1. Introduction
1.1. Problem Statement
1.2. Localization Example
1.2.1. Example I: Mobile Robot in a Hallway
1.2.2. Markov Localization
2. The Bayes Filter
2.1. Algorithm I: Bayes Filter
2.2. Example II: Is the door open or close?
2.3. Map Based Localization
2.3.1. Markov Localization
2.3.2. Grid Localization
2.3.3. Montecarlo localization
2.3.4. EKF Localization
3. Gaussian Filters: KF & EKF
3.1. Gaussian Random Variables
3.2. Gaussian Random Vectors
3.3. Linear transformations of GRV
3.4. Example III: Monobot With odometry and position fixes
3.5. Example IV: 1 DOF AUV with constant Velocity Model & Velocity Updates
3.6. Linear Stochastic Systems
3.7. The Kalman Filter
3.7.1. Derivation of the Kalman Filter From the Bayes Filter
3.7.2. Algorithm II: The Kalman Filter
3.7.3. Example III: Monobot with odometry and position updates
3.7.4. Example IV: 1 DOF AUV with constant Velocity Model & Velocity Updates
3.8. The Extended Kalman Filter
3.8.1. Derivation of the EKF as a KF with a 1st order linear approximation of the nonlinear model
3.8.2. Algorithm III: The Extended Kalman Filter
3.8.3. Example V: 3 DOF Mobile Robot with odometry and position fixes
3.9. The Unescended Kalman Filter
3.10. The Information Filter
4. EKF Localization
4.1. Algorithm IV: EKF Localization
4.2. Initialization
4.3. State Prediction
4.4. Data Association
4.5. Mahalanobis Distance
4.6. Algorithm V: ICNN, Individual Compatibility Nearest Neighbour
4.7. State Update
5. EKF SLAM
5.1. Algorithm VI: Simultaneous Localization and Map Building
5.2. Spatial Relationships
5.3. Initialization
5.4. Adding new features
5.4.1. Referenced to the world
5.4.2. Referenced to the robot
5.5. What is the meaning of the correlation?
5.6. State Prediction
5.7. Data Association
5.8. State Update
5.9. What happens to the correlations?
5.10. Adding new features
5.11. Consistency of the EKF-SLAM
5.12. Data Association
5.13. Algorithm VII: Joint Compatibility Branch and Bound
5.14. Relocation
5.14.1. Geometric Constrains
5.14.2. Algorithm VIII: Relocation_RS
5.14.3. Algorithm IX: RS
5.14.4. Locality
5.15. Mapping Large Environments
5.16. Geometric constraints
6. The Histogram Filter
6.1. Algorithm XXX: The discrete Bayes Filter
6.2. Continuous State
6.3. Decomposition Techniques
6.4. Grid Localization
6.4.1. Algorithm XXX: Grid Localization
6.4.2. Grid Resolutions
6.4.3. Computational considerations
7. Particle Filters
7.1. Algorithm XXX: Basic histogram filter
7.2. Algorithm XXX: Basic particle filter
7.3. Importance Sampling
7.4. Properties
7.5. Montecarlo Localization Localization
7.5.1. Algorithm XXX: MCL
7.5.2. Recovery from failures
7.6. Applications