Location estimation from the ground up:
"This book explains how location-estimation problems are expressed mathematically and the statistical properties of these mathematical models"--
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
siam. Society for Industrial and Applied Mathematics
[2020]
|
| Schriftenreihe: | Fundamentals of algorithms
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | "This book explains how location-estimation problems are expressed mathematically and the statistical properties of these mathematical models"-- |
| Beschreibung: | xv, 200 Seiten Illustrationen, Diagramme |
| ISBN: | 9781611976281 1611976286 |
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| 245 | 1 | 0 | |a Location estimation from the ground up |c Sivan Toledo ; Tel-Aviv University ; Tel-Aviv, Israel |
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Datensatz im Suchindex
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| adam_text | Contents Preface ix Notation xiii 1 Fundamentals 1.1 From Geometric Constraints to Estimation...................................................... 1.2 Other Types of Constraints, Geometric and Otherwise.................................... 1.3 Nested Estimation Problems................................................................................ 1.4 Notes . . . ......................................................................................................... 1.5 Problems........................................................................................ 1 2 4 6 7 7 2 Location-Estimation Systems 2.1 Localization, Navigation, and Mapping............................................................ 2.2 Measuring Angles............................................................................................... 2.3 Measuring Distances............................................................................................ 2.4 Measuring Time of Arrival and Time Difference of Arrival ......................... 2.5 Coordinate Systems............................................................................................ 2.6 Notes..................................................................................................................... 2.7 Problems............................................................................................................... 9 9 10 12 12 14 15 16 3 From Leveling to Linear Least-Squares Problems 19 3.1 Heights from Differences.................................................................................. 20 3.2 Norm
Minimization............................................................................................ 21 3.3 Monotonie Transformations................................................................................... 22 3.4 Notes..................................................................................................................... 22 3.5 Problems............................................................................................................... 23 4 Solving Linear Least-Squares Problems with the QR Factorization 4.1 Easy Problems..................................................................................................... 4.2 Residual-Norm-Preserving Elimination............................................................ 4.3 Ordering the Eliminations.................................................................................. 4.4 The Thin QR Factorization.................................. 4.5 Other Ways to Compute the QR Factorization ................................................ 4.6 Computational Complexity and Sparsity......................................................... 4.7 Notes..................................................................................................................... 4.8 Problems......................................................... 29 29 30 31 32 32 33 33 34 5 Projections and Reductions to Linear Equations 5.1 The Pythagorean Theorem................................................................................... 39 39 v
vi Contents 5.2 5.3 5.4 5.5 5.6 5.7 The Normal Equations and the Equilibrium Equations.......................................40 The Cholesky Factorization................................................................................... 41 Orthogonal Projections..........................................................................................43 The Pseudoinverse............................................................................................... 44 Notes..................................................................................................................... 44 Problems............................................................................................................... 44 6 Estimation through Optimization: Probabilistic Justifications 6.1 Best Linear Unbiased Estimators....................................................................... 6.2 Generalized Least Squares and Decorrelation ................................................ 6.3 Maximum-Likelihood Estimators...................................................................... 6.4 Maximum Likelihood for Additive Gaussian Noise......................................... 6.5 Outliers and an Algorithm to Detect Them...................................................... 6.6 Notes..................................................................................................................... 6.7 Problems............................................................................................................... 47 47 49 50 51 53 53 54 7 Rank Deficient Problems and the SVD 57
