Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation


Terejanu, G., Singla, P., Singh, T., and Scott, P.


IEEE Transactions on Automatic Control, 56(9).


A nonlinear filter is developed by representing the state probability 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 Kalman filter. The novelty in the proposed method is that the weights of the Gaussian kernels are updated at every time-step, by solving a convex optimization problem posed by requiring the Gaussian sum approximation to satisfy the Fokker-Planck-Kolmogorov equation for continuous-time dynamical systems and the Chapman-Kolmogorov equation 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.

author={Terejanu, G. and Singla, P. and Singh, T. and Scott, P.D.}, 
journal={Automatic Control, IEEE Transactions on}, title={Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation}, 
month={sept. }, 
pages={2151 -2156}, 
keywords={Chapman-Kolmogorov equation;Fokker-Planck-Kolmogorov equation;Gaussian density kernels;Gaussian sum approximation;adaptive Gaussian sum filter;continuous time dynamical system;convex optimization problem;discrete time dynamical system;linear system theory;nonlinear Bayesian estimation;nonlinear filter;numerical simulation;state probability density function;Bayes methods;Gaussian processes;adaptive filters;approximation theory;continuous time filters;convex programming;discrete time filters;linear systems;nonlinear filters;probability;},