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Target tracking using delayed measurements with implicit constraints

In target tracking, standard sensors as radar and EO/IR observe the target with a negligible delay, since the speed of light is much larger than the speed of the target. This contribution studies the case where the ratio of the target and the propagation speed is not negligible, as is the case in sensor networks with microphones, geophones or sonars for instance, where the speed of air, ground waves and water cause a state dependent and stochastic delay of the observations. The proposed approach utilizes a temporary augmentation of the state vector with the observation delay, and sampling based approaches are suggested for modifying standard filters as the extended Kalman filter, unscented Kalman filters and possibly particle filters. An application example with bearing only tracking using a single microphone array is used as an illustration.