7.1 A Motivating Example: Too Many Nuisance Parameters................................ 57 7.2 Another Motivating Example: Not Enough Information................................ 58 7.3 The Singular-Value Decomposition................................................................... 60 7.4 Numerical Issues and the Truncated SVD......................................................... 60 7.5 Solving Linear Least-Squares Problems with the SVD....................................... 61 7.6 Eliminating Nuisance Parameters...................................................................... 62 7.7 Notes......................................................................................................................... 63 7.8 Problems............................................................................................................... 63 8 Solving Nonlinear Least-Squares Problems 67 8.1 Taylor Polynomials............................................................................................ 67 8.2 Recognizing a Minimum and Gradient Descent................................................ 69 8.3 Newton’s Method............................................................................................... 70 8.4 Gauss-Newton Methods...................................................................................... 72 8.5 Derivative-Free Optimization: The Nedler-Mead Method.................................72 8.6 Stopping Criteria...................................................................................................... 74 8.7
Notes..................................................................................................................... 75 8.8 Problems............................................................................................................... 75 9 Evaluating Derivatives 9.1 Symbolic Derivatives......................................................................................... 9.2 Matrix Calculus.................................................................................................. 9.3 Correctness of the Newton Step......................................................................... 9.4 Derivatives of Transformed Least-Squares Problems...................................... 9.5 Notes..................................................................................................................... 9.6 Problems............................................................................................................... 10 Time-of-Arrival Localization and Separability 87 10.1 GNSS Time-of-Arrival Observation Equations................................................ 87 10.2 Time-of-Arrival Transmitter Localization......................................................... 89 10.3 Separable Nonlinear Least-Squares Problems................................................... 90 10.4 Exploiting Separability Using Nonorthogonal Elimination............................. 91 10.5 Notes......................................................................................................................... 93 10.6
Problems............................................................................................................... 93 79 79 81 83 83 84 85
Contents vii 11 A Posteriori Error Analysis 97 11.1 Probabilistic Analysis of the Residual................................................................... 97 11.2 Error Estimation.................................................................................................. 98 11.3 The Jacobian of a Minimizer............................................................................ 99 11.4 A Gauss-Newton Approximation of the Jacobian .............................................101 11.5 Notes....................................................................................................................... 102 11.6 Problems................................................................................................................. 103 12 A Priori Analysis: The Cramer-Rao Bound 105 12.1 Gradients of the Likelihood and Its Logarithm..................................................105 12.2 The Fisher Information Matrix and the Cramer-Rao Bound............................107 12.3 CRLB for Additive Gaussian Noise.....................................................................109 12.4 Examples................................................................................................................. Ill 12.5 Notes....................................................................................................................... 113 12.6 Problems................................................................................................................. 113 13 Arrival-Time Estimation 115 13.1 From Maximum Likelihood to Cross
