实例介绍
【实例简介】
《state estimation for robotics》这本书非常全面的介绍了SLAM后端优化所需要的相关理论知识
Revision history 1 Sept 2015 First draft released 15 Dec 2015 Added a new section to Chapter 3 on recursive discrete-time smoothers and their relationship to the batch solution; fixed a few typos 17 Dec 2015 Fixed a lew ly pos in the new section on smoothers 14 an 2016 Added historical note regarding Stanley Schmidts role in EKF Lo Chapter 4 20 Mar 2016 Clarified in the introduction and probability chapter Chat 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 Chaptcr 7 30Mar2016Aded“ 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 although 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 typo in x definition on SE(3) identity page in Chapte 19 Apr 2016 Added acronym list, clarified ISPKF experiment sec tion. removed embarrassing uses of "maximum a pri- ori' 20 Apr 2016 Added index to back 21 Apr 2016 Ran spellchecker on whole book 28 Apr 2016 Adjusted sentence at start of introduction to reflect actual contents of intro 2 May 2016 Added missing yo to z in(3. 12); added missing neg- alive sign lo(3.14a) 9 May 2016 Fixed a bunch more little typos while proofreading Contents Acronyms and Abbreviations Notation Foreword 1 Introduction 1.1 A Littlc History 1.2 Sensors measurements and problem definition 1.3 How This Book is Organized v11345 1.4 Relationship to Other Books Part I Estimation Machinery 2 Primer on Probability Theory 2. 1 Probability density Functions 2.1.1 Definitions 79990 2.1.2 Bayes'Rule and Inference 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 13 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-Morrison-Woodbury Identity 22 2.2.8 Passing a Gaussian Through a onlinearit 23 2.2.9 Shannon Information of a gaussian 2 2.2.10 Mutual Information of a.oint Gaussian PDF 8 2.2.11 Cramer-Rao Lower Bound Applied to Gaussian PDFs 29 2. 3 Gaussian Processes 30 2. 41 Summary 31 2.5 Exercises 32 Linear-Gaussian estimation 3.1 Batch Discrete-Time Estimat 35 3.1.1 Problem se 3.1.2Ma A Posterion 3.1.3B 42 3.1. 4 Existe d Observability 3.1.5 MAP Covariance 48 3.2 Recursive Discrete- Time thing 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 Kalman Filter via MAP 3.3.3 Kalman Filter via Bavesian Inference 3.3.4 Kalman Filter via Gain Optimization 3.3.5 Kalman Filter Discussion 68 3.3.6 Error Dynam 3.3.7 Existence, Uniqueness, and Observability 70 3.4 Batch Continuous-Timc Estimation 3.4.1 Gaussian Process regression 3.4.2 A Class of Exactly Sparse Gaussian Process Priors 75 3. 4.3 Linear Time-Invariant Case 3.4. 4 Relationship to Batch Discrete-Time stimation 3.5 Summar 3.6 Exercises 86 4 Nonlinear Non-Gaussian estimation 4.1 Introduct 4.1.1 Full Bayesian Estimation 90 4.1.2 Maxin 4.2 Recursive Discrete-Time estimation 91 4.2.1 Problem S 4.2. 2 Bavcs Filter 95 4.2.3 Extended Kalman Filter 4.2. 4 Gcncralizcd Gaussian Filter 4.2.5 Iterated Extended Kalman Filter 103 4.2.6 EkF is a map estimator 104 4.2.7 Alternatives for Passing PDFs through nonlinearities 4.2.8 Particle filter 114 4.2.9Si point kalma Filt 116 2.10 Iterated Sigmapoint, Ka 121 4.2.11 ISPKF Seeks the Posterior mean 124 4.2.12 Taxonomy of Filters 125 4.3 Batch Discrete-Time estimation 125 4.3.1 Maximum A Posterior 126 4.3.2 Bavesian Inference 4. 