Discrete-Time Kalman Filter Error Bounds in the Presence of Misspecified Measurements

The performance of a discrete time Kalman filter in the presence of a misspecified measurement equation is considered. Analytical and easily calculable numerical bounds for the increment in filtering error energy are provided in an adversarial setting by formulating a high-dimensional optimization problem which is solvable via its Lagrange dual, a scalar convex optimization problem. The performance bounds are obtained for finite and infinite horizons.