# Exact Consistency Tests for Gaussian Mixture Filters using Normalized Deviation Squared Statistics

arXiv: https://arxiv.org/abs/2312.17420 · HTML: https://mlsanity.com/paper/2312.17420/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 29 Dec 2023.

## Builds on (most cited first, 4 of 4)

- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Weak in the NEES?: Auto-tuning Kalman Filters with Bayesian Optimization](https://mlsanity.com/paper/1807.08855/) (2018)
- [Discrete and Continuous, Probabilistic Anticipation for Autonomous Robots in Urban Environments](https://mlsanity.com/paper/1309.0766/) (2013)

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

- [New methods to compute the generalized chi-square distribution](https://mlsanity.com/paper/2404.05062/) (2024)

## Abstract (arXiv)

We consider the problem of evaluating dynamic consistency in discrete time probabilistic filters that approximate stochastic system state densities with Gaussian mixtures. Dynamic consistency means that the estimated probability distributions correctly describe the actual uncertainties. As such, the problem of consistency testing naturally arises in applications with regards to estimator tuning and validation. However, due to the general complexity of the density functions involved, straightforward approaches for consistency testing of mixture-based estimators have remained challenging to define and implement. This paper derives a new exact result for Gaussian mixture consistency testing within the framework of normalized deviation squared (NDS) statistics. It is shown that NDS test statistics for generic multivariate Gaussian mixture models exactly follow mixtures of generalized chi-square distributions, for which efficient computational tools are available. The accuracy and utility of the resulting consistency tests are numerically demonstrated on static and dynamic mixture estimation examples.