Computationally efficient toeplitz approximation of structured covariance under a rank constraint

Bosung Kang, Vishal Monga, Muralidhar Rangaswamy

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    Disturbance covariance estimation is a centrally important problem in radar space-time adaptive processing (STAP). Because training is invariably scarce, estimators that exploit inherent structure and physical radar constraints are needed in practice. This paper develops a new computationally efficient estimator that obtains a Toeplitz approximation of the structured interference covariance under a rank constraint. Previous work has shown that exact maximum likelihood (ML) estimation of Toeplitz covariance matrix has no closed-form solution, and most versions of this problem result in iterative estimators that are computationally expensive. Our proposed solution focuses on a computationally efficient approximation and involves a cascade of two closed-form solutions. First, we obtain the rank-constrained ML estimator whose merits have recently been established firmly for radar STAP. The central contribution of this paper is the rank-preserving Toeplitz approximation, which we demonstrate can be modeled as an equality-constrained quadratic program and also admits a closed form. Extensive performance evaluation on both simulated and knowledge-aided sensor signal processing and expert reasoning data confirms that the proposed estimator yields unbeatable performance for radar STAP under the previously stated conditions of rank and Toeplitz constraints.

    Original languageEnglish (US)
    Article number7073532
    Pages (from-to)775-785
    Number of pages11
    JournalIEEE Transactions on Aerospace and Electronic Systems
    Volume51
    Issue number1
    DOIs
    StatePublished - Jan 1 2015

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    Space time adaptive processing
    Radar
    Cascades (fluid mechanics)
    Maximum likelihood estimation
    Covariance matrix
    Maximum likelihood
    Signal processing
    Sensors

    All Science Journal Classification (ASJC) codes

    • Aerospace Engineering
    • Electrical and Electronic Engineering

    Cite this

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    abstract = "Disturbance covariance estimation is a centrally important problem in radar space-time adaptive processing (STAP). Because training is invariably scarce, estimators that exploit inherent structure and physical radar constraints are needed in practice. This paper develops a new computationally efficient estimator that obtains a Toeplitz approximation of the structured interference covariance under a rank constraint. Previous work has shown that exact maximum likelihood (ML) estimation of Toeplitz covariance matrix has no closed-form solution, and most versions of this problem result in iterative estimators that are computationally expensive. Our proposed solution focuses on a computationally efficient approximation and involves a cascade of two closed-form solutions. First, we obtain the rank-constrained ML estimator whose merits have recently been established firmly for radar STAP. The central contribution of this paper is the rank-preserving Toeplitz approximation, which we demonstrate can be modeled as an equality-constrained quadratic program and also admits a closed form. Extensive performance evaluation on both simulated and knowledge-aided sensor signal processing and expert reasoning data confirms that the proposed estimator yields unbeatable performance for radar STAP under the previously stated conditions of rank and Toeplitz constraints.",
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    Computationally efficient toeplitz approximation of structured covariance under a rank constraint. / Kang, Bosung; Monga, Vishal; Rangaswamy, Muralidhar.

    In: IEEE Transactions on Aerospace and Electronic Systems, Vol. 51, No. 1, 7073532, 01.01.2015, p. 775-785.

    Research output: Contribution to journalArticle

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