An implementation method for the discrete Kalman filter with applications to large-scale systems. (English) Zbl 0553.93070
An interesting implementation procedure is developed for use in a covariance propagation problem involving a discrete Kalman filter. Using a matrix continued fraction (MCF) method for the calculation of the covariance matrix, the final implementation requires one matrix inversion involving a sequence of controllability matrices, observability matrices, and an initial condition matrix. Using various procedures, a numerical comparison in terms of computing time and computer storage is made between the approach developed here and the conventional method. This algorithm is intended to be used as an alternative method to implement the Kalman filter. For certain classes of large-scale systems, the MCF method provides both a reduction of computer time and computer storage. An example is worked to illustrate the applicability of the approach presented here.
MSC:
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 30B70 | Continued fractions; complex-analytic aspects |
| 62M20 | Inference from stochastic processes and prediction |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 93A15 | Large-scale systems |
| 68Q25 | Analysis of algorithms and problem complexity |
| 93E11 | Filtering in stochastic control theory |
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