Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering
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...
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| Format: | Article |
| Idioma: | English |
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IEEE
2021-01-01
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| Col·lecció: | IEEE Access |
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| Accés en línia: | https://ieeexplore.ieee.org/document/9475033/ |
| _version_ | 1830092340500365312 |
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| author | Hee-Seung Kim Lingyi Zhang Adam Bienkowski Krishna R. Pattipati |
| author_facet | Hee-Seung Kim Lingyi Zhang Adam Bienkowski Krishna R. Pattipati |
| author_sort | Hee-Seung Kim |
| collection | DOAJ |
| description | 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 were presented in our previous study. This paper presents stochastic gradient descent 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. More significantly, these algorithms 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 algorithms stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated stochastic gradient descent algorithms. The comparative evaluation of the proposed methods on a number of test cases demonstrates their computational efficiency and accuracy. |
| first_indexed | 2024-12-16T17:36:45Z |
| format | Article |
| id | doaj.art-a6da10ed48f4421a93d3eb0a3fd72fdf |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-16T17:36:45Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a6da10ed48f4421a93d3eb0a3fd72fdf2022-12-21T22:22:44ZengIEEEIEEE Access2169-35362021-01-019992209923410.1109/ACCESS.2021.30949639475033Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman FilteringHee-Seung Kim0https://orcid.org/0000-0002-6628-4304Lingyi Zhang1https://orcid.org/0000-0003-4556-6668Adam Bienkowski2https://orcid.org/0000-0002-4738-8749Krishna R. Pattipati3https://orcid.org/0000-0002-0565-181XDepartment of Electrical and Computer Engineering, University of Connecticut, Storrs, CT, USADepartment of Electrical and Computer Engineering, University of Connecticut, Storrs, CT, USADepartment of Electrical and Computer Engineering, University of Connecticut, Storrs, CT, USADepartment of Electrical and Computer Engineering, University of Connecticut, Storrs, CT, USAEstimation 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 were presented in our previous study. This paper presents stochastic gradient descent 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. More significantly, these algorithms 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 algorithms stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated stochastic gradient descent algorithms. The comparative evaluation of the proposed methods on a number of test cases demonstrates their computational efficiency and accuracy.https://ieeexplore.ieee.org/document/9475033/Adaptive Kalman filteringnoise covariance estimationAdamRMS propbold-driverstochastic gradient descent |
| spellingShingle | Hee-Seung Kim Lingyi Zhang Adam Bienkowski Krishna R. Pattipati Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering IEEE Access Adaptive Kalman filtering noise covariance estimation Adam RMS prop bold-driver stochastic gradient descent |
| title | Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering |
| title_full | Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering |
| title_fullStr | Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering |
| title_full_unstemmed | Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering |
| title_short | Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering |
| title_sort | multi pass sequential mini batch stochastic gradient descent algorithms for noise covariance estimation in adaptive kalman filtering |
| topic | Adaptive Kalman filtering noise covariance estimation Adam RMS prop bold-driver stochastic gradient descent |
| url | https://ieeexplore.ieee.org/document/9475033/ |
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