Storage efficient particle filters for the out of sequence measurement problem

We propose a particle filter based solution which uses auxiliary fixed point smoothers to the problem of out of sequence measurements. Three different cases, namely, auxiliary extended Kalman smoother, auxiliary unscented Kalman smoother and auxiliary particle smoother are considered for the auxiliary fixed point smoother. The proposed filter which can effectively combine out of sequence measurements with arbitrary delay uses minimum storage requirements as opposed to a recently proposed alternative. The performance of our filters is compared to the other alternative in the literature using a simulated scenario of a target with a highly nonlinear motion dynamics and measurement relations. For this purpose, an extension of the alternative method is also proposed enabling it to work with nonlinear state dynamics.