State Estimation Considering Negative Information with Switching Kalman and Ellipsoidal Filtering

State estimation concepts like the Kalman filter heavily rely on potentially noisy sensor data. In general, the estimation quality depends on the amount of sensor data that can be exploited. However, missing observations do not necessarily impair the estimation quality but may also convey exploitable information on the system state. This type of information-noted as negative information-often requires specific measurement and noise models in order to take advantage of it. In this paper, a hybrid Kalman filter concept is employed that allows using both stochastic and set-membership representations of information. In particular, the latter representation is intended to account for negative information, which can often be easily described as a bounded set in the measurement space. Depending on the type of information, the filtering step of the proposed estimator adaptively switches between Gaussian and ellipsoidal noise representations. A target tracking scenario is studied to evaluate and discuss the proposed concept.