Neural Projection Filter: Learning Unknown Dynamics Driven by Noisy Observations.

Area of Science:

• Machine Learning
• Dynamical Systems
• Stochastic Processes

Background:

• Continuous state-space models (SSMs) are crucial for modeling dynamic systems.
• Existing filtering techniques face challenges with high-dimensional and nonlinear systems.
• Noisy sequential observations complicate state estimation in SSMs.

Purpose of the Study:

• To propose a novel neural stochastic differential equation (SDE) framework called the neural projection filter (NPF).
• To theoretically investigate the approximation capacity and convergence properties of NPF.
• To develop and evaluate a data-driven filter based on NPF for enhanced state estimation.

Main Methods:

• Developing neural stochastic differential equations (SDEs) for noisy sequential observations.
• Proving the universal approximation theorem for NPF, demonstrating its ability to approximate SDE solutions.
• Establishing the convergence of NPF dynamics to target dynamics under specific conditions.
• Empirically comparing NPF against state-of-the-art filters.

Main Results:

• NPF provides a theoretical guarantee for approximating solutions of SDEs driven by semimartingales.
• The proposed data-driven NPF filter demonstrates convergence to the true system dynamics.
• NPF significantly outperforms existing filters in nonlinear cases, showing robustness and efficiency.
• NPF successfully handles high-dimensional systems (e.g., 100-D cubic sensor) in real-time, unlike SOTA methods.

Conclusions:

• NPF offers a powerful and versatile framework for state estimation in continuous state-space models.
• The theoretical underpinnings of NPF support its practical effectiveness.
• NPF represents a significant advancement for real-time, high-dimensional state estimation, particularly in challenging nonlinear scenarios.