Progressive Bayesian methods formulate the Bayesian update as continuously pseudo-time probability density evolution to perform posterior state estimation.In this paper we derive a novel Gaussian nonlinear filter based on progressive Bayesian framework.A progressive Bayesian solution is firstly derived under linear Gaussian condition.It is proved that the moment evolution of the dynamic system determined by linear Gaussian solution possess the consistency with Kalman-Bucy filter for constant state estimation.For nonlinear system

by using first order Taylor expansion

an approximate solution is derived and the resultant progressive extended Kalman filter is presented.Simulation results demonstrate the superior performance of progressive extended Kalman filter over extended Kalman filter

moreover the performance degrading of nonlinear filtering caused by narrow shape likelihood is avoided.