Asymptotic Statistical Performance of Local Polynomial Wigner Distribution for the Parameters Estimation of Cubic-Phase Signal With Application in ISAR Imaging of Ship Target

Abstract

The parameters estimation of cubic-phase signal based on local polynomial Wigner distribution (LPWD) was proposed in the author's previous paper, and it outperforms the traditional algorithms in inverse synthetic aperture radar (ISAR) imaging of maneuvering target. The contribution of this paper is that the asymptotic statistical performance of LPWD for the parameters estimation of cubic-phase signal is analyzed theoretically, and the asymptotic statistical results are derived for all the estimated parameters via the first-order perturbation principle. Then, the LPWD is used in ISAR imaging of ship target with complex motion, and the high-quality instantaneous ISAR images can be obtained.Index Terms-Asymptotic statistical performance, cubic-phase signal, inverse synthetic aperture radar (ISAR), local polynomial Wigner distribution (LPWD).

ISAR Imaging of Nonuniformly Rotating Targets With Low SNR Based on Third Order Autocorrelation Function

“…Remark 2: The cross-terms of the TOAF-based method contain 6 items under two-component CPSs. While for these algorithms which have FOAFs, such as in [22]- [29], the number of cross-terms is 14. Thus the TOAF-based method may have a better cross-term suppression performance than these algorithms.…”

“…However, its signal-to-noise ratio (SNR) threshold is high because it only complete energy accumulation in the lag time domain. To improve the anti-noise performance, the local polynomial Winger distribution (LPWD) [22], the Keystone time-Chirp rate distribution (KTCRD) [23], the scaled Fourier transform (SFT)-based method [24], the chirp rate-quadratic chirp rate distribution (CRQCRD) [25], the modified Lv's distribution (MLVD) [26], the modified CRQCRD (MCRQCRD) [27], the generalized decoupling technique (GDT) [28] and the coherently integrated generalized CPF (CIGCPF) [29], have been presented.…”

Inverse synthetic aperture radar imaging of targets with complex motion based on the local polynomial ambiguity function

“…6 with experimental ship data. [10][11][12][13][14]18,[19][20][21][22][23] In Ref. 9 For targets with complex motion, in which rotational motion may cause higher-order phase terms, the traditional LFM signal model is not appropriate.…”

“…9 For targets with complex motion, in which rotational motion may cause higher-order phase terms, the traditional LFM signal model is not appropriate. 21,22 However, after compensating the third-order term with the estimated parameter, the LPWD algorithm estimates the secondorder coefficient using CPF method, which does lead to the heavy computational burden due to the Fourier transform with respect to the nonuniformly spaced data. [10][11][12][13][14] With regard to the parameter estimation of CPS, numerous algorithms, including the cubic phase function (CPF), 15,16 the higher-order ambiguity function, 17 the product generalized CPF (PGCPF), 18 the product high-order matched-phase transform, 19 and the modified version of CPF (MCPF), 14 have been addressed, but all of them involve multilinear transformation and discrete Fourier transform for the nonuniformly spaced signal sample, which result in extensive crossterms under multi-CPSs and undesirable computational complexity.…”

“…Then the ISAR imaging algorithm 21,22 is also proposed based on LPWD. Then the ISAR imaging algorithm 21,22 is also proposed based on LPWD.…”