OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY
The problem of obtaining the equations for the a posteriori probability density of a stochastic Markov process with a linear measurement model. Unlike common approaches based on consideration as a criterion for optimization of the minimum mean square error of estimation, in this case, the optimizati...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Belarusian National Technical University
2016-03-01
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| Series: | Sistemnyj Analiz i Prikladnaâ Informatika |
| Subjects: | |
| Online Access: | https://sapi.bntu.by/jour/article/view/88 |
| Summary: | The problem of obtaining the equations for the a posteriori probability density of a stochastic Markov process with a linear measurement model. Unlike common approaches based on consideration as a criterion for optimization of the minimum mean square error of estimation, in this case, the optimization criterion is considered the maximum a posteriori probability density of the process being evaluated.The a priori probability density estimated Gaussian process originally considered a differentiable function that allows us to expand it in a Taylor series without use of intermediate transformations characteristic functions and harmonic decomposition. For small time intervals the probability density measurement error vector, by definition, as given by a Gaussian with zero expectation. This makes it possible to obtain a mathematical expression for the residual function, which characterizes the deviation of the actual measurement process from its mathematical model.To determine the optimal a posteriori estimation of the state vector is given by the assumption that this estimate is consistent with its expectation – the maximum a posteriori probability density. This makes it possible on the basis of Bayes’ formula for the a priori and a posteriori probability density of an equation Stratonovich-Kushner.Using equation Stratonovich-Kushner in different types and values of the vector of drift and diffusion matrix of a Markov stochastic process can solve a variety of filtration tasks, identify, smoothing and system status forecast for continuous and for discrete systems. Discrete continuous implementation of the developed algorithms posteriori assessment provides a specific, discrete algorithms for the implementation of the on-board computer, a mobile robot system. |
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| ISSN: | 2309-4923 2414-0481 |