Fuzzy Rules for Recursive Bayesian Filtering in Multi-Process State Models
Systems under the influence of uncertain dynamic processes can pose a distinct challenge for predictive estimators, especially in the case where there are multiple non-linear processes influencing the system state to varying degree. In a wide range of application domain problems, including sensing data and target tracking, there are complex system processes that occur simultaneously or consecutively at unknown intervals. The general case can by modelled using a Markov-switching state space model, where each SSM represents a process affecting the state. The challenge lies in the weighting of each process’s effect. Current solutions use a switching probability matrix to weight an inference that propagates a set of parallel Kalman filters. However, the switching probability can drastically affect the results, and in real world cases it is often unknown and potentially highly variable. The alternative approach presented approaches to problem by combining aspects of fuzzy inference with a recursive Bayesian inference. Based on predictions of the state in each SSM of the switching model, the corresponding pdfs of the estimated observation can be considered membership functions to fuzzy sets over each component process. Each process can be considered a linguistic value in the overall SSM. The resulting derivation gives great flexibility and has an intuitive setup. Under certain conditions, inferring the switching probability can be shown to be equivalent to probabilistic models, such as a Gaussian mixture model.