3.3 Maximum Likelihood 135 4.34D 140 Contents 4.4 Batch continuous-Time estimation 141 4.4.1 Motion model 141 44.2 Observation model 144 4.4.3 Bayesian Inference 144 4.4.4 Algorithm Summary 145 4.5 Summary 146 4.6 Exercises 47 5 Biases, Correspondences, and Outliers 8 5.1 Handling Input/Measurement biases 149 5.1.1 Bias Effects on the Kalman filte 149 5.1.2 Unknown Input bias 152 5.1.3 Unknown measurement bias 5.2 Data associatioil 156 5.2.1 External Data Association 157 5.2.2 Intcrnal Data Association 157 5. 3 Handling Outliers 158 5.3.1 RANSAC 159 5.3.2 M-Estil 160 5.1 Summary 162 5.5 Exercises 162 Part Ii Three-Dimensional Machinery 165 6 Primer on Thrcc-Dimcnsional Gcomctry 167 6.1 Vectors and reference frames 16′ G.1.1 Refe 168 6.1.2 Dot Product 6.1.3 Cross Product 169 6.2 Rotations 170 6.2.1 Rotation matrices 170 6.2.2 Principa I Rota.tions 171 6.2.3 Alternate Rotation RepresentatioNs 172 6.2.4 Rotational Kinematics 6.2.5P g Rotations 182 63P 186 6.3.1 Transformation matrices 187 obotics conventions G 3.3 Frenet-Serret Frame 190 6. 4 Sensor Models 193 6.1.1 Perspective Camera 193 6.4.2 Stereo Camera 200 6.4.3 Range-Azimuth-Elevation 6.4. 4 Inertial Measurement Unit 203 6.5 Sullnarv 205 6.6 Exercise 206 7 Matrix Lie Groups 209 7.1 Geomety 7.1.1 cial Orthogonal and special Euclidean G 209 7.1.2 Lie Algebras 21 7.1.3E tial m 213 7. 1.4 Adjoints 219 7. 1. 5 Baker-Campbell-Hausdorff 7.1.6 ista Volu 7.1.7 Interpolation 232 7. 1.9 Calculus and Optimization 7.1.10 Identitics 7.2 Kinematics 7.2.1 Rotations 246 7. 2.2 Poses 7.2.3 Linearized Rotations 252 7.2.1 Linearized p 7.3 Probability and statistics 258 7.3.1 Gaussian Random Varia bles and pips 7.3.2U Linty on a Rotated Vector 263 7.3.3C 265 7.3.4 Fusing Pose 7.3.5 Propagating Uncertainty Through a Nonlincar Camera Modcl 276 7.4S1 2S3 7.5 Exercises 284 Part Ili Applications 287 8 Pose estimation problems 289 8.1 Point-Cloud Alignment 8.1.1 Problcm Setup 290 8.1.2 Unit-Length Quaternion Solution 290 8. 1.3 Rotation Matrix Solution atrix solution 8.2 Point-Cloud Tracking 311 8.2.1 Problem Setup 311 8.2.2 Motion priors 8.2.3 Measurement model 313 8.2.4 kF Solution 714 8.2.5 Batch Maximum a Posteriori solution 8.3 Pose-Graph relaxation 321 8.3.1 Problem Set 8.3.2 Batch Maximum Likelihood Solution 8.3.3 Initialization 325 8.3.4 Exploiting Sp 325 8.3.5 Chain Examp 32 Contents IX Pose-and-Point estimation problems 329 9. 1 Bundle Adjustment 9.1.1 Problem Setup 330 9.1.2 Measurement Model 330 9.1.3 Maximum Likelihood Solution 334 9.1.4 Exploiting Sparsity 9.1.5 Interpolation Example 340 9.2 Simultaneous Localization and Mapping 344 9.2.1 Problem Setup 344 9.2.2 Batch Maximum a Posteriori Solution 345 9.2.3 Exploiting Sparsity 9.2.4 Example 347 10 Continuous-Time estimation 249 10.1 Motion prior 349 349 10.1.2 Simplificati 10.2 Simultaneous trajectory Estimation and Mapping 10.2.1 Problem Setup 355 10.2.2 Measurement Model 10.2.3 Batch Maximum a Posteriori solution 356 10.2.4 xploiting Sparsity 10.2.5 Interpolation 10.2.6Pc 359 Refe 361 Inde 【实例截图】
【核心代码】
