Linear Time-Varying Parameter Estimation: Maximum A Posteriori Approach via Semidefinite Programming

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We study the problem of identifying a linear time-varying output map from measurements and linear time-varying system states, which are perturbed with Gaussian observation noise and process uncertainty, respectively. Employing a stochastic model as prior knowledge for the parameters of the unknown output map, we reconstruct their estimates from input/output pairs via a Bayesian approach to optimize the posterior probability density of the output map parameters. The resulting problem is a non-convex optimization, for which we propose a tractable linear matrix inequalities approximation to warm-start a first-order subsequent method. The efficacy of our algorithm is shown experimentally against classical Expectation Maximization and Dual Kalman Smoother approaches.

Original languageEnglish
Pages (from-to)73-78
Number of pages6
JournalIEEE Control Systems Letters
Publication statusPublished - 2024

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  • Estimation
  • identification
  • linear matrix inequalities
  • optimization
  • semidefinite programming


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