A The Linear Regression Kalman Filter

Abstract

The Linear Regression Kalman Filter (LRKF, Sect. 4.2) has the following properties:

• 1 it linearizes the process and measurement functions by statistical linear regression of the functions through a number of regression points in state space;

• 2 it defines the uncertainty due to linearization errors on the linearized process or measurement function as the sample covariance matrix of the deviations between the function values of the nonlinear and the linearized function in the regression points.

This appendix contains the derivation of the process and measurement update of this LRKF (Sects. A.2 and A.3). First, Sect. A.1 describes the linear regression formulas.