Procedia Engineering 29 (2012) 3429 – 3433

1877-7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2012.01.507

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Procedia Engineering 00 (2011) 000–000

ProcediaEngineering

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2012 International Workshop on Information and Electronics Engineering (IWIEE)

Marine Target Detection from Nonstationary Sea-Clutter Based On Topological Data Analysis

Lei Nie*, Weidong Jiang, Qiang Fu College of Electronic Science and Engineering, National University of Defense Technology

Changsha410073, Hunan, China

Abstract

Due to the instinct complexity and the large scale non-stationary of so-called sea-clutter, radar backscatters from ocean surface, it is always challenging to detect the weak marine target. In classical statistical approaches, the sea-clutter is modeled as several kinds of stochastic processes, which are found inadequate, especially in high sea-state circumstances. Therefore it is reasonable to discover the underlying dynamics that is responsible for generating the time series of sea-clutter. In this work, we take into account of the marine target detection from the X-Band sea-clutter datasets with low Signal-Clutter-Ratio, and propose adequate methods to process these non-stationary data, including Empirical Mode Decomposition and Topological Data Analysis. Both theoretical simulation and experimental results indicate the proposed methods’ usefulness of for marine target detection, which is implemented by extract different structural features from measured sea-clutter data. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology Keywords: marine target detection; sea-clutter; time series; non-stationary; topological data analysis

1. Introduction

Sea clutter is defined as the electromagnetic wave backscatter from a patch of ocean surface illuminated by radar signals. In this paper, we mainly take into account the particular case of signal transmitted by high-resolution coastal radars, working at low grazing angles. Measurable modeling of sea clutter is an important precondition in many research areas and practical applications, such as salvage and

* Corresponding author. Tel.: +86-0731-84573498. E-mail address: nielei@nudt.edu.cn.

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marine radar signal processing. In recent years, both statistical and non-statistical model approaches have made advancement [1-4].

The common purpose of classical statistical models of sea clutter is trying to explain the amplitude statistics of sea clutter, and this approach can be separated in two parts. One aspect simply involve empirical fitting of distributions to the observed clutter data, and the other aspect concerns the theoretical basis of a statistical model for the selection of the clutter behavior, which can be used for synthetic generation of representative clutter signals, ideally physically well-grounded and mathematically tractable.

As a one-dimensional stochastic process, the global probability density function (pdf) of sea clutter can be descript by the below physical and phenomenological model [3] :

12( ) ( )( ) 2

v

v

b b xp x K b x

v −

⋅ ⋅⎛ ⎞= ⋅ ⋅ ⋅⎜ ⎟Γ ⎝ ⎠ (1)

where ( )vK x is the modified Bessel function of order v , b is the scale parameter and v is the shape parameter. As a two and multi-dimensional stochastic process, sea clutter can be generated by extending the number of correlation dimensions, which copes with real measured data better, but encounter difficulties in exploiting this model into a detection algorithm.

Nonlinear dynamics are basic to the characterization of many physical phenomena encountered in practice [5]. The dynamical model study on sea clutter, despite still in its early stages, is an important step forward from the classical statistical approaches. Accounting for time in an explicit manner, the information content of the input data is transferred directly to the model parameters evolving over time in nonlinear dynamical approach. Furthermore, the dynamical modeling challenges the classical detection algorithms, whose foundation is mainly statistical. All the known models of clutter have their limitations and may not exactly match any modeled condition. Especially, the statistics of sea clutter (amplitude distribution) vary with polarization, resolution cell size, sea state and wind conditions.

Recent years, Topological Data Analysis methods are being developed for data sets on which the natural structure is not a metric, but rather a partial order [6-8]. Aimed to extract global structure from representations in a strictly lower dimension, this approach turns out to be an ideal tool for intelligent data analysis [9]. The main method used by topological data analysis is[10]:firstly, replace a set of data points with a family of simplicial complexes, indexed by a proximity parameter; then, analyze these topological complexes via algebraic topology-specifically, via the new theory of persistent homology; finally, encode the persistent homology of a data set in the form of a parameterized version of a Betti number which will be called a barcode.

