实例介绍
【实例简介】
STATE ESTIMATION FOR ROBOTICS Timothy D. Barfoot SLAM入门经典
Revision history 1 Sept 2015 First draft released 15 Dec 2015 Added a new section to Chapter 3 on recursive discrete-Cime smoothers and their relationship to the batch solution; fixed a few typos 17 Dec 2015 Fixed a lew ty pos in the new section on smoothers 14 Jan 2016 Addcd historical notc regarding Stanley Schmidts role in EkF to Chapter 4 20 Mar 2016 Clarificd in thc introduction and probability chapter that we use a bayesian view of probability and ap proach to estimation in this book 26 Mar 2016 Fixed subscript typos in (3. 126),(3.127),(4.33) (4.34),(4.42) 29 Mar 2016 Added a note on Jacobi's formula to the section on the matrix exponential in Chapter 7 30Mar2016 Added“ squared” in front of“ Mahalanobis distance to match actual definition 8 Apr 2016 Added a footnote at start of probability chapter ac- knowledging that we work with probability densities Lthough the classical formal approach is to start from probability distributions; also made a table in Chap ter 7 fit inside the margins 11 Apr 2016 Fixed ty po in x delinition on SE 3) identity page in Chapter 7 19 Apr 2016 Added acronym list, clarified ISPKF experiment sec- tion, removed embarrassing uses of 'maximum a pri OL 20 Apr 2016 Added index to back 21 Apr 2016 Ran spellchecker on whole book 28 Apr 2016 Adjustcd sentence at start of introduction to rcflcct actual contents of intro 2 May 2016 Addcd missing yo to z in(3. 12); addcd missing ncg- ative sign to (3. 14a 9 May 2016 Fixed a bunch more little typos while proofreading IV Revision History 12 July 2016 Fixed typo in third line of( 9.12 22 July 2016 Various small typos 15 Aug 2016 Clarified the scalar case is deterministic in Section 2.2.8, changc to= in(2.70) 22 Aug 2016 Rewrote the M-estimation section and added a new scction (5. 3. 3)on covariance estimation and its con- nection to M-estimation 29 Aug 2016 Madc a fcw tweaks to Scction 7. 1.9 on Lic group op timization including a new figure(7.3) 16 Nov 2016 Fixed minor typos in text 6 nov 2016 In helpful Lents from Greg Chirikiian 2 Dec 2016 Added missing brackets in(8.126) and followons 10 Dec 2016 A few more typos fixed Contents Acronyms and Abbreviations Notation Foreword Introduction 1.1 A Littlc History 2 Sensors. Measurements. and Problem Definition 1. 3 How This Book is Organized 1345 1.4 Relationship to Other books Part I Estimation Machinery 2 Primer on Probability Theory 2. 1 Probability densily Functions 7999 2.1.1 Definitions 2. 1. 2 Bayes'Rule and Inference 10 2.1.3 Moments of Pdfs 2.1.4 Sample Mean and Covariance 2.1.5 Statistically Independent, Uncorrelated 2.1.6 Shannon and mutual Information 2.1.7 Cramer-Rao Lower Bound and Fisher Information 2.2 Gaussian Probability Density Functions 14 2. 2.1 Definitions 2. 2.2 Isserlis, theorem 15 2.2.3 Joint Gaussian PDFs. Their Factors and Inference 2.2.4 Statistically Independent, Uncorrelated 2.2.5 Linear Change of Variables 19 2. 2.6 Product of gaussians 21 2.2.7 Sherman-Mo 22 2.2.8 Passing a Gaussian Through a Nonlinearity 2.2.9 Shannon information of a gaussian 27 2.2.10 Mutual Information of a. oint Gaussian PDl 29 2.2.11 Cramer-Rao lower Bound applied to (aussian PI)I,s 29 2. 