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Noise Covariance Estimation in Adaptive Kalman Filtering via sequential Mini-batch Stochastic Gradient Descent Algorithms

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posted on 29.05.2021, 12:18 by Hee-Seung KimHee-Seung Kim, Lingyi ZhangLingyi Zhang, Adam BienkowskiAdam Bienkowski, Krishna Pattipati

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.

Funding

N00014-18-1-1238

N00014-21-1-2187

N00173-16-1-G905

80NSSC19K1076

History

Email Address of Submitting Author

hee-seung.kim@uconn.edu

Submitting Author's Institution

University of Connecticut

Submitting Author's Country

South Korea