Fundamentals of Kalman Filtering: A Practical Approach, Second Edition
Containing numerous real-life problems and examples presented in detail, this text demonstrates the many ways in which Kalman filters can be designed.
TABLE OF CONTENTS Fundamentals of Kalman Filtering: A Practical Approach, Second Edition
Chapter 15: Fading-Memory Filter
Introduction
Even though the main topic of this text is Kalman filtering, there are filters other than Kalman filters. An alternative simple digital-noise filter is known as a fading-memory filter. [1], [2] The fading-memory filter is recursive and weights new measurements more heavily than older measurements. Its structure is nearly identical to the linear polynomial Kalman filter, but its algorithm for gain calculation is much simpler than solving Riccati equations, and the fading-memory filter is therefore less computationally burdensome. This chapter will discuss the properties of the fading-memory filter and via a simple tracking example, compare the performance of both fading-memory and Kalman filters.
[1]Bar-Shalom, Y., and Li, X. R., Estimation and Tracking Principles, Techniques, and Software, Artech House, Boston, 1993, pp. 272 292.
[2]Brookner, E., Tracking and Kalman Filtering Made Easy, Wiley, New York, 1998, pp. 14 66.
Fading-Memory-Filter Structure and Properties
The recursive formulas for first-, second-, and third-order recursive fading-memory filters and their gains are displayed in Table 15.1. We can see from the table that the fading-memory-filter estimate is essentially the old estimate plus a gain times a residual (difference between current measurement and previous estimate). In fact the structure of the fading-memory filter is identical to the linear polynomial Kalman filter. The only difference between the filters is that the fading-memory-filter gains are constants, whereas the Kalman-filter gains are time varying. We can see from Table 15.1 that the fading-memory filter requires less computation than the Kalman filter because the Riccati...
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