3 Gaussian Processes 31 2. 4 Summary 32 2.5 Exercises 32 Contents Linear-Gaussian estimation 35 3.1 Batch Discrete-Time estimation 35 3.1.1 Problem setul 3.1.2 Maximum a Posteriori 7 3.1.3 Bavesian Inference 42 3.1.4 Existence, Uniqueness, and Observability 3.1.5 MAP Covariance 48 3.2 Recursive discrete- Time Smoothin 3.2. 1 Exploiting Sparsity in the Batch Solution 50 3.2.2 Cholesky Smoother 51 3.2.3 Rauch-Tung-Striebel Smoother 3.3 Recursive Discrete-Time Filtering 56 3.3. 1 Factoring the Batch Solution 57 3.3.2 Kalan Filter via MAP 3.3.3 Kallan Filter via Bayesian Inference 3.3.4 Kalman fille 3.3.5 Kalman Filter Discussion 3.3.6 Error dynamics 3.3.7E nd observability 3.1 Batch Continuous-Timc Estimation 3.4.1 Gaussian Process Regression 3.4.2 A Class of Exactly Sparse Gaussian Process Priors 3.4.3 Linear Time-Invariant Case 81 3.4.4 elationship to Batch D)iscrete-Time Estimation 3.5 Summa 3.6 Exercises 8 4 Nonlinear Non-Gaussian estimation 4.1.1 Full Bayesian Estimation 4.1.2 Maximum a posteriori estimation 4.2 Recursive discrete- Time estimation 94 1.2.1 Problem Setup 94 4.2.2 Bayes Filter 95 4.2.3 Extended Kalman Filter 4.2.4 Generalized Gaussian Filter 4.2.5 Iterated Extended Kalman filter 103 4,2. 6 IeKF is a MAP Estimator 104 4.2.7 Alternatives for Passing PDFs through Nonlinearities 05 4.2.8 article ilter 14 4.2.9 Sigmapoint Kalman Filt 116 4.2.10 Iterated Sigmapoint. Kalman Filter 121 4.2.11 ISPKF Seeks the Posterior mean 124 4.2.12 Taxonomy of Filters 12 4.3 Batch Discrete-Time Estimation 125 4.3.1 Maximum A Posterior 4.3.2B 4.3.3 Maximum likelihood 4.3.4 Discussion 140 Contents Vll 4.4 Batch Continuous-Time estimation 141 4.4.1 Motion model 4. 4.2 Obseryation model 144 4.4.3 Bayesian Inference 144 4.4.4 Algorithm Summary 145 4.5 Summary 146 4.6 Exercises 147 Biascs, Correspondences, and outliers 148 5. 1 Handling Input/Measurement Biases 149 5.1.1 Bias effects on the Kalman filter 149 5.1.2 Unknown Input Bias 152 5.13 nknown measurement, Bias 154 5.2 Data Association 156 5.2.1 ExTernal Data Associalion 157 5.2.2 Internal Dala association 157 5.3 Handling Outliers 158 5.3.1 RANSAC 159 5.3.2 M-Estimation 160 5.3.3 Covariance Estimation 163 5.4 Summary 165 5.5 Exercises 16:5 Part Ii Three-Dimensional Machinery 167 6 Primer on Thrcc-Dimcnsional Gcomctry 6.1 Vectors and Reference frames 169 6.1.1|efe 6.1.2 Dot Product 170 6.1.3 Cross Product 17 6. 2 Rotations 172 6.2.1 Rotation Matrices 172 6.2.2 Principal rotations 6.2.3 Alternate Rotation Representations 174 6.2.4 Rotational kinematics 180 6.2.5 Perturbing rotations 184 6.3 Poses 188 6.3.1 Transformation Matrices 189 6.3.2 Robotics conventions 190 6.3.3 Frenet-Serret frame 6.4 Sensor Models 195 6.4.1 Perspective Camera. 195 6.4.2 Stereo Camera 202 6.4.3 Range-Azimuth-Elevation 204 6. 4. 4 mertial measurernent Unit 205 6.5 Summary 207 6.6 Exercises 208 Matrix Lie Groups 211 7.1 Geomet 211 7.1.1 Special Orthogonal and Special Euclidean Group 211 7.1.2 Lie algebras 213 7.1.3E tial m 215 7. 1. 4 Adjoint 221 7.1.5 Baker-Campbell-Hausdorff 7.1.6 ist ance, Volume, Integration 7.1.7 Interpolat 234 7. 1. 8 Homogeneous Puints 239 7. 1.9 Calculus and optimization 240 7. 