State Feedback Control and Kalman Filtering with MATLAB/Simulink Tutorials

8Addressing Computational Issues in KF

8.1 Introduction

Computational issues in real‐time applications when using the Kalman filter are very important. It sometimes happens that the Kalman filter is correct in theory and in simulation studies, however, they will not work in a real system. One of the main causes for this type of failures is the finite precision arithmetic existed in the computational devices such as micro‐controllers or other low‐cost computational devices.

The objective of this chapter is to address the real‐time computational issues in the Kalman filter. There are two topics discussed. The first topic is related to the computation of Kalman gain in real‐time. Because it requires the operation of matrix inversion, in the absence of a library, the implementation using a micro‐controller presents a challenge in itself. To address these potential challenges for real‐time applications, Section 8.2 introduces the sequential Kalman filter in order to avoid the matrix inversion in the computation of Kalman gain. In a digital processor, the arithmetic is finite precision, meaning that only a certain number of bits are used to represent the numbers from the Kalman filter equations. In Section 8.3 the Kalman filter using factorization is discussed which may have the potential to double the accuracy and is relevant for real‐time implementations. MATLAB tutorials are given ...