This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems in the presence of multi-sensor measurement delay. The delay occurs in a multi-step and asynchronous manner, and the delay probability of each sensor is assumed to be known or unknown. Firstly, a new model is constructed to describe the measurement process, based on which a new particle filter is developed with the ability to fuse multi-sensor information in the case of known delay probability.In addition, an online delay probability estimation module is introduced in the particle filtering framework, which leads to another new filter that can be implemented without the prior knowledge of delay probability. More importantly, since there is no complex iterative operation, the resulting filter can be implemented recursively and is suitable for many real-time applications. Simulation results show the effectiveness of the proposed filters.
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