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A novel STAP algorithm via volume cross-correlation function on the Grassmann manifold

Jia-Mian Li, Jian-Yi Chen, Bing-Zhao Li

TL;DR

The paper addresses STAP performance degradation under limited training samples and target leakage by introducing BGVCF-STAP, which integrates THPD-based smoothing, Brauer disk-based clutter/target discrimination, and volume cross-correlation on the Grassmann manifold to estimate the clutter covariance and compute the STAP filter. By mapping THPD training samples to subspaces and measuring subspace distances with VCF, the method preserves the positive definiteness and geometric structure of covariance matrices. The key contributions are a THPD-based training framework, Brauer-bound-driven target screening, and a subspace-VCF CCM estimation pipeline with gradient-descent refinement, yielding robust clutter suppression and improved detection in heterogeneous environments. Experimental results on both simulated and Mountain-Top measured data demonstrate significant performance gains over conventional STAP approaches, highlighting the approach’s practical impact for radar clutter suppression without strong distribution assumptions.

Abstract

The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture the intrinsic geometric and structural properties of the covariance matrix, thus limiting the utilization of structural information in the data. To address these issues, the proposed algorithm begins by constructing Toeplitz Hermitian positive definite (THPD) matrices from the training samples. The Brauer disc (BD) theorem is then employed to filter out THPD matrices containing target signals, retaining only clutter-related matrices. These clutter matrices undergo eigendecomposition to construct the Grassmann manifold, enabling CCM estimation through the volume cross-correlation function (VCF) and gradient descent method. Finally, the filter weight vector is computed for filtering. By fully leveraging the structural information in radar data, this approach significantly enhances both accuracy and robustness of clutter suppression. Experimental results on simulated and measured data demonstrate superior performance of the proposed algorithm in heterogeneous environments.

A novel STAP algorithm via volume cross-correlation function on the Grassmann manifold

TL;DR

The paper addresses STAP performance degradation under limited training samples and target leakage by introducing BGVCF-STAP, which integrates THPD-based smoothing, Brauer disk-based clutter/target discrimination, and volume cross-correlation on the Grassmann manifold to estimate the clutter covariance and compute the STAP filter. By mapping THPD training samples to subspaces and measuring subspace distances with VCF, the method preserves the positive definiteness and geometric structure of covariance matrices. The key contributions are a THPD-based training framework, Brauer-bound-driven target screening, and a subspace-VCF CCM estimation pipeline with gradient-descent refinement, yielding robust clutter suppression and improved detection in heterogeneous environments. Experimental results on both simulated and Mountain-Top measured data demonstrate significant performance gains over conventional STAP approaches, highlighting the approach’s practical impact for radar clutter suppression without strong distribution assumptions.

Abstract

The performance of space-time adaptive processing (STAP) is often degraded by factors such as limited sample size and moving targets. Traditional clutter covariance matrix (CCM) estimation relies on Euclidean metrics, which fail to capture the intrinsic geometric and structural properties of the covariance matrix, thus limiting the utilization of structural information in the data. To address these issues, the proposed algorithm begins by constructing Toeplitz Hermitian positive definite (THPD) matrices from the training samples. The Brauer disc (BD) theorem is then employed to filter out THPD matrices containing target signals, retaining only clutter-related matrices. These clutter matrices undergo eigendecomposition to construct the Grassmann manifold, enabling CCM estimation through the volume cross-correlation function (VCF) and gradient descent method. Finally, the filter weight vector is computed for filtering. By fully leveraging the structural information in radar data, this approach significantly enhances both accuracy and robustness of clutter suppression. Experimental results on simulated and measured data demonstrate superior performance of the proposed algorithm in heterogeneous environments.
Paper Structure (13 sections, 1 theorem, 29 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 1 theorem, 29 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Signal model and related theory
  3. Signal model
  4. Toeplitz Hermitian positive definite matrix
  5. VCF on the Grassmann manifold
  6. Proposed BGVCF-STAP algorithm
  7. Calculation of the THPD matrix
  8. Distinguish clutter-plus-noise and targets
  9. Estimation of CCM based on GVCF
  10. Experimental result and analysis
  11. Simulated data
  12. Measured data
  13. Conclusion

Key Result

Theorem 1

Brauer Disk Theorem RN98: Suppose $R = [r_{ij}]$ is an $n$-th order complex Toeplitz matrix, with $r_{ii} = r_0$, and $n \geq 2$. Let $\sigma(R)$ denote the eigenvalues of $R$. Then, where $\mathrm{Y}\left(R\right)$ is the union of the Brauer circle sets of the symmetric matrix $R$.

Figures (10)

  • Figure 1: Algorithm flowchart.
  • Figure 2: Schematic diagram of distance measurement on manifolds.
  • Figure 3: Spatial–temporal Capon spectrum.
  • Figure 4: Brauer bound for clutter-plus-noise and targets under different numbers of training samples. (a) number of samples = 25. (b) number of samples = 50.
  • Figure 5: Spatial and Doppler slice beampattern. (a) spatial slice beampattern of target1. (b) spatial slice beampattern of target2. (c) Doppler slice beampattern.
  • ...and 5 more figures

Theorems & Definitions (1)

  • Theorem 1