Efficient Computation of the Continuous-Discrete Extended Kalman Filter Sensitivities Applied to Maximum Likelihood Estimation

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Abstract

In this paper, we present and compare different methods for computing the likelihood function and its gradient. We consider nonlinear continuous-discrete models described by a system of stochastic differential equations (SDEs) with discrete-time measurements. The problem of maximum likelihood estimation (MLE) is formulated as a nonlinear program (NLP) and it is solved numerically using a gradient-based single shooting algorithm. The estimates of the mean and its covariance are computed using a continuous-discrete extended Kalman filter (CDEKF). We derive analytical expressions for the gradient of the likelihood function. We discuss some aspects of the implementation of MLE for non-stiff systems. In particular, we present an efficient way of computing the state covariance matrix and its gradient using explicit Runge-Kutta schemes. We verify our implementation using a numerical example related to type 1 diabetes and demonstrate how to apply it for nonlinear parameter estimation.
Original languageEnglish
Title of host publicationProceedings of 2019 IEEE 58th Conference on Decision and Control
PublisherIEEE
Publication date2019
Pages6983-6988
ISBN (Print)9781728113975
DOIs
Publication statusPublished - 2019
Event58th IEEE Conference on Decision and Control - Palais des Congrès et des Expositions Nice Acropolis, Nice, France
Duration: 11 Dec 201913 Dec 2019
Conference number: 58
https://cdc2019.ieeecss.org/

Conference

Conference58th IEEE Conference on Decision and Control
Number58
LocationPalais des Congrès et des Expositions Nice Acropolis
CountryFrance
CityNice
Period11/12/201913/12/2019
Internet address

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