Noise Covariance Estimation in Adaptive Kalman Filtering via sequential
Mini-batch Stochastic Gradient Descent Algorithms
Abstract
Estimation of unknown noise covariances in a Kalman filter is a problem
of significant practical interest in a wide array of applications.
Although this problem has a long history, reliable algorithms for their
estimation were scant, and necessary and sufficient conditions for
identifiability of the covariances were in dispute until recently.
Necessary and sufficient conditions for covariance estimation and a
batch estimation algorithm. This paper presents stochastic gradient
descent (SGD) algorithms for noise covariance estimation in adaptive
Kalman filters that are an order of magnitude faster than the batch
method for similar or better root mean square error (RMSE) and are
applicable to non-stationary systems where the noise covariances can
occasionally jump up or down by an unknown magnitude. The computational
efficiency of the new algorithm stems from adaptive thresholds for
convergence, recursive fading memory estimation of the sample
cross-correlations of the innovations, and accelerated SGD algorithms.
The comparative evaluation of the proposed method on a number of test
cases demonstrates its computational efficiency and accuracy.