Low-rank filter and detector for multidimensional data based on an alternative unfolding HOSVD: application to polarimetric STAP

EURASIP Journal on Advances in Signal Processing

Table 1 Description of the LR filters and LR detectors provided by AU-HOSVD for polarimetric STAP

Partition	Filters	Detectors	Ranks	Methods
$A_{1} = {1, 2, 3}$	${\hat{W}}_{lr (1, 2, 3)}$	${\hat{Λ}}_{(1, 2, 3)}$	r ₁₂₃	Vector
$A_{1} = {1}$ , $A_{2} = {2}$ , $A_{3} = {3}$	${\hat{W}}_{lr (1 / 2 / 3)}$	${\hat{Λ}}_{(1 / 2 / 3)}$	r₁, r₂, r₃	HOSVD
$A_{1} = {1, 2}$ , $A_{2} = {3}$	${\hat{W}}_{lr (1, 2 / 3)}$	${\hat{Λ}}_{(1, 2 / 3)}$	r₁₂, r₃	AU-HOSVD
$A_{1} = {1}$ , $A_{2} = {2, 3}$	${\hat{W}}_{lr (1 / 2, 3)}$	${\hat{Λ}}_{(1 / 2, 3)}$	r₁, r₂₃	AU-HOSVD
$A_{1} = {1, 3}$ , $A_{2} = {2}$	${\hat{W}}_{lr (1, 3 / 2)}$	${\hat{Λ}}_{(1, 3 / 2)}$	r₁₃, r₂	AU-HOSVD