Filtering Jump Markov Systems with Partially Known Dynamics: A Model-Based Deep Learning Approach

TL;DR

The paper addresses real-time state estimation in Jump Markov Systems with unknown noise statistics and mode-transition dynamics. It introduces JMFNet, a model-based deep learning framework comprising a Mode Prediction NN and a Mode-Augmented KalmanNet that jointly infer discrete modes and continuous states via alternating least squares training. Empirical results across linear and nonlinear tasks—including target tracking, pendulum dynamics, Lorenz attractors, and traffic data—show JMFNet outperforms classical model-based filters, particle filters, and non-switching neural baselines, with pronounced gains in nonstationary or high-noise regimes. The approach is demonstrated to be robust to initialization and model mismatches and scalable to long-horizon sequences, suggesting significant practical impact for high-stakes JMS applications.

Abstract

This paper presents the Jump Markov Filtering Network (JMFNet), a novel model-based deep learning framework for real-time state-state estimation in jump Markov systems with unknown noise statistics and mode transition dynamics. A hybrid architecture comprising two Recurrent Neural Networks (RNNs) is proposed: one for mode prediction and another for filtering that is based on a mode-augmented version of the recently presented KalmanNet architecture. The proposed RNNs are trained jointly using an alternating least squares strategy that enables mutual adaptation without supervision of the latent modes. Extensive numerical experiments on linear and nonlinear systems, including target tracking, pendulum angle tracking, Lorenz attractor dynamics, and a real-life dataset demonstrate that the proposed JMFNet framework outperforms classical model-based filters (e.g., interacting multiple models and particle filters) as well as model-free deep learning baselines, particularly in non-stationary and high-noise regimes. It is also showcased that JMFNet achieves a small yet meaningful improvement over the KalmanNet framework, which becomes much more pronounced in complicated systems or long trajectories. Finally, the method's performance is empirically validated to be consistent and reliable, exhibiting low sensitivity to initial conditions, hyperparameter selection, as well as to incorrect model knowledge

Figures (12)

• Figure 1: The proposed JMFNet architecture. The mode prediction NN $\boldsymbol{\theta}_m$ processes the most recent $\boldsymbol{y}_t$ in order to assign probabilities to each mode. For each mode $j$, the prediction step is performed, and the input vectors $\boldsymbol{I}_t^{(j)}$ are constructed and passed at the mode-augmented KalmanNet $\boldsymbol{\theta}_K$. The resulting KG approximation can then construct the new state estimates $\mathbf{x}_{t|t}^{(j)}$. Finally, the resulting outputs are fused using probabilities $\boldsymbol{\mu}_{t,\boldsymbol{\theta}_m}$ as weights, resulting in the final state estimate.
• Figure 2: Example trajectories for the considered 2D target tracking application with different noise levels and of different time horizons, considering $q_{\rm CV}=0.5$, $q_{\rm CT}=2$, and $r_{\rm CT}=r_{\rm CV}=5$.
• Figure 3: State estimation scores for the linear 2D motion model with $M=2$ modes, considering a horizon length of $T=50$ and the Gaussian noise configuration of Fig. \ref{['fig:example_trajectories_target_trackin']}.
• Figure 4: State estimation performance difference between the proposed filter and KalmanNet for the linear 2D motion model with $M=2$ modes versus different Gaussian noise levels $r_m$.
• Figure 5: State estimation scores for the linear 2D motion model with $M=4$ modes and a time horizon of $T=2000$, considering three different noise types.