The design of parallel square-root covariance Kalman filters using algorithm engineering

Abstract

Megson and Comish (1994) have defined techniques using a systematic approach to derive a parallel algorithm for Riccati type equations. In this paper these techniques will be used to derive a full three-dimensional Hierarchical Signal Flow Graph (HSFG) for the square-root covariance Kalman filter (SRCKF) algorithm. This novel flow graph involves matrix-matrix multiplication. Givens rotations and the Schur complement algorithms. Simple projection techniques detailed in (Megson, 1992; S.V. Rajopadhye and R.M. Fujimoto, 1990) are used to form two-dimensional descriptions of the algorithm. From these, parallel algorithms for the SRCKF can be generated using algorithm engineering techniques. As an extended example of algorithm engineering techniques given by Megson (1992, 1994), the parallel algoritjms in the form of systolic architectures proposed by Gaston et al. (1990) and by Brown and Gaston (1994), are derived in detail.