Manoeuvring Target Tracking Using a Multiple-Model Bootstrap Filter

Abstract

The Kalman filter (Sorensen 1966) is the optimal solution to the Bayesian estimation problem for a given linear, stochastic, state-space system with additive Gaussian noise sources of known statistics. The solution is possible since all densities in the system are Gaussian, and remain so under system transformation, and thus closed-form expressions for these are always available in terms of their first and second moments. However, if the model used by the filter does not match the actual system dynamics, the filter will tend to diverge, such that the actual errors fall outside the range predicted by the filter’s estimate of the error covariance. By introducing some degree of uncertainty into the filter, small deviations from the actual system can be tracked. This also ensures that the filter gain does not fall to zero, and thus measurements are always used to update the state estimate. The practicality of this approach for large model mismatch problems is limited however.