Elsevier

Signal Processing

Volume 148, July 2018, Pages 78-90
Signal Processing

Detection of low-velocity and floating small targets in sea clutter via income-reference particle filters

https://doi.org/10.1016/j.sigpro.2018.02.005Get rights and content

Highlights

  • PW-SIRV and PW-LFM models are respectively given for sea clutter and nonlinear FM targets.

  • A FB-IRPF is proposed to estimate the instantaneous Doppler curve of low-velocity or floating small targets in sea clutter.

  • Adaptive combined GLRT detector via FB-IRPF is proposed to detect small targets.

  • The proposed detector attains best overall detection performance than the fractal-based detector and tri-feature-based detector.

Abstract

In this paper, an adaptive composite generalized likelihood ratio test (GLRT) detector using the forward-backward income-reference particle filter (FB-IRPF) for signal estimation is proposed to detect low-velocity and floating small targets in high-resolution sea clutter. In integration duration of the order of seconds, target returns with nonlinear Doppler modulation and amplitude slow fluctuation are parameterized by a piecewise linear frequency modulated (PW-LFM) model equipped by a two-dimensional dynamic system of unknown statistics. Correspondingly, temporal nonstationary sea clutter time series is modelled into a piecewise spherical invariant random vector (PW-SIRV) sequences. By introducing the optimal test statistic at each piece as the user-defined cost and embedding it into the route of the forward-backward cost-reference particle filter (FB-CRPF), the FB-IRPF is developed to estimate the state sequence of a PW-LFM signal and to integrate its income at all the pieces. Using the integrated income as the test statistic, the adaptive composite GLRT is derived. It is compared with the fractal-based detector and tri-feature-based detector in a recognized sea clutter dataset for small target detection. The results show that the proposed detector attains better overall detection performance and is complementary with the tri-feature-based detector to some extent.

Introduction

Detection of low-velocity and floating small targets on the sea surface is a necessary but difficult task for high-resolution radars operating at low grazing angles [1], [2], [3]. Due to their weak returns and small Doppler offsets, detection requires long integration time and high spatial resolution of radar. Long integration time improves the integration gain of target returns when a tactical method is available and high spatial resolution lowers the power level of sea clutter. During long integration time, target movement with swell and wave results in amplitude fluctuation and complex instantaneous Doppler curve of target returns. Due to high spatial resolution, strong non-Gaussianity and temporal nonstationarity of sea clutter make it difficult to mitigate sea clutter [4], [5], [6].

Analysis and modeling of sea clutter is the prerequisite to mitigate it. In short integration time, target returns have a simple form and thus it is pivotal to develop the optimum coherent detection matching the characteristics of sea clutter [7], [8], [9]. For K-distributed sea clutter, the optimum coherent detector has a closed-form solution using the modified Bessel functions [8]. For high-resolution sea clutter with heavy tails and inverse Gamma distributed texture, the optimum coherent detector is the generalized likelihood ratio test linear-threshold detector (GLRT-LTD) [9] and its simple expression is tenable for real-time implementation. The optimum coherent detection is suited for short integration time because of requirement of constant Doppler offset of target returns and limitation of spatial non-stationarity of sea clutter. Due to limited integration gain, those coherent detection methods can find fast moving targets or slowly moving targets with high signal-to-clutter ratio (SCR).

In order to find low-velocity or floating small targets such as small boats, driftwoods and icebergs, a long integration time from several hundred milliseconds to several seconds is required. In such a long integration time, both target returns and sea clutter time series have rather complex behaviors. Target returns are complicated by unknown amplitude and Doppler modulations and sea clutter time series is modeled as compound-Gaussian stochastic process with time-varying texture. In [10], [11], the fractal and multifractal characteristics of high-resolution sea clutter amplitude time series are revealed and the fractal-based detectors were developed. Those detectors are simple in implementation and can obtain fair results in floating small target detection when the observation time for a decision is long enough (over four seconds). For steady moving small targets whose Doppler offset keeps constant during integration, in order to alleviate the conflict between a long integration time and limited reference cells due to spatial non-stationarity of sea clutter, the block-adaptive and subband adaptive detectors were proposed [12], [13]. However, they are unsuited for non-steady moving targets with time-varying Doppler offset. For low-velocity and floating small targets with complicated Doppler characteristics, the three commonly-used test statistics in radar target detection are embedded into the framework of the anomaly detection [14] to form the tri-feature-based detector [2] by using the fast convexhull learning algorithm. It attains rather good performance in the X-band IPIX database, a recognized database for sea-surface small target detection [15].

Focusing on the Doppler modulation modeling of target returns, various detection methods using time-frequency analysis were developed in noise or clutter environments. By modeling target returns as linear frequency modulated (LFM) signals, the Radon ambiguity transform is used for signal detection in noise [16]. Other time-frequency distributions (TFDs) can be used for LFM signal detection in noise or clutter [17], [18]. When target returns are modeled into unknown nonlinear frequency modulated (FM) signals, nonparametric methods can implement effective detection in a long integration time [19], [20]. TFD-based nonparametric methods have low integration gain in low SNR or SCR and require very high computational cost unacceptable by practical radar systems.

