Neural-Network-Augmented Tobit Kalman Filter With Adaptive Covariance for Censored State Estimation

Abstract

To estimate states from censored or saturated measurements, the Tobit Kalman Filter (TKF) was developed. However, model errors or mismatches can impair the performance of the TKF, resulting in lower estimation accuracy. In order to increase the TKF’s accuracy and robustness, this study proposes three significant improvements. First, the correlation between the states and the expectation of censoring indicator variables, which predict the occurrence of saturation, is explicitly incorporated into the filtering framework. Second, a neural network, trained online, is augmented to the process model, which allows the filter to dynamically adjust to model mismatches. Third, the theoretical convergence analysis and simulations, based on accepted benchmarks in the literature, are used to assess our proposed Neural-Network-Augmented Tobit Kalman Filter (NN-TKF). Simulation results demonstrate that the NN-TKF outperforms the standard TKF and other estimation methods.