《state estimation for robotics》这本书非常全面的介绍了SLAM后端优化所需要的相关理论知识
Revision history 1 Sept 2015 First draft released 15 Dec 2015 Added a new section to Chapter 3 on recursive discrete-time smoothers and their relationship to the batch solution; fixed a few typos 17 Dec 2015 Fixed a lew ly pos in the new section on smoothers 14 an 2016 Added historical note regarding Stanley Schmidts role in EKF Lo Chapter 4 20 Mar 2016 Clarified in the introduction and probability chapter Chat 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 Chaptcr 7 30Mar2016Aded“ 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 although 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 typo in x definition on SE(3) identity page in Chapte 19 Apr 2016 Added acronym list, clarified ISPKF experiment sec tion. removed embarrassing uses of "maximum a pri- ori' 20 Apr 2016 Added index to back 21 Apr 2016 Ran spellchecker on whole book 28 Apr 2016 Adjusted sentence at start of introduction to reflect actual contents of intro 2 May 2016 Added missing yo to z in(3. 12); added missing neg- alive sign lo(3.14a) 9 May 2016 Fixed a bunch more little typos while proofreading Contents Acronyms and Abbreviations Notation Foreword 1 Introduction 1.1 A Littlc History 1.2 Sensors measurements and problem definition 1.3 How This Book is Organized v11345 1.4 Relationship to Other Books Part I Estimation Machinery 2 Primer on Probability Theory 2. 1 Probability density Functions 2.1.1 Definitions 79990 2.1.2 Bayes'Rule and Inference 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 13 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-Morrison-Woodbury Identity 22 2.2.8 Passing a Gaussian Through a onlinearit 23 2.2.9 Shannon Information of a gaussian 2 2.2.10 Mutual Information of a.oint Gaussian PDF 8 2.2.11 Cramer-Rao Lower Bound Applied to Gaussian PDFs 29 2. 3 Gaussian Processes 30 2. 41 Summary 31 2.5 Exercises 32 Linear-Gaussian estimation 3.1 Batch Discrete-Time Estimat 35 3.1.1 Problem se 3.1.2Ma A Posterion 3.1.3B 42 3.1. 4 Existe d Observability 3.1.5 MAP Covariance 48 3.2 Recursive Discrete- Time thing 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 Kalman Filter via MAP 3.3.3 Kalman Filter via Bavesian Inference 3.3.4 Kalman Filter via Gain Optimization 3.3.5 Kalman Filter Discussion 68 3.3.6 Error Dynam 3.3.7 Existence, Uniqueness, and Observability 70 3.4 Batch Continuous-Timc Estimation 3.4.1 Gaussian Process regression 3.4.2 A Class of Exactly Sparse Gaussian Process Priors 75 3. 4.3 Linear Time-Invariant Case 3.4. 4 Relationship to Batch Discrete-Time stimation 3.5 Summar 3.6 Exercises 86 4 Nonlinear Non-Gaussian estimation 4.1 Introduct 4.1.1 Full Bayesian Estimation 90 4.1.2 Maxin 4.2 Recursive Discrete-Time estimation 91 4.2.1 Problem S 4.2. 2 Bavcs Filter 95 4.2.3 Extended Kalman Filter 4.2. 4 Gcncralizcd Gaussian Filter 4.2.5 Iterated Extended Kalman Filter 103 4.2.6 EkF is a map estimator 104 4.2.7 Alternatives for Passing PDFs through nonlinearities 4.2.8 Particle filter 114 4.2.9Si point kalma Filt 116 2.10 Iterated Sigmapoint, Ka 121 4.2.11 ISPKF Seeks the Posterior mean 124 4.2.12 Taxonomy of Filters 125 4.3 Batch Discrete-Time estimation 125 4.3.1 Maximum A Posterior 126 4.3.2 Bavesian Inference 4. 