Correlation...............................................115 13.2 Signal Engineering................................................................................................. 117 13.3 Algorithms.............................................................................................................. 120 13.4 Modulation and Complex Signals........................................................................121 13.5 Arrival-Time Estimation for Complex Signals..................................................124 13.6 GPS Signals...........................................................................................................125 13.7 Notes....................................................................................................................... 127 13.8 Problems................................................................................................................. 128 14 Cross Correlation Using the Fast Fourier Transform 133 14.1 The Structure of Circulant Matrices.....................................................................134 14.2 The Discrete Fourier Transform and Circulant Matrices..................................135 14.3 The Fast Fourier Transform................................................................................. 137 14.4 Notes....................................................................................................................... 138 14.5 Problems................................................................................................................. 138 15 Kalman Variations: Least
Squares for Dynamical Systems 141 15.1 Where Will the Cannonball Land? .....................................................................141 15.2 Linear Discrete Dynamical Systems.....................................................................142 15.3 A Least-Squares Formulation.............................................................................. 144 15.4 Rank Considerations.............................................................................................. 144 15.5 The Paige-Saunders Algorithm...........................................................................144 15.6 Smoothing, Interpolation, Filtering, and Prediction........................................... 147 15.7 Computing the Variance of the Estimates........................................................... 149 15.8 Notes........................................................................................................................151 15.9 Problems................................................................................................................. 152 16 Carrier-Phase Observations and Integer Least Squares 155 16.1 GPS Carrier-Phase Constraints........................................................................... 155 16.2 Eliminating the Real Parameters ........................................................................158 16.3 Integer Least Squares (the Closest Vector Problem) ........................................ 161 16.4 Searching and Pruning...........................................................................................162
Contents viii 16.5 16.6 16.7 The LLL Basis Reduction Algorithm..................................................................163 Notes........................................................................................................................165 Problems................................................................................................................. 166 A Mathematical Background 169 A.l Trigonometry and Complex Numbers................................................................... 169 A.2 Linear Algebra.........................................................................................................169 A.3 Calculus...................................................................................................................171 A.4 Probability............................................................................................................... 172 В Solutions 175 Bibliography 195 Index 199
Contents Preface ix Notation xiii 1 Fundamentals 1.1 From Geometric Constraints to Estimation...................................................... 1.2 Other Types of Constraints, Geometric and Otherwise.................................... 1.3 Nested Estimation Problems................................................................................ 1.4 Notes . . . ......................................................................................................... 1.5 Problems........................................................................................ 1 2 4 6 7 7 2 Location-Estimation Systems 2.1 Localization, Navigation, and Mapping............................................................ 2.2 Measuring Angles............................................................................................... 