Sequential Filtering in the Presence of Uniform Measurement Errors

This paper presents a sequential filtering strategy using observations corrupted with uniform measurement noise. While the Kalman filter remains the best linear estimator of the state, other filtering techniques provide minimum variance optimal estimates, a trait only enjoyed by the Kalman filter when the underlying noises are, in fact, Gaussian. This work develops a new approximate optimal estimator for uniform measurement noises. The resulting recursion requires just slightly more computational time to complete a measurement update than the Kalman filter, which generally cannot be claimed by other optimal strategies such as the particle or Gaussian mixture filters.