RELATIONSHIP BETWEEN WEIGHTS AND STANDARD ERRORS
10.4 STATISTICS OF WEIGHTED OBSERVATIONS
10.5 WEIGHTS IN ANGLE OBSERVATIONS
10.6 WEIGHTS IN DIFFERENTIAL LEVELING
10.7 PRACTICAL EXAMPLES
PROBLEMS
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
12.1 INTRODUCTION
12.2 OBSERVATION EQUATION
12.3 UNWEIGHTED EXAMPLE
12.4 WEIGHTED EXAMPLE
12.5 REFERENCE STANDARD DEVIATION
12.6 ANOTHER WEIGHTED ADJUSTMENT
12.7 SOFTWARE
PROBLEMS
PROGRAMMING PROBLEMS
CHAPTER 13: PRECISIONS OF INDIRECTLY DETERMINED QUANTITIES
13.1 INTRODUCTION
13.2 DEVELOPMENT OF THE COVARIANCE MATRIX
13.3 NUMERICAL EXAMPLES
13.4 STANDARD DEVIATIONS OF COMPUTED QUANTITIES
PROBLEMS
PROGRAMMING PROBLEMS
NOTE
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
15.1 INTRODUCTION
15.2 AZIMUTH OBSERVATION EQUATION
15.3 ANGLE OBSERVATION EQUATION
15.4 ADJUSTMENT OF INTERSECTIONS
15.5 ADJUSTMENT OF RESECTIONS
15.6 ADJUSTMENT OF TRIANGULATED QUADRILATERALS
PROBLEMS
PROGRAMMING PROBLEMS
NOTE
CHAPTER 16: ADJUSTMENT OF HORIZONTAL SURVEYS: TRAVERSES AND HORIZONTAL NETWORKS
16.1 INTRODUCTION TO TRAVERSE ADJUSTMENTS
16.2 OBSERVATION EQUATIONS
16.3 REDUNDANT EQUATIONS
16.4 NUMERICAL EXAMPLE
16.5 MINIMUM AMOUNT OF CONTROL
16.6 ADJUSTMENT OF NETWORKS
16.7 χ2 TEST: GOODNESS OF FIT
PROBLEMS
PROGRAMMING PROBLEMS
NOTE
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
23.1 INTRODUCTION
23.2 LINEARIZATION OF EQUATIONS
23.3 MINIMUM NUMBER OF CONSTRAINTS
23.4 EXAMPLE ADJUSTMENT
23.5 BUILDING AN ADJUSTMENT
23.6 COMMENTS ON SYSTEMATIC ERRORS
23.7 SOFTWARE
PROBLEMS
PROGRAMMING PROBLEMS
NOTES
CHAPTER 24: COMBINING GNSS AND TERRESTRIAL OBSERVATIONS
24.1 INTRODUCTION
24.2 THE HELMERT TRANSFORMATION
24.3 ROTATIONS BETWEEN COORDINATE SYSTEMS
24.4 COMBINING GNSS BASELINE VECTORS WITH TRADITIONAL OBSERVATIONS
24.5 ANOTHER APPROACH TO TRANSFORMING COORDINATES BETWEEN REFERENCE FRAMES
24.6 OTHER CONSIDERATIONS
PROBLEMS
PROGRAMMING PROBLEMS
NOTES
CHAPTER 25: ANALYSIS OF ADJUSTMENTS
25.1 INTRODUCTION
25.2 BASIC CONCEPTS, RESIDUALS, AND THE NORMAL DISTRIBUTION
25.3 GOODNESS OF FIT TEST
25.4 COMPARISON OF GNSS RESIDUAL PLOTS
25.5 USE OF STATISTICAL BLUNDER DETECTION
PROBLEMS
NOTES
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
B.1 INTRODUCTION
B.2 INVERSE MATRIX
B.3 THE INVERSE OF A 2 × 2 MATRIX
B.4 INVERSES BY ADJOINTS
B.5 INVERSES BY ELEMENTARY ROW TRANSFORMATIONS
B.6 EXAMPLE PROBLEM
PROBLEMS
PROGRAMMING PROBLEMS
APPENDIX C: NONLINEAR EQUATIONS AND TAYLOR'S THEOREM
C.1 INTRODUCTION
C.2 TAYLOR SERIES LINEARIZATION OF NONLINEAR EQUATIONS
C.3 NUMERICAL EXAMPLE
C.4 USING MATRICES TO SOLVE NONLINEAR EQUATIONS
C.5 SIMPLE MATRIX EXAMPLE
C.6 PRACTICAL EXAMPLE
C.7 CONCLUDING REMARKS
PROBLEMS
PROGRAMMING PROBLEMS
APPENDIX D: THE NORMAL ERROR DISTRIBUTION CURVE AND OTHER STATISTICAL TABLES
D.1 DEVELOPMENT FOR NORMAL DISTRIBUTION CURVE EQUATION
D.2 OTHER STATISTICAL TABLES
NOTE
APPENDIX E: CONFIDENCE INTERVALS FOR THE MEAN
APPENDIX F: MAP PROJECTION COORDINATE SYSTEMS
F.1 INTRODUCTION
F.2 MATHEMATICS OF THE LAMBERT CONFORMAL CONIC MAP PROJECTION
F.3 MATHEMATICS FROM THE TRANSVERSE MERCATOR
F.4 STEREOGRAPHIC MAP PROJECTION
F.5 REDUCTION OF OBSERVATIONS
NOTES
APPENDIX G: COMPANION WEBSITE
G.1 INTRODUCTION
G.2 FILE FORMATS AND MEMORY MATTERS
G.3 SOFTWARE
G.4 USING THE SOFTWARE AS AN INSTRUCTIONAL AID
APPENDIX H: ANSWERS TO SELECTED PROBLEMS
BIBLIOGRAPHY
INDEX
END USER LICENSE AGREEMENT
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