2.3 Measuring Distances............................................................................................ 2.4 Measuring Time of Arrival and Time Difference of Arrival ......................... 2.5 Coordinate Systems............................................................................................ 2.6 Notes..................................................................................................................... 2.7 Problems............................................................................................................... 9 9 10 12 12 14 15 16 3 From Leveling to Linear Least-Squares Problems 19 3.1 Heights from Differences.................................................................................. 20 3.2 Norm
Minimization............................................................................................ 21 3.3 Monotonie Transformations................................................................................... 22 3.4 Notes..................................................................................................................... 22 3.5 Problems............................................................................................................... 23 4 Solving Linear Least-Squares Problems with the QR Factorization 4.1 Easy Problems..................................................................................................... 4.2 Residual-Norm-Preserving Elimination............................................................ 4.3 Ordering the Eliminations.................................................................................. 4.4 The Thin QR Factorization.................................. 4.5 Other Ways to Compute the QR Factorization ................................................ 4.6 Computational Complexity and Sparsity......................................................... 4.7 Notes..................................................................................................................... 4.8 Problems......................................................... 29 29 30 31 32 32 33 33 34 5 Projections and Reductions to Linear Equations 5.1 The Pythagorean Theorem................................................................................... 39 39 v
vi Contents 5.2 5.3 5.4 5.5 5.6 5.7 The Normal Equations and the Equilibrium Equations.......................................40 The Cholesky Factorization................................................................................... 41 Orthogonal Projections..........................................................................................43 The Pseudoinverse............................................................................................... 44 Notes..................................................................................................................... 44 Problems............................................................................................................... 44 6 Estimation through Optimization: Probabilistic Justifications 6.1 Best Linear Unbiased Estimators....................................................................... 6.2 Generalized Least Squares and Decorrelation ................................................ 6.3 Maximum-Likelihood Estimators...................................................................... 6.4 Maximum Likelihood for Additive Gaussian Noise......................................... 6.5 Outliers and an Algorithm to Detect Them...................................................... 6.6 Notes..................................................................................................................... 6.7 Problems............................................................................................................... 47 47 49 50 51 53 53 54 7 Rank Deficient Problems and the SVD 57
7.1 A Motivating Example: Too Many Nuisance Parameters................................ 57 7.2 Another Motivating Example: Not Enough Information................................ 58 7.3 The Singular-Value Decomposition................................................................... 60 7.4 Numerical Issues and the Truncated SVD......................................................... 60 7.5 Solving Linear Least-Squares Problems with the SVD....................................... 61 7.6 Eliminating Nuisance Parameters...................................................................... 62 7.7 Notes......................................................................................................................... 63 7.8 Problems............................................................................................................... 63 8 Solving Nonlinear Least-Squares Problems 67 8.1 Taylor Polynomials............................................................................................ 67 8.2 Recognizing a Minimum and Gradient Descent................................................ 69 8.3 Newton’s Method............................................................................................... 70 8.4 Gauss-Newton Methods...................................................................................... 72 8.5 Derivative-Free Optimization: The Nedler-Mead Method.................................72 8.6 Stopping Criteria...................................................................................................... 74 8.7