Piecewise parametric modeling is an effective way to characterize nonlinear FM signals [21], [22]. In [21], signals are modeled into the chirplet chain, i.e., piecewise LFM (PW-LFM) signals in order to find weak gravitational wave chirps from noise, where the dynamic programming is used to estimate the parameters of signals. In [22], the PW-LFM signal model and cost-reference particle filters (CRPF) are combined to detect nonlinear FM signals in noise by using the forward-backward CRPF (FB-CRPF) with a user-defined cost. For complicated signals under a piecewise parametric model, parameter estimation from observations with noise or clutter is the key of signal detection. In terms of different statistical assumptions, various types of particle filters have been developed for piecewise parameter estimation [23], [24]. Among them, the CRPFs [25], [26], [27] have a strong adaptability because of the least statistical assumption and flexible user-defined costs. Detection of low-velocity and floating small targets on sea surface involves in piecewise parameter estimation in sea clutter, which keeps an open issue now.

In this paper, small target returns with complicated Doppler characteristics are first modeled into nonlinear FM signals with piecewise linear Doppler frequencies, where piecewise constant amplitudes and the parameter evolution from one piece to the next is modeled as a linear dynamic system of unknown parameters. Simultaneously, high-resolution sea clutter time series are modeled as piecewise spherical invariant random vector (PW-SIRV) sequence with the inverse Gamma distributed texture. Second, under the assumption that the parameters of signal model are known, the adaptive composite GLRT detector is derived, where the adaptive GLRT-LTD test statistics at all the pieces are integrated. Third, the forward-backward income-reference particle filter (FB-IRPF) is proposed to estimate signal parameters from the observation time series with sea clutter. Substituting the estimates into the adaptive composite GLRT detector yields a new detector to find low-velocity and floating small targets in sea clutter. It realizes the optimal short integrated gain thanks to the proposed PW-SIRV model and the FB-IRPF algorithm, which makes it effectively find the low-velocity and floating small targets embedded in high resolution sea clutter. Finally, a fully analysis and comparison of the adaptive composite GLRT detector are given by the IPIX database. The experimental results show that the proposed detector attains the best overall detection performance than the fractal-based detector and tri-feature-based detector.

This paper is organized as follows. In Section 2, two models of The PW-LFM signal model and PW-SIRV clutter model are addressed. The composite GLRT detector is derived and its optimality and constant false alarm rate (CFAR) property are discussed. In Section 3, the FB-IRPF is proposed to estimate signal parameters and the adaptive composite GLRT detector via the FB-IRPF for state sequence estimation is obtained. In Section 4, the proposed detector is compared with the existing detectors in IPIX radar database. Finally, we conclude our paper in Section 5.

Section snippets

Composite GLRT detector in PW-LFM signal model and PW-SIRV clutter model

In this section, the return time series of low-velocity or floating target in an observation time of the order of seconds is modeled into a PW-LFM signal and sea clutter time series is modeled by the PW-SIRV model with inverse Gamma distributed texture. Then, under the assumption that signal parameters are known, the composite GLRT detector is derived. Moreover, its CFAR property is discussed.

Forward and backward state space models

Under the PW-LFM signal model and PW-SIRV clutter model, search of the approximation solution in (13) is changed into finding the estimation of Doppler frequency at each subinterval. In this way, particle filters (PFs) are suited for state estimation of nonlinear dynamic systems, which are widely used in target tracking and detection [23], [24], [25], [26]. Here, the state space models for forward and backward system are treated.

Assume that the instantaneous Doppler curve of target returns is a

Real sea clutter dataset for comparison

The IPIX radar database [15] is available to compare the proposed detector with the early fractal-based detector [10] and the recent tri-feature-based detector [2]. Twelve datasets collected at the dwelling mode are used. The first ten datasets were collected at the Dartmouth, Nova, Scotia, Canada, in 1993. The radar is with a carrier frequency of 9.3 GHz, range resolution of 30 m, the pulse repetition frequency (PRF) of 1000 Hz, and a low grazing angle (0.33° or so). The test target is an

Conclusions

In this paper, the adaptive composite GLRT detector using the FB-IRPF state estimation is proposed to detect floating small targets in high-resolution sea clutter. The long integration time brings time-varying characteristics of target returns and temporal nonstationarity of sea clutter. The PW-LFM signal model and the PW-SIRV clutter model with inverse Gamma texture are suggested to characterize signals and sea clutter. In each piece, the adaptive GLRT test statistic is used as the income to

References (33)

  • S. Wang, X. Chen, Y. Wang, et al., Nonlinear squeezing time–frequency transform for weak signal detection, Signal...
  • K.D. Ward et al.

    Sea clutter: scattering, the K distribution and Radar Performance (The Second version)

    (2013)
  • J. Carretero-Moya et al.

    Statistical analysis of a high -resolution sea clutter database

    IEEE Trans. Geosci. Remote Sens.

    (2010)
  • E. Conte et al.

    Mitigation techniques for non-Gaussian sea clutter

    IEEE J. Oceanic Eng.

    (2004)
  • Y. Dong

    Optimal coherent radar detection in a K-distributed clutter environment

    IET Radar Sonar Navig

    (2012)
  • K.J. Sangston et al.

    Coherent radar target detection in heavy-tailed compound -Gaussian clutter

    IEEE Trans. Aerosp. Electron. Syst.

    (2012)
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