Linear Time-Varying Parameter Estimation
Maximum A Posteriori Approach via Semidefinite Programming
S. Vakili (TU Delft - Team Manuel Mazo Jr)
Mohammad Khosravi (TU Delft - Team Khosravi)
P. Esfahani (TU Delft - Team Peyman Mohajerin Esfahani)
M. Mazo Espinosa (TU Delft - Team Manuel Mazo Jr)
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Abstract
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.