Optimal and Robust State Estimation

6Unbiased FIR State Estimation

The arithmetic mean is the most probable value.

Carl F. Gauss [53], p. 244

It is usually taken for granted that the right method for determining the constants is the method of least squares.

Karl Pearson [146], p. 266

6.1 Introduction

Optimal state estimation requires information about noise and initial values, which is not always available. The requirement of initial values is canceled in the optimal unbiased or ML estimators, which still require accurate noise information. Obviously, these estimators can produce large errors if the noise statistics are inaccurate or the noise is far from Gaussian. In another extreme method of state estimation that gives UFIR estimates corresponding to the LS, the observation mean is tracked only under the zero mean noise assumption. Designed to satisfy only the unbiasedness constraint, such an estimator discards all other requirements and in many cases justifies suboptimality by being more robust. The great thing about the UFIR estimator is that, unlike OFIR, OUFIR, and ML FIR, it only needs an optimal horizon of points to minimize MSE. It is worth noting that determining requires much less effort than noise statistics. Given , the UFIR state estimator, which has no other tuning factors, appears to be the ...