Handling spuriosity in the Kalman filter

The Kalman filter, which is in popular use in various branches of engineering, is essentially a least squares procedure. One well-recognized concern in this least squares procedure is its non-robustness to spuriously generated observations that give rise to outlying observations, rendering the Kalman filter unstable, with devastating consequences in some situations. Much evidence exists that data almost always contain a small proportion of spuriously generated observations, and indeed, one wild observation can make the Kalman filter unstable. To handle this, we introduce a new recursive estimation scheme which is found to be robust to spurious observations. Examples are given to illustrate the new scheme.