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...
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| Format: | Article |
| Language: | English |
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Belarusian National Technical University
2016-03-01
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| Series: | Системный анализ и прикладная информатика |
| Subjects: | |
| Online Access: | https://sapi.bntu.by/jour/article/view/88 |
| _version_ | 1826557717907505152 |
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| author | A. A. Lobaty Y. F. Yacina N. N. Arefiev |
| author_facet | A. A. Lobaty Y. F. Yacina N. N. Arefiev |
| author_sort | A. A. Lobaty |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T01:20:43Z |
| format | Article |
| id | doaj.art-86dcd4a0466d481a8385b6fe12c40655 |
| institution | Directory Open Access Journal |
| issn | 2309-4923 2414-0481 |
| language | English |
| last_indexed | 2025-03-14T08:33:02Z |
| publishDate | 2016-03-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Системный анализ и прикладная информатика |
| spelling | doaj.art-86dcd4a0466d481a8385b6fe12c406552025-03-02T13:01:34ZengBelarusian National Technical UniversityСистемный анализ и прикладная информатика2309-49232414-04812016-03-0101354179OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITYA. A. Lobaty0Y. F. Yacina1N. N. Arefiev2Belarusian National Technical UniversityBelarusian National Technical UniversityBelarusian National Technical UniversityThe 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.https://sapi.bntu.by/jour/article/view/88mathematical model, state space, stochastic equations, optimization criteria, the expectation, the demolition of the vector, diffusion matrix |
| spellingShingle | A. A. Lobaty Y. F. Yacina N. N. Arefiev OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY Системный анализ и прикладная информатика mathematical model, state space, stochastic equations, optimization criteria, the expectation, the demolition of the vector, diffusion matrix |
| title | OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY |
| title_full | OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY |
| title_fullStr | OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY |
| title_full_unstemmed | OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY |
| title_short | OPTIMAL ESTIMATION OF RANDOM PROCESSES ON THE CRITERION OF MAXIMUM A POSTERIORI PROBABILITY |
| title_sort | optimal estimation of random processes on the criterion of maximum a posteriori probability |
| topic | mathematical model, state space, stochastic equations, optimization criteria, the expectation, the demolition of the vector, diffusion matrix |
| url | https://sapi.bntu.by/jour/article/view/88 |
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