2]
0.0.1 #1
0.0.1 #1
Robust Kalman Filtering
1. State-Space Models and Outliers
1.1 Outliers and Robustness Problems
1.1.1 Example 1
1.1.2 Additive Outliers
1.1.3 Innovation Outliers
1.1.4 Other Types of Outliers
1.2 Examples of AO's and IO's in XploRe
1.2.1 Example 2
1.2.2 Example 3
1.3 Problem Setup
2. Classical Method: Kalman Filter
2.1 Features of the Classical Kalman Filter
2.2 Optimality of the Kalman Filter
3. Robustifying Least Squares: the rLS filter
3.1 Derivation
3.2 Calibration
3.3 Examples
3.3.1 Example 5
3.3.2 Example 5
3.3.3 Example 6
3.4 Possible Extensions
4. Robustified Regression: the rIC filter
4.1 Filtering Problem as a Regression Problem
4.2 Robust Regression Estimates
4.3 Variants: Separate Clipping
4.4 Criterion for the Choice of
4.5 Examples
4.5.1 Example 7
4.5.2 Example 8
4.5.3 Example 9
4.6 Possible Extensions
5. Excursion: Generating Multivariate Robust Influence Curves for Normal Scores
5.1 Definition of IC
5.2 General Algorithm
5.2.1 Arbitrary Dimension
5.2.2 One Dimension
5.3 Polar Representation and Explicite Calculations
5.3.1 Polar Representation
5.3.2 Explicit Calculations for the Absolute Value
5.4 Integrating along the Directions
5.5 Short Description of the Auxiliary Routines Used
Bibliography