Frequency-weighted state estimation with application to estimation in the presence of sensor bias

Abstract

This paper introduces a general state-estimation methodology, frequency-weighted linear quadratic Gaussian estimation (FWLQGE) that enables a control designer to modify a standard LQG estimator to account for sensor imperfections. Using FWLQGE, a designer can account explicitly for colored sensor noise (i.e., the noise spectrum varies as a function of frequency). Alternatively, the designer can use the frequency dependent degree of freedom as a mechanism to specify the relative confidence in a sensor's output. Presented is a technique for solving the FWLQGE problem with existing software tools by simply augmenting the system matrices. Also presented is an example demonstrating how the procedure can be used to account for sensor biases. Here, FWLQGE is compared with two classic methods: state augmentation and post-sensor filtering, It is shown that while all methods can be made to yield equivalent estimators, FWLQGE incorporates a design degree of freedom that is intuitively appealing allowing an explicit trade off between bias rejection and estimator performance. Simulation and experimental results are presented.