Robust observer control and smoothing in the framework of possibility theory: application to target motion analysis

Machine intelligence for reasoning and decision making under uncertainty has shown a growing importance. There are various methods for model-based autonomous decision making based on observations and prior knowledge both of which are treated as being uncertain. Recent researches demonstrate possibility theory provides effective tool for uncertain knowledge representation and reasoning. Possibility theory is based on the theory of fuzzy sets which is similar to that of the theory of probability in relation to measure theory. In this thesis, two application scenarios, i.e. sensor control and smoothing for bearings-only tracking, are explored. The goal of sensor control in surveillance is to maximize the overall utility of a surveillance system. A new reward function based on possibility theory is developed in order to deal with uncertainties caused by imperfect or mismatched models. In the past, a wide range of solutions based on the Bayesian probabilistic framework had been developed, but unavoidably there is a significant drawback: if the mathematical models are mismatched, they do not work well. Quantitative possibility theory, however, provides the simplest framework for statistical reasoning with imprecise probabilities, and can provide a tool for uncertainty propagation with limited statistical or subjective information. A new method to measure the information gain based on quantitative possibility theory also is developed and combined with the framework of possibilistic filtering. Simulation results show this method produces more robust results than the Rényi-divergence under the Bayesian probabilistic framework in the presence of a model mismatch. Particle smoothing can be used to further refine filtering results by using future measurements, and improve the performance of particle filters on tackling nonlinear, non-Gaussian filtering problems, possibility particle filter based on outer measures has demonstrated superior performance in bearings-only tracking target motion analysis, especially in model-mismatched cases. Anew method based on Forward- Backward smoother and possibility theory is developed to implement a possibilistic smoothing scheme which can work in conjunction with the possibility particle filter to improve accuracy of state estimation. The simulation results demonstrate the possibilistic particle forward-backward smoothing performs well and improves bearings-only tracking performance. Furthermore, possiblistic smoothing also demonstrates better performance than probabilistic smoothing in model-mismatched case.