一类耦合的拟线性抛物型PDE系统解的概率解释，许晓明，，本文通过引入一类新型的倒向随机微分方程——带随机违约时间的BSDE,得到了如下耦合的拟线性抛物型PDE系统解的概率解释：egin{equation*}

Sabastian Thrun经典机器人教材

英文名：Mit - Probabilistic Graphical Models - Principles and Techniques.pdf， 中文名：概率图模型,概率图论模型 机器学习选用教材

The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a so-what feeling about Bayesian inference. In fact, this was the author's own prior opinion.

Probabilistic Graphical Models Principles and Techniques。pdf，英文，高清。

这里是 ShowMeAI 持续分享的【开源eBook】系列！内容覆盖机器学习、深度学习、数据科学、数据分析、大数据、Keras、TensorFlow、PyTorch、强化学习、数学基础等各个方向。整理自各平台的原作者公开分享（审核大大请放手） ◉ 简介：数值算法从『可计算的量』中近似地计算出『难以处理的量』，或者说，从数据中推断出一个潜在的量。因此计算程序可被视作 learning machine，使用贝叶斯推理来建立更灵活有效的计算算法。概率数值计算正式确立了『机器学习』和『应用数学』之间的联系。本书提供了大量的背景材料（还有数据、工作实例、练习及解答），更适用于AI、CS、统计学、应用数学的研究生。 ◉ 目录： 第一章：数学背景 第二章：整合 第三章：线性代数 第四章：局部优化 第五章：全局优化 第六章：求解常微分方程 第七章：前沿 第八章：习题答案

SALBP-1-模拟退火 该算法是一种概率方法，用于逼近简单装配线平衡问题的全局最优值。 Linux构建 要构建此应用程序，请在父目录中执行make build 。 用法 ./salbp1-sa[OPTIONS]... OPTIONS: -c (SALBP1 maximum time per station. Default: 6) -t (initial temperature. Default: 1) -l (stop condition. Default: 0.000001) -d (cools temperature to (temperature_decay*temperature

布卢姆 该软件包实现了通用用法的布隆过滤器。 它使用FNV和一个简单的技巧来计算所需的k个散列。 特征 初始化Bloom Filter仅需要过滤器的大小和哈希函数的数量。 使用Uint8Array TypedArray来确保最小的内存占用。 使用位操作对我们的位集进行操作意味着更好的性能（需要进行一次测试）。 FNV哈希和简单的线性哈希用作哈希函数。 可以通过将不同的元素类型（数字，字符串）转换为字符串来插入它们。 用法 const BloomFilter = require ( 'bloomf' ) ; const filterSize = 10 ; const kHashes = 3 ; const bl = new BloomFilter ( filterSize , kHashes ) ; bl . insert ( 3 ) ; bl . insert ( "bloblo"

Probability and Computing - Randomized Algorithms and Probabilistic Analysis中文版 作者Michael Mitzenmacher， Eli Upfal

