Analysis of the Effects of Model Mismatch and Flat MMF for Estimating Particle Motion

In this report, we analyze the performance degradation due to three classes of model mismatch: parameter jumping, undermodeling and overmodeling, in estimating the particle motion by using the orthogonal polynomials to model the trajectory. We find that these model mismatches make the \u27optimal estimator\u27 to have large bias and mean squared error. For the case of undermodeling, the estimation error increases, in general, without a bound as the observation interval increases. We then propose the Finite Lifetime Alternately Triggered Multiple Model Filter (FLAT MMF), as a solution. FLAT MMF is a filter composed of a set of K identical conventional state estimation filters, each triggered alternately. After the last filter is triggered, the oldest one is triggered again and so on. The structure of Multiple Model Filter is used to combine these estimates optimally, in the sense of minimum mean squared error. We find that the ratio of weightings in FLAT MMF are related to some independent non-central χ2 random variables. Consequently, we show that the FLAT MMF can provide an estimate that follows abrupt changes in the trajectory and has the small bias for undermodeling. For the case of overmodeling or the case that the trajectory model matches to the actual motion, the estimate does not degrade significantly. A number of simulations are conducted to illustrate the estimation performance degradation due to the model mismatches for the conventional Kalman filter and the performance improvement as the proposed FLAT MMF is used