Multi-sensor particle filtering with multi-step randomly delayed measurements

This paper develops particle filtering for multi-sensor systems with randomly delayed measurements, where the general case that random delay can be multi-step rather than one-step or two-step is considered. Moreover, different sensors can have different delay steps and delay probabilities. Random delays are assumed to be mutually independent for different sensors and modelled by a separate sequence of random variables obeying discrete distributions. Since random delay leads to the actual measurements being dependent rather than independent given states, and this dependence becomes more complicated with the increase of random delay step, a new formula of the local likelihood density is proposed and then a new weighting scheme is adopted in particle filtering to deal with these difficulties. The proposed method is applied to two examples to testify its effectiveness and superiority.