Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters

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Journal Title
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Conference article in proceedings
Date
2020-09
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Mcode
Degree programme
Language
en
Pages
6
Series
Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020, IEEE International Workshop on Machine Learning for Signal Processing
Abstract
In this article, we propose automatic differentiation based methods for parameter estimation in non-linear state-space models. We use extended Kalman filter and cubature Kalman filters for approximating the negative log-likelihood (i.e., the energy function) of the parameter posterior distribution and compute the gradients and Hessians of this function by using automatic differentiation of the filter recursions. The proposed approach enables computing MAP estimates and forming Laplace approximations for the parameter posterior without a need for implementing complicated derivative recursions or manual computation of Jacobians. The methods are demonstrated in parameter estimation problems on a pendulum model and coordinated turn model.
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Keywords
Automatic differentiation, Cubature Kalman filter, Extended Kalman filter, Non -linear state space model, Parameter estimation
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Citation
Gorad , A , Zhao , Z & Särkkä , S 2020 , Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters . in Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020 . , 9231844 , IEEE International Workshop on Machine Learning for Signal Processing , IEEE , IEEE International Workshop on Machine Learning for Signal Processing , Espoo , Finland , 21/09/2020 . https://doi.org/10.1109/MLSP49062.2020.9231844