Convergence analysis for the Gaussian mixture implementation of the CBMeMBer filter
ZHANG Guang-hua
LIAN Feng
HAN Chong-zhao
WANG Ting-ting
Abstract：The convergence for the Gaussian mixture (GM) implementation of the cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter is studied. This paper proves that the GM–CBMeMBer filter converges uniformly to the true CBMeMBer filter in the linear Gaussian model as the number of Gaussians in the mixture tends to infinity. In addition, this paper proves the extended Kalman (EK) filter approximations of the GM–CBMeMBer filter in weak nonlinear condition—EK–GM–CBMeMBer filter, converges uniformly to the true CBMeMBer filter as the covariance of each Gaussian term tends to zero. The purpose of this paper is to theoretically present the convergence results of the CBMeMBer filter’s GM implementation, perfecting the theoretical research of the CBMeMBer filter for the multi-target tracking problem.
Keywords：multi-target trackingrandom finite setmulti-BernoulliGaussian mixtureconvergence analysis
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 1405-1411 )