Mismatched Filter Design Applied to 1D and 2D Sinusoidal Models

The paper first derives expressions for the MSE and bias of a mismatched linear filter applied to an arbitrary trajectory and describes how such expressions can be used for process noise selection. The performance of such algorithms when applied to the selection of process noise terms for a 1D sinusoidal dynamic model and for a 2D weaving dynamic model is then considered. Previously, the only algorithm specifically designed for process noise selection of 1D sinusoidal models is a 1995 paper by Sudano. Optimal gains are compared with suboptimal techniques in 1D and 2D, including with Sudano’s algorithm. It is shown that the algorithm optimizing over the explicit MSE outperforms the other techniques both in minimizing the MSE and also in guaranteeing that the peak error is never worse than “connecting the dots” between measurements.