Notes..................................................................................................................... 75 8.8 Problems............................................................................................................... 75 9 Evaluating Derivatives 9.1 Symbolic Derivatives......................................................................................... 9.2 Matrix Calculus.................................................................................................. 9.3 Correctness of the Newton Step......................................................................... 9.4 Derivatives of Transformed Least-Squares Problems...................................... 9.5 Notes..................................................................................................................... 9.6 Problems............................................................................................................... 10 Time-of-Arrival Localization and Separability 87 10.1 GNSS Time-of-Arrival Observation Equations................................................ 87 10.2 Time-of-Arrival Transmitter Localization......................................................... 89 10.3 Separable Nonlinear Least-Squares Problems................................................... 90 10.4 Exploiting Separability Using Nonorthogonal Elimination............................. 91 10.5 Notes......................................................................................................................... 93 10.6
Problems............................................................................................................... 93 79 79 81 83 83 84 85
Contents vii 11 A Posteriori Error Analysis 97 11.1 Probabilistic Analysis of the Residual................................................................... 97 11.2 Error Estimation.................................................................................................. 98 11.3 The Jacobian of a Minimizer............................................................................ 99 11.4 A Gauss-Newton Approximation of the Jacobian .............................................101 11.5 Notes....................................................................................................................... 102 11.6 Problems................................................................................................................. 103 12 A Priori Analysis: The Cramer-Rao Bound 105 12.1 Gradients of the Likelihood and Its Logarithm..................................................105 12.2 The Fisher Information Matrix and the Cramer-Rao Bound............................107 12.3 CRLB for Additive Gaussian Noise.....................................................................109 12.4 Examples................................................................................................................. Ill 12.5 Notes....................................................................................................................... 113 12.6 Problems................................................................................................................. 113 13 Arrival-Time Estimation 115 13.1 From Maximum Likelihood to Cross
Correlation...............................................115 13.2 Signal Engineering................................................................................................. 117 13.3 Algorithms.............................................................................................................. 120 13.4 Modulation and Complex Signals........................................................................121 13.5 Arrival-Time Estimation for Complex Signals..................................................124 13.6 GPS Signals...........................................................................................................125 13.7 Notes....................................................................................................................... 127 13.8 Problems................................................................................................................. 128 14 Cross Correlation Using the Fast Fourier Transform 133 14.1 The Structure of Circulant Matrices.....................................................................134 14.2 The Discrete Fourier Transform and Circulant Matrices..................................135 14.3 The Fast Fourier Transform................................................................................. 137 14.4 Notes....................................................................................................................... 138 14.5 Problems................................................................................................................. 138 15 Kalman Variations: Least
