Parallel Kalman filtering on the Connection Machine

Abstract

A parallel algorithm for square root Kalman filtering is developed and implemented on the Connection Machine (CM). The algorithm makes efficient use of parallel prefix or scan operations which are primitive instructions in the CM. Performance measurements show that the CM filter runs in time linear in the state vector size. This represents a great improvement over serial implementations which run in cubic time. A specific multiple target tracking application is also considered, in which several targets (e.g., satellites, aircrafts and missiles) are to be tracked simultaneously, each requiring one or more filters. A parallel algorithm is developed which, for fixed size filters, runs in constant time, independent of the number of filters simultaneously processed. serial implementations which run in cubic time. A specific multiple target tracking application is also considered, in which several targets (e.g., satellites, aircrafts and missiles) are to be tracked simultaneously, each requiring one or more filters. A parallel algorithm is developed which, for fixed size filters, runs in constant time, independent of the number of filters simultaneously processed.

Parallelization of the Kalman filter on multicore computational platforms

“…However, many systems do not require the square root form to maintain numerical stability. As it will be shown here, the implementation and parallelization can be made far more efficient for the KF in the standard form, than the implementation proposed in Palis and Krecker (1990).…”

“…For filtering problems that require special attention to numerical stability, the square root formulation is to prefer (Bierman, 1977). Parallelization of the square root form of the KF is investigated in Palis and Krecker (1990), where mainly the Givens rotation step is parallelized. However, many systems do not require the square root form to maintain numerical stability.…”

“…However, many of these schemes are hardware-specific with respect to such architectures as e.g. the Connection Machine (Palis & Krecker, 1990), distributed memory machines (Lyster et al, 1997) and systolic arrays (Shaffer, 1987) and thus are not directly suitable for a multicore implementation. Other parallelization solutions suffer from the presence of sequentially executed sections that prevent significant speedup (Tang, Cui, & Chen, 2005;Willner, Chang, & Dunn, 1976).…”

Fault-Tolerant Recursive Least-Squares Computations on a Mesh-Connected Parallel Processor

“…Another study employs the connection machineexamined to implement a Kalman filtering algorithm [23]. The intention of the study was to prove that commercial hardware systems are feasible alternatives to specialized systolic arrays and networks.…”

Small SIMD Matrices for CERN High Throughput Computing

“…Even though optimizing Kalman filter tracking is an old problem [21], existing implementations are not efficient for many small systems.…”