MSE-optimal measurement dimension reduction in Gaussian filtering

We present a framework for measurement dimension reduction in Gaussian filtering, defined in terms of a linear operator acting on the measurement vector. This operator is optimized to minimize the Cramér-Rao bound of the estimate's mean squared error (MSE), yielding a measurement subspace from which elements minimally worsen the filter MSE performance, as compared to filtering with the original measurements. This is demonstrated with Kalman filtering in a linear Gaussian setting and various non-linear Gaussian filters with an on-line adaption of the operator. The proposed method improves computational time in exchange for a quantifiable and sometimes negligibly worsened MSE of the estimate.