An approach to the test of the sensor information fusion Kalman filter is proposed. It is based on the introduced statistics of mathematical expectation of the spectral norm of a normalized innovation matrix. The approach allows for simultaneous test of the mathematical expectation and the variance of innovation sequence in real time and does not require a priori information on values of the change in its statistical characteristics under faults. Using this approach, fault detection algorithm for the sensor information fusion Kalman filter is developed.

Fault detection in sensor information fusion Kalman filter

For many applications in signal processing and control it is crucial that estimates of the state vector in a dynamic system can be obtained in real time. This poses the problem of producing algorithms that are fast enough to enable online execution. In this article, it is investigated how two of the most popular and powerful state estimation algorithms, the Kalman filter and the particle filter, can be efficiently implemented in parallel on a multicore architecture. The proposed parallel implementations are analyzed in terms of hardware requirements, such as memory bandwidth and available cache memory, to provide the desired speedup. The algorithms are exemplified by and evaluated in an adaptive filtering and a bearings-only tracking application. In the cases when original algorithms have been modified for parallelization, the accuracy of the estimates obtained is evaluated in comparison with that of the sequential algorithm. It is found that linear speedup, in the number of cores used, can indeed be achieved without loss of accuracy, for both state estimation algorithms.

Efficient Parallel Implementation of State Estimation Algorithms on Multicore Platforms

A triangular processor array has been developed for implementing recursive-least-squares computations. The throughput is O(n/sup 0/), which means that data vectors are fed in at a rate that is independent of the problem size. The corresponding least-squares solutions then run out of the array at the same rate. The overall efficiency is roughly 67%. This array is believed to be the first to implement a complete RLS algorithm in a stable and efficient manner. >

A systolic array for recursive least squares computations

The Kalman filter algorithms are computationally intensive, therefore, parallel processing could be an option to meet the timing performance requirements. In this paper detailed research and experimentation have been done for parallel processing of the Kalman filter and the extended Kalman filter based on operating system and multiple general purpose processors that support shared memory. The time comparison of the various methods is analyzed with respect to real-time spacecraft vehicle parameters estimation and a slight time reduction in the parallel Kalman filter has been observed compared with sequential method.

Notice of Violation of IEEE Publication Principles A parallel processing Kalman filter for spacecraft vehicle parameters estimation

Parallelization and cache memory bandwidth demand of a Kalman filter for single output systems on multicore computers are investigated and exemplified by an adaptive filtering application. By breaking the data dependencies through a re-organization of calculations, an almost completely parallel algorithm is obtained. Analysis of the resulting algorithm brings about an estimate of the memory bandwidth necessary for a linear in the number of cores speedup. An evaluation of the parallel algorithm on two different shared-memory multicore architectures has been performed. It is found that linear speedup in the number of used cores can indeed be achieved provided a sufficient memory bandwidth is offered by the hardware.

/pdf/efficient-parallel-implementation-of-a-kalman-filter-for-3dlt7vp1hd.pdf

Efficient parallel implementation of a Kalman filter for single output systems on multicore computational platforms

The paper presents an approach to implementing the parallel Kalman filter. The parallel Kalman filter is computationally intensive and hence complex due to the inherent matrix operations. Often, the filter cannot be computed in real time when the system has a large number of state variables. A method is discussed for achieving almost real-time performance. In addition, a method for determining stability of the Kalman filter is presented. This method involves the use a paradigm that achieves high performance and close to real time results while maintaining accuracy for the Kalman filter. In addition, the paradigm shows an improvement of the processor utilization over other implementations and provides flexibility in terms of the hardware used for implementation.

Parallel processing and stability analysis of the Kalman filter

The paper evaluates a paradigm for the efficient utilization of commercially available processors to implement serial algorithms on a parallel architecture. We present an architecture based on this paradigm as well as an algorithm for the parallel solution of a nonhomogeneous system of linear equations with constant coefficients. Major advantages stem from its systolic-like array structure and the versatility of fully programmable processor elements. The method uses a Givens rotation implementation of the well known QR factorization. Unlike other direct methods of factorization followed by backsubstitution, this implementation of the algorithm avoids the backsubstitution bottleneck. The computational complexity of this feedforward direct method of solving nonsingular systems of linear equations is similar to that of QR matrix factorization. Due to the programmability of the processor in the array, the mapping of this algorithm extends to an entire family of algorithms. We map this family of algorithms onto the novel architecture and present a comprehensive performance analysis. Performance results identify the algorithm/architecture combination as a cost effective, efficient method which exhibits speedup that is directly proportional to the number of processors used.

Hak-Lim Ko

Papers

Parallel processing and stability analysis of the Kalman filter

An algorithm and architecture for the parallel solution of systems of linear equations