Minimum Mean Square Error Estimation Under Gaussian Mixture Statistics

2011/08/17 by John T. Flam, John T. Flåm, Saikat Chatterjee +7
Computer Science · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #Blind Source Separation Techniques #FOS: Mathematics #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1108.3410

arxiv created 2011/08/17 · openalex publication_date 2011/08/17 · arxiv updated 2011/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a generalization of the more familiar and simpler Gaussian signal and Gaussian noise instance. We present the necessary theoretical foundation and derive the MMSE estimator for x in a closed form. Furthermore, we provide upper and lower bounds for its mean square error (MSE). These bounds are validated through Monte Carlo simulations.

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