Informatics and Applications
2020, Volume 14, Issue 1, pp 17-23
NUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS II: ADDITIVE NOISE CASE
Abstract
The note is a sequel of investigations initialized in the article Borisov, A. 2019. Numerical schemes of Markov jump process filtering given discretized observations I: Accuracy characteristics. Inform. Appl. 13(4):68-75.
The basis is the accuracy characteristics of the approximated solution of the filtering problem for the state of homogeneous Markov jump processes given the continuous indirect noisy observations. The paper presents a number of the algorithms of their numerical realization together with the comparative analysis. The class of observation systems under investigation is bounded by ones with additive observation noises. This presumes that the observation noise intensity is a nonrandom constant. To construct the approximation, the authors use the left and midpoint rectangle rule of the accuracy order 2 and 3, respectively, and the Gaussian quadrature of the order 5. Finally, the presented numerical schemes have the accuracy of the order 1 /2, 1, and 2.
[+] References (9)
- Borisov, A. 2018. Fil'tratsiya sostoyaniy markovskikh skachkoobraznykhprotsessovpo diskretizovannym nablyu- deniyam [Filtering ofMarkovjump processes by discretized observations]. Informatika i ee Primeneniya - Inform. Appl. 12(3):115-121. doi: 10.14357/19922264180316.
- Borisov, A. 2019. Chislennye skhemy fil'tratsii markov- skikh skachkoobraznykh protsessov po diskretizovannym nablyudeniyam I: kharakteristiki tochnosti [Numerical schemes of Markov jump process filtering given discretized observations I: Accuracy characteristics]. Informatika i ee Primeneniya - Inform. Appl. 13(4):68- 75. doi: 10.14357/19922264190411.
- Wonham, W 1964. Some applications of stochastic differ-ential equations to optimal nonlinear filtering. SIAMJ. Control Optim. 2:347-369.
- Borisov, A. 2018. Wonham filtering by observations with multiplicative noises. Automat. Rem. Contr. 79(1):39-50. doi: 10.1134/S0005117918010046.
- Kloeden, P., and E. Platen. 1992. Numerical solution of stochastic differential equations. Berlin: Springer. 636 p.
- Yin, G., Q. Zhang, and Y. Liu. 2004. Discrete-time approx-imation of Wonham filters. J. Control Theory Applications 2:1-10.
- Platen, E., and R. Rendek. 2010. Quasi-exact approximation of hidden Markov chain filters. Commun. Stoch. Anal. 4(1):129-142.
- Baauerle, N., I. Gilitschenski, and U. Hanebeck. 2016. Exact and approximate hidden Markov chain filters based on discrete observations. Statistics Risk Modeling 32(3-4):159- 176.
- Isaacson, E., and H. Keller. 1994. Analysis of numerical methods. New York, NY: Dover Publications. 541 p.
[+] About this article
Title
NUMERICAL SCHEMES OF MARKOV JUMP PROCESS FILTERING GIVEN DISCRETIZED OBSERVATIONS II: ADDITIVE NOISE CASE
Journal
Informatics and Applications
2020, Volume 14, Issue 1, pp 17-23
Cover Date
2020-03-30
DOI
10.14357/19922264200103
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Markov jump process; optimal filtering; additive and multiplicative observation noises; stochastic differential equation; analytical and numerical approximation
Authors
A. V. Borisov 
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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