Alternating minimization for simultaneous estimation of a latent variable and identification of a linear continuous-time dynamic system

TL;DR

This paper introduces a convex alternating minimization method for jointly estimating a hidden state and identifying a linear continuous-time system from a single input-output pair, grounded in Bayesian MAP estimation.

Contribution

It presents a novel convex optimization framework for simultaneous state estimation and system identification in continuous-time systems, with proven convergence guarantees.

Findings

Convergence to a local minimum is established.

The method effectively estimates latent states and system dynamics.

The approach is based on a Bayesian maximum a posteriori formulation.

Abstract

We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian maximum a posteriori estimators. Our scheme takes the form of a convex alternating minimization, over the trajectories and the dynamic model respectively. We prove its convergence to a local minimum which verifies a two point-boundary problem for the (latent) state variable and a tensor product expression for the optimal dynamics.