A Single-pass Noise Covariance Estimation Algorithm in Multiple-model
Adaptive Kalman Filtering for Non-stationary Systems
Abstract
Estimation of unknown noise covariances in a Kalman filter is a problem
of significant practical interest in a wide array of applications. This
paper presents a single-pass stochastic gradient descent (SGD) algorithm
for noise covariance estimation for use in adaptive Kalman filters
applied to non-stationary systems where the noise covariances can
occasionally jump up or down by an unknown magnitude. Unlike our
previous batch method or our multi-pass decision-directed algorithm, the
proposed streaming algorithm reads measurement data exactly once and has
similar root mean square error (RMSE). The computational efficiency of
the new algorithm stems from its one-pass nature, recursive fading
memory estimation of the sample cross-correlations of the innovations,
and the RMSprop accelerated SGD algorithm. The comparative evaluation of
the proposed method on a number of test cases demonstrates its
computational efficiency and accuracy.