Tracking multiple targets in MIMO radar via adaptive asymmetric joint diagonalization with deflation

doi:10.21629/JSEE.2018.04.08

Abstract

Abstract:

In view of the low performance of adaptive asymmetric joint diagonalization (AAJD), especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation (AAJDd) algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure (DOD) and direction of arrival (DOA) directly, avoiding the reuse of the previous moment information in the AAJD algorithm. On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.

Key words: MIMO radar, low complexity, angles tracking, adaptive asymmetric joint diagonalization with deflation (AAJDd), high maneuvering target

Zhengyan ZHANG, Jianyun ZHANG. Tracking multiple targets in MIMO radar via adaptive asymmetric joint diagonalization with deflation[J]. Journal of Systems Engineering and Electronics, 2018, 29(4): 731-741.

Figures/Tables 9

Fig 1

Table 1

AAJDd algorithm eigenvector solution flow"

Initialization:${{{\mathit{\boldsymbol{P}}}}}(0) = {{{\mathit{\boldsymbol{I}}}}}_{P\times P} $, $0<\beta {\leqslant} 1$
Input:${{{\mathit{\boldsymbol{y}}}}}(t)$
Output:$\varphi(t), \theta (t)$
For $t = 1, \cdots, T$
Step 1
for$i = 1, \ldots, P$
${{{\mathit{\boldsymbol{d}}}}}_i (t) = {{{\mathit{\boldsymbol{W}}}}}_i^{-1} (t-1){{{\mathit{\boldsymbol{y}}}}}_i (t)$
$g_i (t) = \beta g_i (t-1)+\|{{{\mathit{\boldsymbol{d}}}}}_i (t)\|^2$
$Q_i (t) = {{{{\mathit{\boldsymbol{d}}}}}_i^{{{\rm{H}}}} (t)} /{g_i (t)}$
$\eta _i(t) = \|{{{\mathit{\boldsymbol{d}}}}}_i (t)\|^2 /{g_i (t)}$
${{{\mathit{\boldsymbol{e}}}}}_i (t) = {{{\mathit{\boldsymbol{y}}}}}_i (t)-{{{\mathit{\boldsymbol{W}}}}}_i (t-1){{{\mathit{\boldsymbol{d}}}}}_i (t)\widehat {{{{\mathit{\boldsymbol{W}}}}}}_i (t) = {{{\mathit{\boldsymbol{W}}}}}_i (t-1)+1/\beta+\eta _i (t){{{\mathit{\boldsymbol{e}}}}}_i (t)Q_i (t)2$
${{{\mathit{\boldsymbol{y}}}}}_{i+1}(t) = {{{\mathit{\boldsymbol{y}}}}}_i (t)-\widehat {{{{\mathit{\boldsymbol{W}}}}}}_i^{-1} (t){{{\mathit{\boldsymbol{d}}}}}_i (t)$
end
Step2
If $t = =1$
$\mathit{\boldsymbol{\mathit{\Psi}}} _r = {{{\mathit{\boldsymbol{W}}}}}_{r1}^{-1} {{{\mathit{\boldsymbol{W}}}}}_{r2} $
eigenvalue decomposition of${\Psi _r}:{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} = {\Psi _r} = T{\Psi _r}{T^{ - 1}}$
take the diagonal elements of$ \mathit{\boldsymbol{\mathit{\Psi}}} _r , {\rm{comprise}} \omega _r $
$ {\Phi _t} = {{{\mathit{\boldsymbol{T}}}}}^{-1}{{{\mathit{\boldsymbol{W}}}}}_{t1}^{-1} {{{\mathit{\boldsymbol{W}}}}}_{t2} {{{\mathit{\boldsymbol{T}}}}} $
take the diagonal elements of$ \mathit{\boldsymbol{\mathit{\Phi}}} _t , {\rm{comprise}} \omega _t $ else
$ \mathit{\boldsymbol{\mathit{\Psi}}} _r = {{{\mathit{\boldsymbol{W}}}}}_{r1}^{-1} {{{\mathit{\boldsymbol{W}}}}}_{r2}$
take the diagonal elements of$ \mathit{\boldsymbol{\mathit{\Psi}}} _r $ comprise ${\omega _r}$
$ \mathit{\boldsymbol{\mathit{\Psi}}} _t = {{{\mathit{\boldsymbol{W}}}}}_{r1}^{-1} {{{\mathit{\boldsymbol{W}}}}}_{r2}$
take the diagonal elements of$ \mathit{\boldsymbol{\mathit{\Psi}}} _t $ comprise ${\omega _t}$ end
using$\left\{\!\!\begin{array}{c} \theta _p = \arcsin \{{\rm angle}[\bm\omega _r (p)]/\pi \\ \varphi _p = \arcsin \{{\rm angle}[\bm\omega _t (p)]/\pi \\ \end{array}\!\!\right\}$ get $\theta(t), \varphi(t)$ end
according to${{{\mathit{\boldsymbol{W}}}}}(t) = [{{{\mathit{\boldsymbol{a}}}}}_t (\varphi _1 )\otimes {{{\mathit{\boldsymbol{a}}}}}_r (\theta _1 ), \ldots, {{{\mathit{\boldsymbol{a}}}}}_t (\varphi _P )\otimes {{{\mathit{\boldsymbol{a}}}}}_r (\theta _P )]$
updated$\widehat {{{{\mathit{\boldsymbol{W}}}}}}(t)$
End

Table 1

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Fig 7

Fig 8

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