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A Single-pass Noise Covariance Estimation Algorithm in Adaptive Kalman Filtering for Non-stationary Systems
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  • Hee-Seung Kim ,
  • Lingyi Zhang ,
  • Adam Bienkowski ,
  • Krishna Pattipati
Hee-Seung Kim
University of Connecticut, University of Connecticut

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Lingyi Zhang
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Adam Bienkowski
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Krishna Pattipati
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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.