# A Kushner-Stratonovich Monte Carlo Filter Applied to Nonlinear Dynamical System Identification

arXiv: https://arxiv.org/abs/1302.3330 · HTML: https://mlsanity.com/paper/1302.3330/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2013.

## Built on by (most cited first, 1 of 1)

- [FINDER: Stochastic Mirroring of Noisy Quasi-Newton Search and Deep Network Training](https://mlsanity.com/paper/2410.14270/) (2024)

## Abstract (arXiv)

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation-prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight- based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter.