Bounding Integrity Risk for Sequential State Estimators in the Presence of Stochastic Modeling Uncertainty

Abstract

A new method is introduced to upper bound integrity risk for sequential state estimators when the autocorrelation functions of measurement noise and disturbance inputs are subject to bounded uncertainties. Integrity risk is defined as the probability of the state estimate error exceeding predefined bounds of acceptability. In the first part of the paper, a new expression is derived that relates the measurement noise and disturbance input autocorrelation functions to the state estimate error vector. Using this relation, an efficient algorithm is developed in the second part of the paper to upper bound the estimation integrity risk when each input autocorrelation function is known to lie between upper and lower bounding functions. Numerical simulations for a one-dimensional position and velocity estimation problem are conducted to demonstrate the practical feasibility and effectiveness of this new bounding method.