英文版高清带书签 Contents Preface xvii Acknowledgments xix I Basics 1 1 Introduction 3 1.1 Uncertainty in Robotics 3 1.2 Probabilistic Robotics 4 1.3 Implications 9 1.4 Road Map 10 1.5 Teaching Probabilistic Robotics 11 1.6 Bibliographical Remarks 11 2 Recursive State Estimation 13 2.1 Introduction 13 2.2 Basic Concepts in Probability 14 2.3 Robot Environment Interaction 19 2.3.1 State 20 2.3.2 Environment Interaction 22 2.3.3 Probabilistic Generative Laws 24 2.3.4 Belief Distributions 25 2.4 Bayes Filters 26 2.4.1 The Bayes Filter Algorithm 26 2.4.2 Example 28 2.4.3 Mathematical Derivation of the Bayes Filter 31 2.4.4 The Markov Assumption 33 2.5 Representation and Computation 34 2.6 Summary 35 2.7 Bibliographical Remarks 36 2.8 Exercises 36 3 Gaussian Filters 39 3.1 Introduction 39 3.2 The Kalman Filter 40 3.2.1 Linear Gaussian Systems 40 3.2.2 The Kalman Filter Algorithm 43 3.2.3 Illustration 44 3.2.4 Mathematical Derivation of the KF 45 3.3 The Extended Kalman Filter 54 3.3.1 Why Linearize? 54 3.3.2 Linearization Via Taylor Expansion 56 3.3.3 The EKF Algorithm 59 3.3.4 Mathematical Derivation of the EKF 59 3.3.5 Practical Considerations 61 3.4 The Unscented Kalman Filter 65 3.4.1 Linearization Via the Unscented Transform 65 3.4.2 The UKF Algorithm 67 3.5 The Information Filter 71 3.5.1 Canonical Parameterization 71 3.5.2 The Information Filter Algorithm 73 3.5.3 Mathematical Derivation of the Information Filter 74 3.5.4 The Extended Information Filter Algorithm 75 3.5.5 Mathematical Derivation of the Extended Information Filter 76 3.5.6 Practical Considerations 77 3.6 Summary 79 3.7 Bibliographical Remarks 81 3.8 Exercises 81 4 Nonparametric Filters 85 4.1 The Histogram Filter 86 4.1.1 The Discrete Bayes Filter Algorithm 86 4.1.2 Continuous State 87 4.1.3 Mathematical Derivation of the Histogram Approximation 89 4.1.4 Decomposition Techniques 92 4.2 Binary Bayes Filters with Static State 94 4.3 The Particle Filter 96 4.3.1 Basic Algorithm 96 4.3.2 Importance Sampling 100 4.3.3 Mathematical Derivation of the PF 103 4.3.4 Practical Considerations and Properties of Particle Filters 104 4.4 Summary 113 4.5 Bibliographical Remarks 114 4.6 Exercises 115 5 Robot Motion 117 5.1 Introduction 117 5.2 Preliminaries 118 5.2.1 Kinematic Configuration 118 5.2.2 Probabilistic Kinematics 119 5.3 Velocity Motion Model 121 5.3.1 Closed Form Calculation 121 5.3.2 Sampling Algorithm 122 5.3.3 Mathematical Derivation of the Velocity Motion Model 125 5.4 Odometry Motion Model 132 5.4.1 Closed Form Calculation 133 5.4.2 Sampling Algorithm 137 5.4.3 Mathematical Derivation of the Odometry Motion Model 137 5.5 Motion and Maps 140 5.6 Summary 143 5.7 Bibliographical Remarks 145 5.8 Exercises 145 6 Robot Perception 149 6.1 Introduction 149 6.2 Maps 152 6.3 Beam Models of Range Finders 153 6.3.1 The Basic Measurement Algorithm 153 6.3.2 Adjusting the Intrinsic Model Parameters 158 6.3.3 Mathematical Derivation of the Beam Model 162 6.3.4 Practical Considerations 167 6.3.5 Limitations of the Beam Model 168 6.4 Likelihood Fields for Range Finders 169 6.4.1 Basic Algorithm 169 6.4.2 Extensions 172 6.5 Correlation-Based Measurement Models 174 6.6 Feature-Based Measurement Models 176 6.6.1 Feature Extraction 176 6.6.2 Landmark Measurements 177 6.6.3 Sensor Model with Known Correspondence 178 6.6.4 Sampling Poses 179 6.6.5 Further Considerations 180 6.7 Practical Considerations 182 6.8 Summary 183 6.9 Bibliographical Remarks 184 6.10 Exercises 185 II Localization 189 7 Mobile Robot Localization: Markov and Gaussian 