Persymmetric generalised adaptive matched filter for range‐spread targets in homogeneous environment

Abstract

This study deals with the problem of adaptively detecting range-spread targets in Gaussian environment, by assuming a persymmetric structure of covariance matrix. A persymmetric detector based on the two-step generalised likelihood ratio test design scheme is devised to reduce secondary data requirement, which ensures the constant false alarm rate property. Moreover, the general closed-form expressions of the probabilities of the false alarm and detection for the proposed detector are derived, in both cases of deterministic and fluctuating scatter models. Furthermore, the compact versions of forenamed expressions are presented in a special case when the joint space-time dimension of the received signal is odd. Finally, the numerical results of these derived statistical expressions are confirmed with those of Monte Carlo trials.

Study on Automatic Evaluation Method of Spoken English Based on Multimodal Discourse Analysis Theory

“…While analyzing language features, it emphasizes the role of visual, auditory, and behavioral symbolic modes such as image, color, sound, and action in discourse. At present, how the various modes interact and how to affect the construction of overall meaning is an important topic of multimodal discourse analysis theory [4,5]. Among them, the study of grammatical rules of various modes restricts the further development of this field.…”

Persymmetric subspace detector for distributed target in partially homogeneous environment

“…Note that, $${\boldsymbol{Z}}_{\mathrm{p}}^{\mathrm{H}}{\widehat{\boldsymbol{M}}}^{-1}{\boldsymbol{Z}}_{\mathrm{p}}$$ in the numerator of (21) can be rewritten as $$${\boldsymbol{Z}}_{\mathrm{p}}^{\mathrm{H}}{\widehat{\boldsymbol{M}}}^{-1}{\boldsymbol{Z}}_{\mathrm{p}}=\gamma {\overline{\boldsymbol{Z}}}_{\mathrm{p}}^{\mathrm{H}}{\overline{\boldsymbol{M}}}^{-1}{\overline{\boldsymbol{Z}}}_{\mathrm{p}}=\gamma {\boldsymbol{N}}_{1}$$$ where $${\overline{\boldsymbol{Z}}}_{\mathrm{p}}={\boldsymbol{M}}^{-1/2}{\boldsymbol{Z}}_{\mathrm{p}}/\sqrt{\gamma },\overline{\boldsymbol{M}}={\boldsymbol{M}}^{-1/2}\widehat{\boldsymbol{M}}{\boldsymbol{M}}^{-1/2}$$. Obviously, under hypothesis H 0 , each column of $${\overline{\boldsymbol{Z}}}_{\mathrm{p}}$$ obeys to a zero‐mean complex circular Gaussian distribution with covariance matrix $${\mathbf{I}}_{N}/2$$ [1], that is, …”

“…In recent years, the problem of detecting a target signal in Gaussian clutter whose statistical property is completely unknown has received wide concerns in the field of radar signal processing [1][2][3][4][5]. For point-like target detection, Kelly's generalised likelihood ratio test (GLRT) [6] is one of the most representative detectors.…”

Subspace gradient tests for range‐spread target detection in structured interference plus Gaussian clutter

“…Moreover, adaptive multichannel detection for targets in the Gaussian clutter with an unknown covariance matrix is an important topic for modern radar systems [6][7][8] and a set of target-free training data is usually assumed to be available [9][10][11] to estimate the unknown clutter covariance matrix in a homogeneous environment (HE) or a partially homogeneous environment (PHE). Herein, the HE indicates that the clutter components in test data share the identical covariance matrix with the training data [12,13]; while the PHE implies that the two clutter covariance matrices coincide only up to a scaling factor implying different clutter powers between the test and training data [14][15][16], which is also further generalised to a fully heterogeneous environment in Refs. [17][18][19].…”