To implement Topological Data Analysis methods on sea-clutter datasets, the original data type should be transformed into the so-called point cloud data, for which global features are certainly present. The complex and massive sea-clutter data flows, which are represented in digital form time series, have hidden, highly nonlinear, geometric structures and properties, as is testified by various research approach: chaotic dynamics, multi-fractal spectrum, et al. The question can be described as: given a phase space χ , one can find its embedded space

dR , then extract essential topological features from its equivalent form.

2. Non-Stationary Signal Processing

In most real systems, the data are most likely to be both nonlinear and non-stationary. A necessary condition to represent nonlinear and non-stationary data is to have an adaptive basis, but most methods are designed for stationary process and few are available in nonlinear and non-stationary data, such as sea-clutter. Here we choose two methods to process the data: Recurrence quantification analysis(RQA) and Empirical Mode Decomposition(EMD).

3431Lei Nie et al. / Procedia Engineering 29 (2012) 3429 – 3433 Author name / Procedia Engineering 00 (2011) 000–000 3

Generally, for complicated signals which are nonlinear and non-stationary, time frequency analysis is still the most powerful tool. As have been discussed by many authors, there are mainly three types of time-frequency analysis: (1) traditional Fourier method, (2) wavelet method, and (3) Hilbert transform method [13]In what follows we briefly discuss the Fourier and wavelet methods, then focus on the Hilbert transform and give examples to illustrate its usefulness for signal processing on the real sea-clutter data.

Huang et.al [14] developed a new method, the Hilbert–Huang transform (HHT), to deal with the problem. The HHT consists of two parts: empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). EMD method generate a collection of intrinsic mode functions (IMF) to realize the decomposition, based on the direct extraction of the energy associated with various intrinsic time scales, which are considered as the most important parameters of the system. Expressed in IMFs, they have well-behaved Hilbert transforms, from which the instantaneous frequencies can be calculated. Thus, we can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMFs. Then, these IMFs, based on and derived from the data, can serve as the basis of that expansion which can be linear or nonlinear as dictated by the data, and it is complete and almost orthogonal.

With consideration to the non-stationary characteristic of sea-clutter, we take the following steps to implement the sifting process of decompose it. Here the input is ( )x t , the mean of its upper and lower envelopes is designated as 1m .

The first protomode 1h is the difference:

1 1( )h x t m= − (2)

Next, iteration:

1 11 11h m h− = (3)

After k times of iteration,

1( 1) 1 1k k kh m h− − = (4)

the approximate local envelope symmetry condition is satisfied, and 1kh becomes the IMF 1c ,i.e.,

1 1kc h= (5)

The sea-clutter data flows represented in the form of IMFs might have hidden, highly nonlinear, geometric structures and properties. Current statistical methods are ill-suited to detect such qualitative structures, so we implement Topological Data Analysis (TDA) method to detect the marine target. Typically, topological analysis has been applied to data sets consisting of large numbers of points in high dimensional spaces. To meet this requirement, we represent all the time series data in the phase space by delay embedding technology.

3. Experiments On Measured Data

Based on the modulating effect of long waves on radar backscattering, the signatures extracted from radar return is verified through the analysis of experimental sea-clutter data collected with McMaster University IPIX radar under varying environmental conditions. The IPIX radar is located at Osborne Head Gunnery Range (OHGR), Dartmouth, Nova Scotia, Canada, on a cliff facing the Atlantic Ocean. The IPIX radar is fully coherent X-band radar with several advanced features [15]: dual-polarized, coherent with an antenna beam width of 1", built-in calibration equipment, and digital control system.

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The radar was mounted in a fixed position on land, 25-30 m above sea level. This height is typical of a ship-mounted radar, and meet the requirement of our low-grazing-angle assumption. It was operated in a dwelling mode, with the antenna pointing along a fixed direction, illuminating a patch of the ocean surface. In such a mode of operation, the temporal character of sea clutter is entirely due to the motion of the sea surface. This particular mode of operation was purposely chosen to focus the research on the interaction between the incident electromagnetic wave and the sea surface solely as a function of time and in the most fundamental sense. In this paper we demonstrate the experimental results relative to the VV polarized data of the data set #17.