1.10 Identities 7.2K 24 7.2.1 Rotations 7.2.2P 2.3 Linearized rotations 254 7. 2. Linearized poses 7.3 Probability and Statistics 260 7.3.1 (a ussian Random Variables and I'iIs 260 7.3.2U 265 7.3.3 Compounding poses 267 7.3.4 Fusing 7.3.5 Propagating Uncertainty Through a Nonlinear Camera Model 27& 7.4 Summary 286 7.5 Exercises Part I Applications 289 8 Pose Estimation problems 291 8. 1 Point-Cloud Alis 291 8.1.1 Problem Setup 8.1.2 Unit-Length Quaternion Solution 292 8.1.3 otation Matrix Solution 296 8.14 ransformation matrix solution 310 8.2 Point-Cloud Tracking 313 8.2.1 Problem Setup 313 8.2.2 Motion PI 8 2.3 Measurement model 315 8.2.4 EKI Solutio 16 8.2.5 Batch maximum a Posteriori solution 319 8.3 Pose-Graph relaxation 323 3.1 Proble 8.3.2 Batch Maximum Likelihood Solution 324 8. 3.3 Initialization 327 8.3.4 Exploiting Sparsity 327 8.3.5 Chain Example 328 Pose-and -Point estimation problems 331 Bundle adjustment. 3 9.1.1 Problem Setup 332 9.1.2 Measurement Model 332 9.1.3 Maximum Likelihood Solution 336 9.1.4 Exploiting Sp 339 9.1.5 Interpolation Example 342 9.2 Simultaneous Localization and Mapping 346 9. 2. 1 Problem Setup 346 9.2.2 Batch Maximum a Posteriori Solution 347 9.2.3 Exploiting Sparsity 348 9.2.4E 349 10 Continuous-Time estimation 35 10.1 Motion prior 351 10.1.1 General 351 10.1.2 Simplification 255 10.2 Simultaneous Trajectory Estimation and Mapping 356 10.2.1 Problem Setup 357 10.2.2 Measurement model 10.2.3 Batch Maximum a Posteriori solution 10.2.4 Exploiting Spa.rsity 359 10.2.5 Interpolation 360 10.2.6P 361 Re/erences 363 Index 369 【实例截图】
【核心代码】
STATE ESTIMATION FOR ROBOTICS Timothy D. Barfoot SLAM入门经典
Revision history 1 Sept 2015 First draft released 15 Dec 2015 Added a new section to Chapter 3 on recursive discrete-Cime smoothers and their relationship to the batch solution; fixed a few typos 17 Dec 2015 Fixed a lew ty pos in the new section on smoothers 14 Jan 2016 Addcd historical notc regarding Stanley Schmidts role in EkF to Chapter 4 20 Mar 2016 Clarificd in thc introduction and probability chapter that we use a bayesian view of probability and ap proach to estimation in this book 26 Mar 2016 Fixed subscript typos in (3. 126),(3.127),(4.33) (4.34),(4.42) 29 Mar 2016 Added a note on Jacobi's formula to the section on the matrix exponential in Chapter 7 30Mar2016 Added“ squared” in front of“ Mahalanobis distance to match actual definition 8 Apr 2016 Added a footnote at start of probability chapter ac- knowledging that we work with probability densities Lthough the classical formal approach is to start from probability distributions; also made a table in Chap ter 7 fit inside the margins 11 Apr 2016 Fixed ty po in x delinition on SE 3) identity page in Chapter 7 19 Apr 2016 Added acronym list, clarified ISPKF experiment sec- tion, removed embarrassing uses of 'maximum a pri OL 20 Apr 2016 Added index to back 21 Apr 2016 Ran spellchecker on whole book 28 Apr 2016 Adjustcd sentence at start of introduction to rcflcct actual contents of intro 2 May 2016 Addcd missing yo to z in(3. 12); addcd missing ncg- ative sign to (3. 