Squares for Dynamical Systems 141 15.1 Where Will the Cannonball Land? .....................................................................141 15.2 Linear Discrete Dynamical Systems.....................................................................142 15.3 A Least-Squares Formulation.............................................................................. 144 15.4 Rank Considerations.............................................................................................. 144 15.5 The Paige-Saunders Algorithm...........................................................................144 15.6 Smoothing, Interpolation, Filtering, and Prediction........................................... 147 15.7 Computing the Variance of the Estimates........................................................... 149 15.8 Notes........................................................................................................................151 15.9 Problems................................................................................................................. 152 16 Carrier-Phase Observations and Integer Least Squares 155 16.1 GPS Carrier-Phase Constraints........................................................................... 155 16.2 Eliminating the Real Parameters ........................................................................158 16.3 Integer Least Squares (the Closest Vector Problem) ........................................ 161 16.4 Searching and Pruning...........................................................................................162
Contents viii 16.5 16.6 16.7 The LLL Basis Reduction Algorithm..................................................................163 Notes........................................................................................................................165 Problems................................................................................................................. 166 A Mathematical Background 169 A.l Trigonometry and Complex Numbers................................................................... 169 A.2 Linear Algebra.........................................................................................................169 A.3 Calculus...................................................................................................................171 A.4 Probability............................................................................................................... 172 В Solutions 175 Bibliography 195 Index 199
|
| adam_txt |
Contents Preface ix Notation xiii 1 Fundamentals 1.1 From Geometric Constraints to Estimation. 1.2 Other Types of Constraints, Geometric and Otherwise. 1.3 Nested Estimation Problems. 1.4 Notes . . . . 1.5 Problems. 1 2 4 6 7 7 2 Location-Estimation Systems 2.1 Localization, Navigation, and Mapping. 2.2 Measuring Angles. 2.3 Measuring Distances. 2.4 Measuring Time of Arrival and Time Difference of Arrival . 2.5 Coordinate Systems. 2.6 Notes. 2.7 Problems. 9 9 10 12 12 14 15 16 3 From Leveling to Linear Least-Squares Problems 19 3.1 Heights from Differences. 20 3.2 Norm
Minimization. 21 3.3 Monotonie Transformations. 22 3.4 Notes. 22 3.5 Problems. 23 4 Solving Linear Least-Squares Problems with the QR Factorization 4.1 Easy Problems. 4.2 Residual-Norm-Preserving Elimination. 4.3 Ordering the Eliminations. 4.4 The Thin QR Factorization. 4.5 Other Ways to Compute the QR Factorization . 4.6 Computational Complexity and Sparsity. 4.7 Notes. 4.8 Problems. 29 29 30 31 32 32 33 33 34 5 Projections and Reductions to Linear Equations 5.1 The Pythagorean Theorem. 39 39 v
vi Contents 5.2 5.3 5.4 5.5 5.6 5.7 The Normal Equations and the Equilibrium Equations.40 The Cholesky Factorization. 41 Orthogonal Projections.43 The Pseudoinverse. 44 Notes. 44 Problems. 44 6 Estimation through Optimization: Probabilistic Justifications 6.1 Best Linear Unbiased Estimators. 6.2 Generalized Least Squares and Decorrelation . 6.3 Maximum-Likelihood Estimators. 6.4 Maximum Likelihood for Additive Gaussian Noise. 6.5 Outliers and an Algorithm to Detect Them. 6.6 Notes. 6.7 Problems. 47 47 49 50 51 53 53 54 7 Rank Deficient Problems and the SVD 57
7.1 A Motivating Example: Too Many Nuisance Parameters. 57 7.2 Another Motivating Example: Not Enough Information. 58 7.3 The Singular-Value Decomposition. 60 7.4 Numerical Issues and the Truncated SVD. 60 7.5 Solving Linear Least-Squares Problems with the SVD. 61 7.6 Eliminating Nuisance Parameters. 62 7.7 Notes. 63 7.8 Problems. 63 8 Solving Nonlinear Least-Squares Problems 67 8.1 Taylor Polynomials. 67 8.2 Recognizing a Minimum and Gradient Descent. 69 8.3 Newton’s Method. 70 8.4 Gauss-Newton Methods. 72 8.5 Derivative-Free Optimization: The Nedler-Mead Method.72 8.6 Stopping Criteria. 74 8.7
Notes. 75 8.8 Problems. 75 9 Evaluating Derivatives 9.1 Symbolic Derivatives. 9.2 Matrix Calculus. 9.3 Correctness of the Newton Step. 9.4 Derivatives of Transformed Least-Squares Problems. 9.5 Notes. 9.6 Problems. 10 Time-of-Arrival Localization and Separability 87 10.1 GNSS Time-of-Arrival Observation Equations. 87 10.2 Time-of-Arrival Transmitter Localization. 89 10.3 Separable Nonlinear Least-Squares Problems. 90 10.4 Exploiting Separability Using Nonorthogonal Elimination. 91 10.5 Notes. 93 10.6
