Zheng, Wei; Han, Juan; Kong, Weijie; Ren, Dewang The particle filter based on random number searching algorithm for parameter estimation. (English) Zbl 1362.62176 Commun. Stat., Simulation Comput. 46, No. 2, 1401-1413 (2017). Summary: This article addresses the issue of parameter estimation in linear system in the presence of Gaussian noises, under which the random number searching algorithm (LJ (Luus and Jaakola) algorithm) is combined with the Rao-Blackwellised particle filter (RBPF) algorithm. This yields the so-called RBPF algorithm based on LJ (RBPF-LJ). Unlike the mature alternatives of generic particle filter, the parameter particles of RBPF-LJ are set as random numbers that search in the parameter value scope, which is regulated based on the estimation result to track the changes of the unknown parameter. The contrasting simulations show that the proposed RBPF-LJ outperform the RBPF as well as the particle filter based on kernel smoothing contraction algorithm on the estimation of the dynamically linear or nonlinear parameter and it can obtain the similar estimation results on the static parameter if some coefficients are regulated. MSC: 62M20 Inference from stochastic processes and prediction 62F10 Point estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 93E11 Filtering in stochastic control theory Keywords:linear Gaussian system; parameter estimation; particle filter algorithm; random number searching algorithm; LJ (Luus and Jaakola) algorithm; Rao-Blackwellised particle filter (RBPF) PDFBibTeX XMLCite \textit{W. Zheng} et al., Commun. Stat., Simulation Comput. 46, No. 2, 1401--1413 (2017; Zbl 1362.62176) Full Text: DOI References: [1] Apolloni B., 2009 38 (9) pp 1950– [2] Crisan D., 1999 5 pp 292– [3] Dearden R., 2004 pp 826– [4] De Freitas N., 2002 pp 1767– [5] De Vylder F., 1992 10 (4) pp 233– [6] Gordon N. J., 1993 140 (2) pp 107– [7] Kalman R. E., 1960 82 (1) pp 35– [8] Liu B. J., 2001 pp 197– [9] Luus R., 1973 19 (4) pp 760– [10] Mahyuddin M. N., 2014 61 (6) pp 2851– [11] Pitt M. K., 1999 94 (446) pp 590– [12] Sorenson H. W., 1971 7 (4) pp 465– [13] Sunahara Y., 1969 13 (7) pp 9– [14] DOI: 10.1109/ASSPCC.2000.882463 · doi:10.1109/ASSPCC.2000.882463 [15] Yee D., 2008 56 (12) pp 5790– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.