14a 9 May 2016 Fixed a bunch more little typos while proofreading IV Revision History 12 July 2016 Fixed typo in third line of( 9.12 22 July 2016 Various small typos 15 Aug 2016 Clarified the scalar case is deterministic in Section 2.2.8, changc to= in(2.70) 22 Aug 2016 Rewrote the M-estimation section and added a new scction (5. 3. 3)on covariance estimation and its con- nection to M-estimation 29 Aug 2016 Madc a fcw tweaks to Scction 7. 1.9 on Lic group op timization including a new figure(7.3) 16 Nov 2016 Fixed minor typos in text 6 nov 2016 In helpful Lents from Greg Chirikiian 2 Dec 2016 Added missing brackets in(8.126) and followons 10 Dec 2016 A few more typos fixed Contents Acronyms and Abbreviations Notation Foreword Introduction 1.1 A Littlc History 2 Sensors. Measurements. and Problem Definition 1. 3 How This Book is Organized 1345 1.4 Relationship to Other books Part I Estimation Machinery 2 Primer on Probability Theory 2. 1 Probability densily Functions 7999 2.1.1 Definitions 2. 1. 2 Bayes'Rule and Inference 10 2.1.3 Moments of Pdfs 2.1.4 Sample Mean and Covariance 2.1.5 Statistically Independent, Uncorrelated 2.1.6 Shannon and mutual Information 2.1.7 Cramer-Rao Lower Bound and Fisher Information 2.2 Gaussian Probability Density Functions 14 2. 2.1 Definitions 2. 2.2 Isserlis, theorem 15 2.2.3 Joint Gaussian PDFs. Their Factors and Inference 2.2.4 Statistically Independent, Uncorrelated 2.2.5 Linear Change of Variables 19 2. 2.6 Product of gaussians 21 2.2.7 Sherman-Mo 22 2.2.8 Passing a Gaussian Through a Nonlinearity 2.2.9 Shannon information of a gaussian 27 2.2.10 Mutual Information of a. oint Gaussian PDl 29 2.2.11 Cramer-Rao lower Bound applied to (aussian PI)I,s 29 2. 3 Gaussian Processes 31 2. 4 Summary 32 2.5 Exercises 32 Contents Linear-Gaussian estimation 35 3.1 Batch Discrete-Time estimation 35 3.1.1 Problem setul 3.1.2 Maximum a Posteriori 7 3.1.3 Bavesian Inference 42 3.1.4 Existence, Uniqueness, and Observability 3.1.5 MAP Covariance 48 3.2 Recursive discrete- Time Smoothin 3.2. 1 Exploiting Sparsity in the Batch Solution 50 3.2.2 Cholesky Smoother 51 3.2.3 Rauch-Tung-Striebel Smoother 3.3 Recursive Discrete-Time Filtering 56 3.3. 1 Factoring the Batch Solution 57 3.3.2 Kalan Filter via MAP 3.3.3 Kallan Filter via Bayesian Inference 3.3.4 Kalman fille 3.3.5 Kalman Filter Discussion 3.3.6 Error dynamics 3.3.7E nd observability 3.1 Batch Continuous-Timc Estimation 3.4.1 Gaussian Process Regression 3.4.2 A Class of Exactly Sparse Gaussian Process Priors 3.4.3 Linear Time-Invariant Case 81 3.4.4 elationship to Batch D)iscrete-Time Estimation 3.5 Summa 3.6 Exercises 8 4 Nonlinear Non-Gaussian estimation 4.1.1 Full Bayesian Estimation 4.1.2 Maximum a posteriori estimation 4.2 Recursive discrete- Time estimation 94 1.2.1 Problem Setup 94 4.2.2 Bayes Filter 95 4.2.3 Extended Kalman Filter 4.2.4 Generalized Gaussian Filter 4.2.5 Iterated Extended Kalman filter 103 4,2. 6 IeKF is a MAP Estimator 104 4.2.7 Alternatives for Passing PDFs through Nonlinearities 05 4.2.8 article ilter 14 4.2.9 Sigmapoint Kalman Filt 116 4.2.10 Iterated Sigmapoint. Kalman Filter 121 4.2.11 ISPKF Seeks the Posterior mean 124 4.2.12 Taxonomy of Filters 12 4.3 Batch Discrete-Time Estimation 125 4.3.1 Maximum A Posterior 4.3.2B 4.3.3 Maximum likelihood 4.3.4 Discussion 140 Contents Vll 4.4 Batch Continuous-Time estimation 141 4.4.1 Motion model 4. 