Problems. 93 79 79 81 83 83 84 85
Contents vii 11 A Posteriori Error Analysis 97 11.1 Probabilistic Analysis of the Residual. 97 11.2 Error Estimation. 98 11.3 The Jacobian of a Minimizer. 99 11.4 A Gauss-Newton Approximation of the Jacobian .101 11.5 Notes. 102 11.6 Problems. 103 12 A Priori Analysis: The Cramer-Rao Bound 105 12.1 Gradients of the Likelihood and Its Logarithm.105 12.2 The Fisher Information Matrix and the Cramer-Rao Bound.107 12.3 CRLB for Additive Gaussian Noise.109 12.4 Examples. Ill 12.5 Notes. 113 12.6 Problems. 113 13 Arrival-Time Estimation 115 13.1 From Maximum Likelihood to Cross
Correlation.115 13.2 Signal Engineering. 117 13.3 Algorithms. 120 13.4 Modulation and Complex Signals.121 13.5 Arrival-Time Estimation for Complex Signals.124 13.6 GPS Signals.125 13.7 Notes. 127 13.8 Problems. 128 14 Cross Correlation Using the Fast Fourier Transform 133 14.1 The Structure of Circulant Matrices.134 14.2 The Discrete Fourier Transform and Circulant Matrices.135 14.3 The Fast Fourier Transform. 137 14.4 Notes. 138 14.5 Problems. 138 15 Kalman Variations: Least
Squares for Dynamical Systems 141 15.1 Where Will the Cannonball Land? .141 15.2 Linear Discrete Dynamical Systems.142 15.3 A Least-Squares Formulation. 144 15.4 Rank Considerations. 144 15.5 The Paige-Saunders Algorithm.144 15.6 Smoothing, Interpolation, Filtering, and Prediction. 147 15.7 Computing the Variance of the Estimates. 149 15.8 Notes.151 15.9 Problems. 152 16 Carrier-Phase Observations and Integer Least Squares 155 16.1 GPS Carrier-Phase Constraints. 155 16.2 Eliminating the Real Parameters .158 16.3 Integer Least Squares (the Closest Vector Problem) . 161 16.4 Searching and Pruning.162
Contents viii 16.5 16.6 16.7 The LLL Basis Reduction Algorithm.163 Notes.165 Problems. 166 A Mathematical Background 169 A.l Trigonometry and Complex Numbers. 169 A.2 Linear Algebra.169 A.3 Calculus.171 A.4 Probability. 172 В Solutions 175 Bibliography 195 Index 199
Contents Preface ix Notation xiii 1 Fundamentals 1.1 From Geometric Constraints to Estimation. 1.2 Other Types of Constraints, Geometric and Otherwise. 1.3 Nested Estimation Problems. 1.4 Notes . . . . 1.5 Problems. 1 2 4 6 7 7 2 Location-Estimation Systems 2.1 Localization, Navigation, and Mapping. 2.2 Measuring Angles. 2.3 Measuring Distances. 2.4 Measuring Time of Arrival and Time Difference of Arrival . 2.5 Coordinate Systems. 2.6 Notes. 2.7 Problems. 9 9 10 12 12 14 15 16 3 From Leveling to Linear Least-Squares Problems 19 3.1 Heights from Differences. 20 3.2 Norm
Minimization. 21 3.3 Monotonie Transformations. 22 3.4 Notes. 22 3.5 Problems. 23 4 Solving Linear Least-Squares Problems with the QR Factorization 4.1 Easy Problems. 4.2 Residual-Norm-Preserving Elimination. 4.3 Ordering the Eliminations. 4.4 The Thin QR Factorization. 4.5 Other Ways to Compute the QR Factorization . 4.6 Computational Complexity and Sparsity. 4.7 Notes. 4.8 Problems. 29 29 30 31 32 32 33 33 34 5 Projections and Reductions to Linear Equations 5.1 The Pythagorean Theorem. 39 39 v
vi Contents 5.2 5.3 5.4 5.5 5.6 5.7 The Normal Equations and the Equilibrium Equations.40 The Cholesky Factorization. 41 Orthogonal Projections.43 The Pseudoinverse. 44 Notes. 44 Problems. 44 6 Estimation through Optimization: Probabilistic Justifications 6.1 Best Linear Unbiased Estimators. 6.2 Generalized Least Squares and Decorrelation . 6.3 Maximum-Likelihood Estimators. 6.4 Maximum Likelihood for Additive Gaussian Noise. 6.5 Outliers and an Algorithm to Detect Them. 6.6 Notes. 6.7 Problems. 47 47 49 50 51 53 53 54 7 Rank Deficient Problems and the SVD 57
7.1 A Motivating Example: Too Many Nuisance Parameters. 57 7.2 Another Motivating Example: Not Enough Information. 58 7.3 The Singular-Value Decomposition. 60 7.4 Numerical Issues and the Truncated SVD. 60 7.5 Solving Linear Least-Squares Problems with the SVD. 61 7.6 Eliminating Nuisance Parameters. 62 7.7 Notes. 63 7.8 Problems. 63 8 Solving Nonlinear Least-Squares Problems 67 8.1 Taylor Polynomials. 67 8.2 Recognizing a Minimum and Gradient Descent. 69 8.3 Newton’s Method. 70 8.4 Gauss-Newton Methods. 72 8.5 Derivative-Free Optimization: The Nedler-Mead Method.72 8.6 Stopping Criteria. 74 8.7
Notes. 75 8.8 Problems. 75 9 Evaluating Derivatives 9.1 Symbolic Derivatives. 9.2 Matrix Calculus. 9.3 Correctness of the Newton Step. 9.4 Derivatives of Transformed Least-Squares Problems. 9.5 Notes. 9.6 Problems. 10 Time-of-Arrival Localization and Separability 87 10.1 GNSS Time-of-Arrival Observation Equations. 87 10.2 Time-of-Arrival Transmitter Localization. 89 10.3 Separable Nonlinear Least-Squares Problems. 90 10.4 Exploiting Separability Using Nonorthogonal Elimination. 91 10.5 Notes. 93 10.6
Problems. 93 79 79 81 83 83 84 85
