  In this letter, a new filtering technique to solve a nonlinear state
estimation problem has been developed. It is well known that for a nonlinear
system, the prior and posterior probability density functions (pdf) are
non-Gaussian in nature. However, in this work, they are assumed as Gaussian and
subsequently mean, and covariance of them are calculated. In the proposed
method, nonlinear functions of process dynamics and measurement are expressed
in a polynomial form with the help of Taylor series expansion. In order to
calculate the prior and the posterior mean and covariance, the functions are
integrated over the Gaussian pdf with the help of Gaussian integral. The
performance of the proposed method is tested in two nonlinear state estimation
problems. The simulation results show that the proposed filter provides more
accurate result than other existing deterministic sample point filters such as
cubature Kalman filter, unscented Kalman filter, etc.
