Deep Filtering

TL;DR

This paper introduces a deep learning-based filtering method that leverages Monte Carlo sampling and neural networks to improve robustness and adaptability over traditional Kalman filters, applicable to linear, nonlinear, and jump models.

Contribution

It presents a novel deep filtering approach that uses Monte Carlo samples and neural networks, reducing the need for model calibration and enhancing robustness.

Findings

Deep filter compares favorably to Kalman and extended Kalman filters.

The method is robust to model discrepancies.

It effectively handles models with jumps and nonlinearity.

Abstract

This paper develops a deep learning method for linear and nonlinear filtering. The idea is to start with a nominal dynamic model and generate Monte Carlo sample paths. Then these samples are used to train a deep neutral network. A least square error is used as a loss function for network training. Then the resulting weights are applied to Monte Carlo sampl\ es from an actual dynamic model. The deep filter obtained in such a way compares favorably to the traditional Kalman filter in linear cases and the extended Kalman filter in nonlinear cases. Moreover, a switching model with jumps is studied to show the adaptiveness and power of our deep filtering method. A main advantage of deep filtering is its robustness when the nominal model and actual model differ. Another advantage of deep filtering is that real data can be used directly to train the deep neutral network. Therefore, one does not need to calibrate the model.