4.2 Obseryation model 144 4.4.3 Bayesian Inference 144 4.4.4 Algorithm Summary 145 4.5 Summary 146 4.6 Exercises 147 Biascs, Correspondences, and outliers 148 5. 1 Handling Input/Measurement Biases 149 5.1.1 Bias effects on the Kalman filter 149 5.1.2 Unknown Input Bias 152 5.13 nknown measurement, Bias 154 5.2 Data Association 156 5.2.1 ExTernal Data Associalion 157 5.2.2 Internal Dala association 157 5.3 Handling Outliers 158 5.3.1 RANSAC 159 5.3.2 M-Estimation 160 5.3.3 Covariance Estimation 163 5.4 Summary 165 5.5 Exercises 16:5 Part Ii Three-Dimensional Machinery 167 6 Primer on Thrcc-Dimcnsional Gcomctry 6.1 Vectors and Reference frames 169 6.1.1|efe 6.1.2 Dot Product 170 6.1.3 Cross Product 17 6. 2 Rotations 172 6.2.1 Rotation Matrices 172 6.2.2 Principal rotations 6.2.3 Alternate Rotation Representations 174 6.2.4 Rotational kinematics 180 6.2.5 Perturbing rotations 184 6.3 Poses 188 6.3.1 Transformation Matrices 189 6.3.2 Robotics conventions 190 6.3.3 Frenet-Serret frame 6.4 Sensor Models 195 6.4.1 Perspective Camera. 195 6.4.2 Stereo Camera 202 6.4.3 Range-Azimuth-Elevation 204 6. 4. 4 mertial measurernent Unit 205 6.5 Summary 207 6.6 Exercises 208 Matrix Lie Groups 211 7.1 Geomet 211 7.1.1 Special Orthogonal and Special Euclidean Group 211 7.1.2 Lie algebras 213 7.1.3E tial m 215 7. 1. 4 Adjoint 221 7.1.5 Baker-Campbell-Hausdorff 7.1.6 ist ance, Volume, Integration 7.1.7 Interpolat 234 7. 1. 8 Homogeneous Puints 239 7. 1.9 Calculus and optimization 240 7. 1.10 Identities 7.2K 24 7.2.1 Rotations 7.2.2P 2.3 Linearized rotations 254 7. 2. Linearized poses 7.3 Probability and Statistics 260 7.3.1 (a ussian Random Variables and I'iIs 260 7.3.2U 265 7.3.3 Compounding poses 267 7.3.4 Fusing 7.3.5 Propagating Uncertainty Through a Nonlinear Camera Model 27& 7.4 Summary 286 7.5 Exercises Part I Applications 289 8 Pose Estimation problems 291 8. 1 Point-Cloud Alis 291 8.1.1 Problem Setup 8.1.2 Unit-Length Quaternion Solution 292 8.1.3 otation Matrix Solution 296 8.14 ransformation matrix solution 310 8.2 Point-Cloud Tracking 313 8.2.1 Problem Setup 313 8.2.2 Motion PI 8 2.3 Measurement model 315 8.2.4 EKI Solutio 16 8.2.5 Batch maximum a Posteriori solution 319 8.3 Pose-Graph relaxation 323 3.1 Proble 8.3.2 Batch Maximum Likelihood Solution 324 8. 3.3 Initialization 327 8.3.4 Exploiting Sparsity 327 8.3.5 Chain Example 328 Pose-and -Point estimation problems 331 Bundle adjustment. 3 9.1.1 Problem Setup 332 9.1.2 Measurement Model 332 9.1.3 Maximum Likelihood Solution 336 9.1.4 Exploiting Sp 339 9.1.5 Interpolation Example 342 9.2 Simultaneous Localization and Mapping 346 9. 2. 1 Problem Setup 346 9.2.2 Batch Maximum a Posteriori Solution 347 9.2.3 Exploiting Sparsity 348 9.2.4E 349 10 Continuous-Time estimation 35 10.1 Motion prior 351 10.1.1 General 351 10.1.2 Simplification 255 10.2 Simultaneous Trajectory Estimation and Mapping 356 10.2.1 Problem Setup 357 10.2.2 Measurement model 10.2.3 Batch Maximum a Posteriori solution 10.2.4 Exploiting Spa.rsity 359 10.2.5 Interpolation 360 10.2.6P 361 Re/erences 363 Index 369 【实例截图】
【核心代码】
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