New Estimators for Mixed Stochastic and Set Theoretic Uncertainty Models: The Vector Case

This work presents new results for state estimation based on noisy observations suffering from two different types of uncertainties. The first uncertainty is a stochastic process with given statistics. The second uncertainty is only known to be bounded, the exact underlying statistics are unknown. State estimation tasks of this kind typically arise in target localization, navigation, and sensor data fusion. A new estimator has been developed, that combines set theoretic and stochastic estimation in a rigorous manner. The estimator is efficient and, hence, well-suited for practical applications. It provides a continuous transition between the two classical estimation concepts, because it converges to a set theoretic estimator, when the stochastic error goes to zero, and to a Kalman filter, when the bounded error vanishes. In the mixed noise case, the new estimator provides solution sets that are uncertain in a statistical sense.