Adaptive Gaussian Sum Filter for
Gabriel Terejanu, Puneet Singla, Tarunraj Singh, Peter Dale Scott · 2011
A nonlinear filter is developed by representing the state prob- ability density function by a finite sum of Gaussian density kernels whose mean and covariance are propagated from one time-step to the next using linear system theory methods such as extended Kalman filter or unscented Kalmanfilter. The novelty in the proposed method is that the weights of the Gaussian kernels are updated at every time-step, by solving a convex opti- mization problem posed by requiring the Gaussian sum approximation to satisfy the Fokker-Planck-Kolmogorov equation for continuous-time dy- namical systems and the Chapman-Kolmogorovequation for discrete-time dynamical systems. The numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function. Index Terms—Gaussian sum filter (GSF), Kalman filter, probability den- sity function (pdf).