191 7.1 A Taxonomy of Localization Problems 193 7.2 Markov Localization 197 7.3 Illustration of Markov Localization 200 7.4 EKF Localization 201 7.4.1 Illustration 201 7.4.2 The EKF Localization Algorithm 203 7.4.3 Mathematical Derivation of EKF Localization 205 7.4.4 Physical Implementation 210 7.5 Estimating Correspondences 215 7.5.1 EKF Localization with Unknown Correspondences 215 7.5.2 Mathematical Derivation of the ML Data Association 216 7.6 Multi-Hypothesis Tracking 218 7.7 UKF Localization 220 7.7.1 Mathematical Derivation of UKF Localization 220 7.7.2 Illustration 223 7.8 Practical Considerations 229 7.9 Summary 232 7.10 Bibliographical Remarks 233 7.11 Exercises 234 8 Mobile Robot Localization: Grid And Monte Carlo 237 8.1 Introduction 237 8.2 Grid Localization 238 8.2.1 Basic Algorithm 238 8.2.2 Grid Resolutions 239 8.2.3 Computational Considerations 243 8.2.4 Illustration 245 8.3 Monte Carlo Localization 250 8.3.1 Illustration 250 8.3.2 The MCL Algorithm 252 8.3.3 Physical Implementations 253 8.3.4 Properties of MCL 253 8.3.5 Random Particle MCL: Recovery from Failures 256 8.3.6 Modifying the Proposal Distribution 261 8.3.7 KLD-Sampling: Adapting the Size of Sample Sets 263 8.4 Localization in Dynamic Environments 267 8.5 Practical Considerations 273 8.6 Summary 274 8.7 Bibliographical Remarks 275 8.8 Exercises 276 III Mapping 279 9 Occupancy Grid Mapping 281 9.1 Introduction 281 9.2 The Occupancy Grid Mapping Algorithm 284 9.2.1 Multi-Sensor Fusion 293 9.3 Learning Inverse Measurement Models 294 9.3.1 Inverting the Measurement Model 294 9.3.2 Sampling from the Forward Model 295 9.3.3 The Error Function 296 9.3.4 Examples and Further Considerations 298 9.4 Maximum A Posteriori Occupancy Mapping 299 9.4.1 The Case for Maintaining Dependencies 299 9.4.2 Occupancy Grid Mapping with Forward Models 301 9.5 Summary 304 9.6 Bibliographical Remarks 305 9.7 Exercises 307 10 Simultaneous Localization and Mapping 309 10.1 Introduction 309 10.2 SLAM with Extended Kalman Filters 312 10.2.1 Setup and Assumptions 312 10.2.2 SLAM with Known Correspondence 313 10.2.3 Mathematical Derivation of EKF SLAM 317 10.3 EKF SLAM with Unknown Correspondences 323 10.3.1 The General EKF SLAM Algorithm 323 10.3.2 Examples 324 10.3.3 Feature Selection and Map Management 328 10.4 Summary 330 10.5 Bibliographical Remarks 332 10.6 Exercises 334 11 The GraphSLAM Algorithm 337 11.1 Introduction 337 11.2 Intuitive Description 340 11.2.1 Building Up the Graph 340 11.2.2 Inference 343 11.3 The GraphSLAM Algorithm 346 11.4 Mathematical Derivation of GraphSLAM 353 11.4.1 The Full SLAM Posterior 353 11.4.2 The Negative Log Posterior 354 11.4.3 Taylor Expansion 355 11.4.4 Constructing the Information Form 357 11.4.5 Reducing the Information Form 360 11.4.6 Recovering the Path and the Map 361 11.5 Data Association in GraphSLAM 362 11.5.1 The GraphSLAM Algorithm with Unknown Correspondence 363 11.5.2 Mathematical Derivation of the Correspondence Test 366 11.6 Efficiency Consideration 368 11.7 Empirical Implementation 370 11.8 Alternative Optimization Techniques 376 11.9 Summary 379 11.10 Bibliographical Remarks 381 11.11 Exercises 382 12 The Sparse Extended Information Filter 385 12.1 Introduction 385 12.2 Intuitive Description 388 12.3 The SEIF SLAM Algorithm 391 12.4 Mathematical Derivation of the SEIF 395 12.4.1 Motion Update 395 12.4.2 Measurement Updates 398 12.5 Sparsification 398 12.5.1 General Idea 398 12.5.2 Sparsification in SEIFs 400 12.5.3 Mathematical Derivation of the Sparsification 401 12.6 