Synthetic approach to optimal filtering.

Area of Science:

• Signal processing
• Machine learning
• Control theory

Background:

• Modern optimal filtering theory primarily uses an analytic approach.
• Recurrent multilayer perceptrons (RMLPs) offer a potential alternative for filter synthesis.

Purpose of the Study:

• To present a synthetic approach for designing optimal recursive filters using RMLPs.
• To evaluate the performance of these 'neural filters' against established methods.

Main Methods:

• Synthesizing filters by training RMLPs with signal/sensor data from simulations or experiments.
• Utilizing RMLPs with hidden layers and optional output feedbacks.
• Comparing neural filter performance to the extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF).

Main Results:

• Trained RMLPs function as recursive filters, optimally representing conditional statistics.
• Neural filters converge to the minimum variance filter as the number of hidden neurons increases.
• Neural filters with few hidden neurons outperformed EKF and IEKF in tested nonlinear systems.

Conclusions:

• The synthetic approach using neural filters provides a powerful alternative to analytic methods in optimal filtering.
• Neural filters demonstrate superior performance for simple nonlinear signal/sensor systems.
• This approach offers a computationally efficient and effective method for designing optimal filters.