Gaussian likelihood based Bernoulli particle filter for non-uniformly quantized interval measurement

Traditional Bayesian estimation uses stochastic but precise measurements or measurement models to estimate the state of a dynamic system. However, in many practical applications, interval measurements representing measurements affected by bounded errors or bias of typically unknown distribution are common and convenient. Recently, joint target detection and tracking in the presence of interval measurements, the quantization observations in wireless sensor networks or the unknown system delays in the distributed surveillance system for example, has drawn much attention. While, partial knowledge of the quantization strategy and the system delay distribution is available to be introduced into the method scheme, which is promising to improve the performance. More specifically, based on the prior knowledge of the non-uniformly quantized interval measurement, a Gaussian likelihood based Bernoulli particle filter algorithm for interval measurement is proposed in this paper. The Gaussian measurement likelihood is defined as the probability density function with the weighted interval center as Gaussian mean and the effective interval length as 3σ confidence. The interval coefficient for calculating the weighted interval center and the target state are estimated jointly and recursively. Simulation results show that the proposed scheme is effective in joint target state and interval coefficient estimate. Furthermore, the proposed method obtains lower position RMSE and higher probability of target existence, compared with the generalized likelihood based Bernoulli particle filter method.