Kalman filter and extended Kalman filter using one-step optimal measurement selection

Motivated by problems in waveform-agile sensing systems, we consider the application of an optimal measurement selection technique to discrete-time Kalman and extended Kalman filters. The optimal linear measurement is selected prior to taking the observation at each step of the filter. The measurement is described through a measurement matrix B that depends on the prior state covariance, the available energy, and the observation noise variance. The tracking performance of this method is compared to that obtained using other measurement techniques. Our simulations suggest that the performance improvement is most pronounced when the dimension of the state space is large, there is a large eigenvalue spread in the prior covariance, and the signal-to-noise ratio is low.