Gaussian approximate filter with progressive measurement update

In this paper, under Bayesian estimation framework, a new Gaussian approximate (GA) filter with progressive measurement update is derived through approximating intermediate progressive joint probability density function (PDF) of state and measurement as Gaussian, and it provides a general framework to design progressive Gaussian filtering. In the proposed method, the continuous PDF needn't to be discretized, and the proposed GA filter has higher Gaussian approximation accuracy of joint PDF of state and measurement than standard GA filter and existing iterated Kalman type filters. The superior performance of the proposed method as compared with existing methods is illustrated in a numerical example concerning bearing only tracking.