Systolic array designs for Kalman filtering

Systolic Kalman filter (SKF) designs based on a triangular array (triarray) configuration are presented. A least squares formulation, which is an expanded matrix representation of the state space iteration, is adopted to develop an efficient iterative QR triangularization and consecutive data prewhitening formulations. This formulation has advantages in both numerical accuracy and processor utilization efficiency. Moreover, it leads naturally to pipelined architectures such as systolic or wavefront arrays. For an n state and m measurement dynamic system, the SKF triarray design uses n(n+3)/2 processors and requires only 4n+m timesteps to complete one iteration of prewhitened Kalman filtering system. This means a speedup factor of approximately n²/4 when compared with a sequential processor. Also proposed for the colored noise case are data prewhitening triarrays which offer compatible speedup performance for the preprocessing stage. Based on a comparison of several competing alternatives, the proposed array processor may be considered a most efficient systolic or wavefront design for Kalman filtering