A Pipelined Kalman Filter Architecture

Abstract

In this chapter, we employ the relaxed look-ahead technique to pipeline the Kalman filter [Ka160] for recursive least-squares estimation. It was shown in [God74] that Kalman filters result in a much faster rate of convergence in the case of channel equalization than the LMS algorithm. The superior performance of the Kalman filter is at the expense of a 0(N ² ) computational complexity, where N is the filter order. This complexity has been reduced to 0(N) via the development of ‘fast’ Kalman algorithms [Fa178]. It is necessary to point out that the term ‘fast’ implies reduced multiply-add complexity rather than high-speed. Architecturally, the original Kalman algorithm [18] is very suitable for a parallel-processing implementation. Indeed, systolic [Kun91] and parallel processing architectures [Azi91] have been proposed for high-speed Kalman filtering. On the other hand, our architecture employs pipelining, which inherently has a much lower complexity than a parallel processing approach. As we