Stochastic differential equations (SDEs) are widely used to model complex stochastic dynamical systems. For observational data that follows stochastic dynamical systems driven by random perturbations, modeling the data using SDEs to capture these dynamics is essential for understanding the underlying probabilistic behaviors. Recently, Neural SDEs have emerged as a powerful tool for modeling continuous-time stochastic dynamics. By naturally accommodating irregular observation intervals and leveraging the adjoint method for memory-efficient computations, Neural SDE provides a flexible framework for continuous-time modeling. This paper proposes a flexible and scalable framework for flexibly learning Neural SDE expressions with Brownian motions as functions of both observed values and time, ensuring that the correct formulations for both the drift and diffusion terms are obtained. Our data-driven Neural SDE identification framework (NSDE-ID) leverages the path signature, which is a collection of all the iterated integrals and efficiently extracts features from time-series data, and incorporates path-dependent distributions, enabling SDE estimation that extends beyond point-in-time predictions. Building upon recent advancements in Neural SDE, our approach is designed to enforce statistical consistency in the learning process, thereby enabling robust modeling of complex dynamics. We demonstrate the efficacy of NSDE-ID on three benchmark SDE parameter estimation problems and analyze its numerical performance and robustness. Overall, NSDE-ID offers a promising new direction for systematically unraveling the continuous stochastic dynamics within observational data through a flexible SDE representation.
In this work, we develop an end-to-end differentiable multi-view visual tracking architecture and explore fine-tuning model parameters via gradient-based optimization and automatic differentiation. We consider a setting with multiple camera nodes distributed in the tracking environment that collaboratively track objects. The architecture that we construct includes within-image-plane deep learning-based detection models, probabilistic camera models, object dynamics models, and an $N$-object Kalman filter-based tracking model. We demonstrate fully differentiable choices for each of these components, enabling learning and fine-tuning of the parameters of all system components based on different forms of supervision. Our results show performance gains for $N$-object tracking when fine-tuning the parameters of the system for end-to-end tracking performance.
Autonomous path planning for radar and sonar sensing faces significant challenges arising from dynamic targets, obstacle occlusions, and low signal-to-noise (SNR) conditions. We propose a hierarchical sensor scheduling framework that combines a long-horizon strategic planner, based on the Rapidly-exploring Random Tree star (RRT*) algorithm, with a fast-adapting tactical planner. Efficient coordination of the two planners is achieved via a novel message passing mechanism, enabling guidance of the sensor out of complex environments while maintaining effective target tracking. Additionally, we introduce an RRT* rerooting strategy that significantly reduces computation time and so expedites the update of the strategic plan. Extensive simulation results demonstrate that our proposed fusion approach outperforms conventional stand-alone short-term and long-term planners in challenging scenarios and low-SNR regimes,
Bayesian filtering problem is considered in linear Gaussian systems with unknown inverse Wishart distributed process noise covariance. A Bayesian filter is formulated to approximate the joint posterior for the state and the process noise covariance. This involves utilizing moment matching and a scale Gaussian mixture approximation of the t-distribution. The proposed filter distinguishes itself by being non-iterative, setting it apart from existing Bayesian solutions given in the literature. The algorithm's performance is demonstrated through its application to a scenario where a target is tracked in two dimensions. Simulation results indicate that the proposed filter achieves similar or better performance compared to state-of-the-art solutions while demanding a reduced computational load.
Space situational awareness requires estimation of satellite tracks with sparse observations. The sparsity of novel information makes critical tasks such as maneuvering target tracking and track initialization challenging. Bayesian inference via Markov-Chain Monte Carlo (MCMC) can improve robustness when compared to recursive estimation, but high-fidelity orbit propagation yields objectionable runtimes in such solvers. This challenge may be mitigated via multi-fidelity methods, i.e., the use of varying fidelity propagators that trade some accuracy for reduced runtime. In this paper, multi-fidelity methods are combined with a delayed acceptance approach in Metropolis-Hastings-based MCMC to reduce runtime for satellites in low-Earth orbits. The delayed acceptance approach is a two-step process. The first considers a sample propagated via a rapid, multifidelity model. In the second step, any preliminarily accepted samples are propagated via the full-fidelity model. This reduces the number of high-fidelity propagations. The multi-fidelity approach also includes proposal density adaptation and produces mixing ratios consistent with optimal rates. This MCMC method is demonstrated for sparse orbit determination in a low-Earth orbit scenario. Accuracy of the multi-fidelity approach is consistent with full-fidelity inference while reducing the runtime by almost a factor of two in the cases considered.