Contents vii 11 A Posteriori Error Analysis 97 11.1 Probabilistic Analysis of the Residual. 97 11.2 Error Estimation. 98 11.3 The Jacobian of a Minimizer. 99 11.4 A Gauss-Newton Approximation of the Jacobian .101 11.5 Notes. 102 11.6 Problems. 103 12 A Priori Analysis: The Cramer-Rao Bound 105 12.1 Gradients of the Likelihood and Its Logarithm.105 12.2 The Fisher Information Matrix and the Cramer-Rao Bound.107 12.3 CRLB for Additive Gaussian Noise.109 12.4 Examples. Ill 12.5 Notes. 113 12.6 Problems. 113 13 Arrival-Time Estimation 115 13.1 From Maximum Likelihood to Cross
Correlation.115 13.2 Signal Engineering. 117 13.3 Algorithms. 120 13.4 Modulation and Complex Signals.121 13.5 Arrival-Time Estimation for Complex Signals.124 13.6 GPS Signals.125 13.7 Notes. 127 13.8 Problems. 128 14 Cross Correlation Using the Fast Fourier Transform 133 14.1 The Structure of Circulant Matrices.134 14.2 The Discrete Fourier Transform and Circulant Matrices.135 14.3 The Fast Fourier Transform. 137 14.4 Notes. 138 14.5 Problems. 138 15 Kalman Variations: Least
Squares for Dynamical Systems 141 15.1 Where Will the Cannonball Land? .141 15.2 Linear Discrete Dynamical Systems.142 15.3 A Least-Squares Formulation. 144 15.4 Rank Considerations. 144 15.5 The Paige-Saunders Algorithm.144 15.6 Smoothing, Interpolation, Filtering, and Prediction. 147 15.7 Computing the Variance of the Estimates. 149 15.8 Notes.151 15.9 Problems. 152 16 Carrier-Phase Observations and Integer Least Squares 155 16.1 GPS Carrier-Phase Constraints. 155 16.2 Eliminating the Real Parameters .158 16.3 Integer Least Squares (the Closest Vector Problem) . 161 16.4 Searching and Pruning.162
Contents viii 16.5 16.6 16.7 The LLL Basis Reduction Algorithm.163 Notes.165 Problems. 166 A Mathematical Background 169 A.l Trigonometry and Complex Numbers. 169 A.2 Linear Algebra.169 A.3 Calculus.171 A.4 Probability. 172 В Solutions 175 Bibliography 195 Index 199 |
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| id | DE-604.BV047018021 |
| illustrated | Illustrated |
| index_date | 2024-07-03T15:58:33Z |
| indexdate | 2024-07-10T09:00:16Z |
| institution | BVB |
| isbn | 9781611976281 1611976286 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032425542 |
| oclc_num | 1205584112 |
| open_access_boolean | |
| owner | DE-739 DE-573 DE-83 |
| owner_facet | DE-739 DE-573 DE-83 |
| physical | xv, 200 Seiten Illustrationen, Diagramme |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | siam. Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Fundamentals of algorithms |
| series2 | Fundamentals of algorithms |
| spelling | Toledo, Sivan (DE-588)1165167573 aut Location estimation from the ground up Sivan Toledo ; Tel-Aviv University ; Tel-Aviv, Israel Philadelphia siam. Society for Industrial and Applied Mathematics [2020] xv, 200 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Fundamentals of algorithms 7 "This book explains how location-estimation problems are expressed mathematically and the statistical properties of these mathematical models"-- Automatische Messung (DE-588)4303176-6 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Ortung (DE-588)4172896-8 gnd rswk-swf Distances / Measurement Distances / Mathematical models Distance measuring instruments, Electronic Automatische Messung (DE-588)4303176-6 s Schätzung (DE-588)4193791-0 s Ortung (DE-588)4172896-8 s Algorithmus (DE-588)4001183-5 s DE-604 Online version Toledo, Sivan Location estimation from the ground up Philadelphia : Society for Industrial and Applied Mathematics, 2020 9781611976298 Fundamentals of algorithms 7 (DE-604)BV017480576 7 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032425542&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032425542&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Toledo, Sivan Location estimation from the ground up Fundamentals of algorithms Automatische Messung (DE-588)4303176-6 gnd Schätzung (DE-588)4193791-0 gnd Algorithmus (DE-588)4001183-5 gnd Ortung (DE-588)4172896-8 gnd |
| subject_GND | (DE-588)4303176-6 (DE-588)4193791-0 (DE-588)4001183-5 (DE-588)4172896-8 |
| title | Location estimation from the ground up |
| title_auth | Location estimation from the ground up |
| title_exact_search | Location estimation from the ground up |
| title_exact_search_txtP | Location estimation from the ground up |
| title_full | Location estimation from the ground up Sivan Toledo ; Tel-Aviv University ; Tel-Aviv, Israel |
| title_fullStr | Location estimation from the ground up Sivan Toledo ; Tel-Aviv University ; Tel-Aviv, Israel |
| title_full_unstemmed | Location estimation from the ground up Sivan Toledo ; Tel-Aviv University ; Tel-Aviv, Israel |
| title_short | Location estimation from the ground up |
| title_sort | location estimation from the ground up |
| topic | Automatische Messung (DE-588)4303176-6 gnd Schätzung (DE-588)4193791-0 gnd Algorithmus (DE-588)4001183-5 gnd Ortung (DE-588)4172896-8 gnd |
| topic_facet | Automatische Messung Schätzung Algorithmus Ortung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032425542&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032425542&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017480576 |
| work_keys_str_mv | AT toledosivan locationestimationfromthegroundup |
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Inhaltsverzeichnis