arXiv subjects

Milad Banitalebi Dehkordi

Publications and source records attributed to Milad Banitalebi Dehkordi.

3 recordsLinked to original sources

arXiv2026

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY↗

arXiv2026

Joint State-Parameter Inference Enhances Estimation Performance in Model-Based Digital Therapeutics for Type 1 Diabetes

Blood glucose estimation is the cornerstone of model-based decision support (DS) and Automated Insulin Delivery (AID) systems. Control systems that rely on physiologic/compartmental models depend heavily on model parameterization, which is either defined using population values or personalized through the user's data. Often, the model parameters are defined as constants. However, under real-world free-living conditions, fixed parameters can limit the accurate reconstruction and estimation of glucose levels and states. In this paper, we propose and discuss a recursive filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying physiological models for Type 1 Diabetes (T1D). Specifically, we employ a Rao-Blackwellized Stein Variational Gradient Descent (RBSVGD) filter to compute the joint posterior distributions of model states and parameters. The proposed approach is applied to the Hovorka glucose-insulin model and validated using data generated by the the Oregon Health & Science University (OHSU) simulator across 20 virtual patients. We perform a comparative analysis against: (i) a standard Extended Kalman Filter (EKF) with fixed model parameters, and (ii) an Augmented Extended Kalman Filter (AEKF) for joint state-parameter estimation. The results demonstrate that the proposed RBSVGD-based framework outperforms both EKF and AEKF approaches not only in terms of the accuracy of glucose estimation, but also in terms of estimated model parameters.

eess.SY↗

arXiv2026

Learning reduced-order latent linear models for Kalman filtering of nonlinear systems

We propose a filtering-oriented end-to-end learning framework to identify reduced-order models explicitly tailored for state estimation in high-dimensional nonlinear systems. An autoencoder (AE) neural network learns a low-dimensional latent representation of the state together with a lifting map to the original space, while a reduced-order linear time-invariant (RO-LTI) model describes the latent dynamics. The AE and RO-LTI model are trained jointly by minimizing a multi-objective loss that combines reconstruction error with a filtering objective based on a differentiable Kalman filter, ensuring that the reduced-order model is tailored for the downstream state estimation task. At inference, filtering is performed entirely in the latent space using the RO-LTI model, and the estimated state is mapped back to the original space via the decoder. Unlike conventional two-stage approaches, in which a reduced-order model is first identified for system approximation and a filter is subsequently designed on top of it, the proposed framework learns a task-oriented reduced-order model whose parameters are shaped entirely by filtering performance rather than system approximation accuracy alone. We further quantify probabilistic bounds on the performance gap between full-order and reduced-order filters using conformal predictions, which do not require assumption on data distribution. The approach is validated on a heat diffusion benchmark, where the full temperature field is reconstructed from sparse measurements.

eess.SY↗