Observation-based filtering of state of a nonlinear dynamical system with random delays

We present a model of a stochastic observation system that allows for time delays between the received observation and the actual state of the observed object that formed these observations. Such delays can occur when observing the movement of an object in a water medium using acoustic sonars and have a significant impact on the accuracy of position tracking. We present equations to solve the optimal mean square filtering problem. Since the practical use of the optimal solution is barely feasible due to its computational complexity, we pay the main attention to an alternative, suboptimal but computationally efficient approach. Specifically, we adapted a conditional minimax nonlinear filter (CMNF) to the proposed model and formulated sufficient existence conditions for its estimate. We conducted a computational experiment on a model that is close to practical needs. The results of the experiment show the effectiveness of CMNF in the model considered. However, they also show a significant decrease in the quality of estimation compared to the model without random observation delays, which can be considered as a motivation for further research into the model and related problems.