TrackDiffuser: Nearly Model-Free Bayesian Filtering with Diffusion Model

TL;DR

TrackDiffuser rethinks Bayesian filtering as a conditional diffusion problem to address state estimation under incomplete or inaccurate models. By learning system dynamics from data and conditioning the diffusion denoising on measurements, it achieves posterior approximations without explicit noise priors or measurement models, while preserving interpretability through a predict-update-like process. Across Gaussian, non-Gaussian, and mismatched conditions, plus real-world data from the Michigan NCLT, TrackDiffuser outperforms traditional MB filters and hybrid methods such as KalmanNet, especially in challenging nonlinear regimes. This approach offers a practical, robust framework for nearly model-free state estimation in real-world sensing where precise SSMs and noise characteristics are unavailable.

Abstract

State estimation remains a fundamental challenge across numerous domains, from autonomous driving, aircraft tracking to quantum system control. Although Bayesian filtering has been the cornerstone solution, its classical model-based paradigm faces two major limitations: it struggles with inaccurate state space model (SSM) and requires extensive prior knowledge of noise characteristics. We present TrackDiffuser, a generative framework addressing both challenges by reformulating Bayesian filtering as a conditional diffusion model. Our approach implicitly learns system dynamics from data to mitigate the effects of inaccurate SSM, while simultaneously circumventing the need for explicit measurement models and noise priors by establishing a direct relationship between measurements and states. Through an implicit predict-and-update mechanism, TrackDiffuser preserves the interpretability advantage of traditional model-based filtering methods. Extensive experiments demonstrate that our framework substantially outperforms both classical and contemporary hybrid methods, especially in challenging non-linear scenarios involving non-Gaussian noises. Notably, TrackDiffuser exhibits remarkable robustness to SSM inaccuracies, offering a practical solution for real-world state estimation problems where perfect models and prior knowledge are unavailable.

Figures (5)

• Figure 1: The framework of TrackDiffuser. Bayesian filtering is modeled as a conditional generative modeling problem to approximate the posterior probability density distribution. In training, historical measurements and true states are combined to form a ground-truth trajectory for the diffusion model, and the current measurements sequence is used as a condition for conditional diffusion sampling to obtain state estimates. In inference, we implement the predict step by taking the prior state estimate as the noise mean, and then implement the update step by recursively denoising with measurements conditional guidance.
• Figure 2: Trajectory visualization of filtering Lorenz attractor SSM with non-linear measurements, $\mathrm{q}^2$ = $\mathrm{r}^2$ = -10 [dB], $T = 40$. TrackDiffuser performs the best, especially in manoeuvring corners.
• Figure 3: Performance under SSM Mismatch. TrackDiffuser demonstrates superior robustness under system dynamics and measurement rotation mismatches.
• Figure 4: System dynamics training-testing mismatch. Performance degradation under approximation with $J$ coefficients. Performance decline relative to the baseline with the accurate state-evolution function.
• Figure 5: NCLT data set, trajectory from session with date 2012-01-22 sampled at 5 Hz.