Amortized Approximate Map Recovery 402 12.7 How Sparse Should SEIFs Be? 405 12.8 Incremental Data Association 409 12.8.1 Computing Incremental Data Association Probabilities 409 12.8.2 Practical Considerations 411 12.9 Branch-and-Bound Data Association 415 12.9.1 Recursive Search 416 12.9.2 Computing Arbitrary Data Association Probabilities 416 12.9.3 Equivalence Constraints 419 12.10 Practical Considerations 420 12.11 Multi-Robot SLAM 424 12.11.1 Integrating Maps 424 12.11.2 Mathematical Derivation of Map Integration 427 12.11.3 Establishing Correspondence 429 12.11.4 Example 429 12.12 Summary 432 12.13 Bibliographical Remarks 434 12.14 Exercises 435 13 The FastSLAM Algorithm 437 13.1 The Basic Algorithm 439 13.2 Factoring the SLAM Posterior 439 13.2.1 Mathematical Derivation of the Factored SLAM Posterior 442 13.3 FastSLAM with Known Data Association 444 13.4 Improving the Proposal Distribution 451 13.4.1 Extending the Path Posterior by Sampling a New Pose 451 13.4.2 Updating the Observed Feature Estimate 454 13.4.3 Calculating Importance Factors 455 13.5 Unknown Data Association 457 13.6 Map Management 459 13.7 The FastSLAM Algorithms 460 13.8 Efficient Implementation 460 13.9 FastSLAM for Feature-Based Maps 468 13.9.1 Empirical Insights 468 13.9.2 Loop Closure 471 13.10 Grid-based FastSLAM 474 13.10.1 The Algorithm 474 13.10.2 Empirical Insights 475 13.11 Summary 479 13.12 Bibliographical Remarks 481 13.13 Exercises 482 IV Planning and Control 485 14 Markov Decision Processes 487 14.1 Motivation 487 14.2 Uncertainty in Action Selection 490 14.3 Value Iteration 495 14.3.1 Goals and Payoff 495 14.3.2 Finding Optimal Control Policies for the Fully Observable Case 499 14.3.3 Computing the Value Function 501 14.4 Application to Robot Control 503 14.5 Summary 507 14.6 Bibliographical Remarks 509 14.7 Exercises 510 15 Partially Observable Markov Decision Processes 513 15.1 Motivation 513 15.2 An Illustrative Example 515 15.2.1 Setup 515 15.2.2 Control Choice 516 15.2.3 Sensing 519 15.2.4 Prediction 523 15.2.5 Deep Horizons and Pruning 526 15.3 The Finite World POMDP Algorithm 527 15.4 Mathematical Derivation of POMDPs 531 15.4.1 Value Iteration in Belief Space 531 15.4.2 Value Function Representation 532 15.4.3 Calculating the Value Function 533 15.5 Practical Considerations 536 15.6 Summary 541 15.7 Bibliographical Remarks 542 15.8 Exercises 544 16 Approximate POMDP Techniques 547 16.1 Motivation 547 16.2 QMDPs 549 16.3 Augmented Markov Decision Processes 550 16.3.1 The Augmented State Space 550 16.3.2 The AMDP Algorithm 551 16.3.3 Mathematical Derivation of AMDPs 553 16.3.4 Application to Mobile Robot Navigation 556 16.4 Monte Carlo POMDPs 559 16.4.1 Using Particle Sets 559 16.4.2 The MC-POMDP Algorithm 559 16.4.3 Mathematical Derivation of MC-POMDPs 562 16.4.4 Practical Considerations 563 16.5 Summary 565 16.6 Bibliographical Remarks 566 16.7 Exercises 566 17 Exploration 569 17.1 Introduction 569 17.2 Basic Exploration Algorithms 571 17.2.1 Information Gain 571 17.2.2 Greedy Techniques 572 17.2.3 Monte Carlo Exploration 573 17.2.4 Multi-Step Techniques 575 17.3 Active Localization 575 17.4 Exploration for Learning Occupancy Grid Maps 580 17.4.1 Computing Information Gain 580 17.4.2 Propagating Gain 585 17.4.3 Extension to Multi-Robot Systems 587 17.5 Exploration for SLAM 593 17.5.1 Entropy Decomposition in SLAM 593 17.5.2 Exploration in FastSLAM 594 17.5.3 Empirical Characterization 598 17.6 Summary 600 17.7 Bibliographical Remarks 602 17.8 Exercises 604 Bibliography 607 Index 639