On the Observability of Gaussian Models using Discrete Density Approximations

TL;DR

This paper introduces a new method for assessing the observability of Gaussian models by using discrete density approximations to generate representative observations and evaluate the maximum a posteriori estimator's properties.

Contribution

The paper presents a novel approach combining discrete density approximations with quantitative measures to test and analyze Gaussian model observability.

Findings

Provides a quantitative measure of observability.

Uses discrete density approximations for efficient testing.

Offers insights into the properties of the MAP estimator.

Abstract

This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the maximum a posteriori estimator. In the first step of the proposed algorithm, the discrete density approximations are used to generate a single representative design observation vector to test for observability. In the second step, a number of carefully chosen design observation vectors are used to obtain information on the properties of the estimator. By using measures like the variance and the so-called local variance, we do not only obtain a binary answer to the question of observability but also provide a quantitative measure.