Optimal Measurements in Kalman Filter

Kalman filter, the gold standard of state estimation, has been used widely in many control theory, machine learning, and signal processing applications. In Kalman filter, the minimum variance state estimation is computed by combining the prior estimation and the output of a noise contaminated measurement. A more informative measurement can improve the precision and confidence of the posterior estimation. Finding the optimal experiment for Kalman filter is the topic of ongoing research. In this article, we introduce a new framework for computing the optimal measurement matrix via connecting the theory of Kalman filter to the theory of principal components. Through a couple of examples we show the performance of the algorithm in using available resources effectively by improving the speed and precision of a high-dimensional data acquisition system.