For nonlinear discrete-time systems where measurements can be randomly delayed by multiple sampling periods, measurements are dependent conditioned on the state trajectory, and the dependence becomes more complicated with the increase of step of random delay. A particle filtering for this system is developed, which is novel in that the likelihood is computed allowing multi step of delay and dependence of measurements. Multi step of delay is dealt with through utilizing the formula of total probability skillfully, and dependence is dealt with through estimating the filtering probability distribution of random delay. The novel particle filtering is applied to two examples to validate its effectiveness and superiority.

对于测量可以被多个采样周期随机延迟的非线性离散时间系统，测量依赖于状态轨迹，并且随着随机延迟步长的增加，依赖性变得更加复杂。为该系统开发了粒子滤波，其新颖之处在于计算似然性允许多步延迟和测量的依赖性。巧妙地利用总概率公式处理多步延迟，通过估计随机延迟的滤波概率分布处理相关性。将新颖的粒子滤波应用于两个例子来验证其有效性和优越性。