To process the time series data of No.9 range bin, we firstly decompose the data into several compositions, then the time-frequency analysis methods could be used on a couple of these compositions. For example, the Doppler frequency shift, this reflects the velocity of the moving target. Generated from radar targets’ returns, radar signature is the base of target identification, and it is proved that radar signature in a joint time-frequency domain is especially useful to catch time- dependent frequency characteristics. As can be seen in Fig.1, clutter composition and signal composition are separated well for further processing.

By acquiring a set of m-dimensional vectors reconstructed from the time series of sea clutter dataset, we can find obvious characteristics of their phase space structures; furthermore, we may use simple Topological Data Analysis methods to discover the structural features from the dataset.

Fig. 1. the sea-clutter data, range bin 9: (a) EMD components, IMF 1~3; (b) time-doppler imaging

(a) (b)

-0.4-0.3

-0.2-0.1

00.1

0.20.3

-0.4

-0.2

0

0.2

0.4-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

(c) (d)

(e)

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Fig. 2. (a) No.14 bin 3-D phase space portrait of sea clutter data set; (b)No.9 bin 3-D phase space portrait of sea clutter data set. (c)No.14 bin phase space topological structures; (d)No.9 bin phase space topological structures; (e) structural features simplified by TDA.

As is shown in Fig. 2, the No.9 rang bin which contains the marine target illustrate a prominent

topological structure compared with the other rang bins.

4. Conclusion And Future Work

In this paper, different approaches of sea-clutter modeling are analyzed. It can be inferred that effect marine target detection from X-band sea-clutter would better adapt the instinct non-stationary characteristics. Furthermore, we introduce the EMD and Topological Data analyzing methods, then apply them to measure these datasets. Experimental results indicate that the model and methods proposed in this paper are reasonable in marine target detection. Future research is required to provide complete procedures of marine target detection from X-band sea-clutter, and testify the stability of the analysis method in expanded datasets. Based on the topological analysis results, the numerical analysis of their topological invariance will be researched

References

[1] N. Xie, H. Leung and H. Chan, “A multiple-model prediction approach for sea clutter modeling,” vol.41, pp. 1491-1502, 2003.

[2] L. Jingsheng, W. Wenguang, S. Jinping and M. Shiyi, “Chaos-based target detection from sea clutter,” Proc. 2009 IET International Radar Conference 2009, April 20, 2009-April 22, 2009.

[3] F. TOTIR, E. RĂDOI, L. ANTON, C. IOANA, A. ŞERBĂNESCU and S. STANKOVIC, “Advanced sea clutter models and their usefulness for target detection,” MTA Review, vol.XVIII, pp. 1-17, 2008.

[4] B. Jiang, H. Wang, X. Li and G. Guo, “Novel method of target detection based on the sea clutter,” vol.55, pp. 3985-3991, 2006.

[5] S. Haykin, R. Bakker and B. W. Currie, “Uncovering nonlinear dynamics-The case study of sea clutter,” Pro. of the IEEE, vol.90, pp. 860-881, 2002.

[6] U. O. C. S. Diego, “Topological Analysis of Partially Ordered Data,” 2010. [7] H. Edelsbrunner, D. Letscher and A. Zomorodian, “Topological persistence and simplification,” Proc.2000 Proceedings of

the 41st Annual Symposium on Foundations of Computer Science, pp. 454. [8] Y. Yao, J. Sun, X. Huang, G. R. Bowman, G. Singh and M. Lesnick, et al., “Topological methods for exploring low-density

states in biomolecular folding pathways,” vol.130, 2009. [9] V. Robins, J. Abernethy and N. Rooney, “Topology and Intelligent Data Analysis,” IDA, pp. 111-122, 2003. [10] S. Group, 2009. G. Carlsson, Topology and Data, Bulletin of the American Mathematical Society, vol 46, Number 2,

pp.255-308, 2009 [11] J. P. Zbilut, N. Thomasson and C. L. Webber, “Recurrence quantification analysis as a tool for nonlinear exploration of

nonstationary cardiac signals,” vol.24, pp. 53-60, 2002. [12] J. P. Zbilut and C. L. Webber Jr, “Embeddings and delays as derived from quantification of recurrence plots,” vol.171, pp.

199-203, 1992.