Sequential State and Unknown Parameter Estimation Strategy and its Application to a Sensor Fusion Problem

Soft-sensing and state-space-based methods play crucial roles in fault-tolerant sensor fusion schemes. Kalman filtering is one of the most employed sensor fusion methods. In practice, filtering (or state estimation) is sensitive to initial conditions, variations in model parameters, and faults in sensors and actuators. Cumulatively, these uncertainties that affect the state estimator can be modeled as unknown parameters. In this article, we present the development of a discrete-time minimum variance unbiased estimator (MVUE) that is robust to a class of unknown parameters. The estimation gain of MVUE is designed to facilitate unbiased state estimates in the presence of unknown parameters. We then use the innovations that are generated by the proposed state estimator (MVUE) to estimate the unknown parameters, thus proposing a sequential state and unknown parameter estimation strategy. The development of the decoupled state and unknown parameter estimation strategy is motivated by the fault-tolerant sensor fusion exercise for railway track geometry inspection. This exercise aims to formulate the state-space realization of the track geometry inspection problem to enable sequential state and unknown parameter estimation. The track geometry parameters, initial conditions, and sensor faults are considered unknown parameters for the application. The simulation analysis shows the importance of developing the trinity of the state-space realization for track geometry inspection, the state estimation framework, and the decoupled unknown parameter estimator.