3.3 Maximum Likelihood 135 4.34D 140 Contents 4.4 Batch continuous-Time estimation 141 4.4.1 Motion model 141 44.2 Observation model 144 4.4.3 Bayesian Inference 144 4.4.4 Algorithm Summary 145 4.5 Summary 146 4.6 Exercises 47 5 Biases, Correspondences, and Outliers 8 5.1 Handling Input/Measurement biases 149 5.1.1 Bias Effects on the Kalman filte 149 5.1.2 Unknown Input bias 152 5.1.3 Unknown measurement bias 5.2 Data associatioil 156 5.2.1 External Data Association 157 5.2.2 Intcrnal Data Association 157 5. 3 Handling Outliers 158 5.3.1 RANSAC 159 5.3.2 M-Estil 160 5.1 Summary 162 5.5 Exercises 162 Part Ii Three-Dimensional Machinery 165 6 Primer on Thrcc-Dimcnsional Gcomctry 167 6.1 Vectors and reference frames 16′ G.1.1 Refe 168 6.1.2 Dot Product 6.1.3 Cross Product 169 6.2 Rotations 170 6.2.1 Rotation matrices 170 6.2.2 Principa I Rota.tions 171 6.2.3 Alternate Rotation RepresentatioNs 172 6.2.4 Rotational Kinematics 6.2.5P g Rotations 182 63P 186 6.3.1 Transformation matrices 187 obotics conventions G 3.3 Frenet-Serret Frame 190 6. 4 Sensor Models 193 6.1.1 Perspective Camera 193 6.4.2 Stereo Camera 200 6.4.3 Range-Azimuth-Elevation 6.4. 4 Inertial Measurement Unit 203 6.5 Sullnarv 205 6.6 Exercise 206 7 Matrix Lie Groups 209 7.1 Geomety 7.1.1 cial Orthogonal and special Euclidean G 209 7.1.2 Lie Algebras 21 7.1.3E tial m 213 7. 1.4 Adjoints 219 7. 1. 5 Baker-Campbell-Hausdorff 7.1.6 ista Volu 7.1.7 Interpolation 232 7. 1.9 Calculus and Optimization 7.1.10 Identitics 7.2 Kinematics 7.2.1 Rotations 246 7. 2.2 Poses 7.2.3 Linearized Rotations 252 7.2.1 Linearized p 7.3 Probability and statistics 258 7.3.1 Gaussian Random Varia bles and pips 7.3.2U Linty on a Rotated Vector 263 7.3.3C 265 7.3.4 Fusing Pose 7.3.5 Propagating Uncertainty Through a Nonlincar Camera Modcl 276 7.4S1 2S3 7.5 Exercises 284 Part Ili Applications 287 8 Pose estimation problems 289 8.1 Point-Cloud Alignment 8.1.1 Problcm Setup 290 8.1.2 Unit-Length Quaternion Solution 290 8. 1.3 Rotation Matrix Solution atrix solution 8.2 Point-Cloud Tracking 311 8.2.1 Problem Setup 311 8.2.2 Motion priors 8.2.3 Measurement model 313 8.2.4 kF Solution 714 8.2.5 Batch Maximum a Posteriori solution 8.3 Pose-Graph relaxation 321 8.3.1 Problem Set 8.3.2 Batch Maximum Likelihood Solution 8.3.3 Initialization 325 8.3.4 Exploiting Sp 325 8.3.5 Chain Examp 32 Contents IX Pose-and-Point estimation problems 329 9. 1 Bundle Adjustment 9.1.1 Problem Setup 330 9.1.2 Measurement Model 330 9.1.3 Maximum Likelihood Solution 334 9.1.4 Exploiting Sparsity 9.1.5 Interpolation Example 340 9.2 Simultaneous Localization and Mapping 344 9.2.1 Problem Setup 344 9.2.2 Batch Maximum a Posteriori Solution 345 9.2.3 Exploiting Sparsity 9.2.4 Example 347 10 Continuous-Time estimation 249 10.1 Motion prior 349 349 10.1.2 Simplificati 10.2 Simultaneous trajectory Estimation and Mapping 10.2.1 Problem Setup 355 10.2.2 Measurement Model 10.2.3 Batch Maximum a Posteriori solution 356 10.2.4 xploiting Sparsity 10.2.5 Interpolation 10.2.6Pc 359 Refe 361 Inde 【实例截图】
【核心代码】
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