Mathematical Problems in Engineering

Volume 2018, Article ID 4146212, 10 pages

https://doi.org/10.1155/2018/4146212

## Low-Altitude and Slow-Speed Small Target Detection Based on Spectrum Zoom Processing

^{1}School of Electronic and Information Engineering, Beihang University, Beijing 100191, China^{2}Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50011, USA^{3}National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China

Correspondence should be addressed to Jinping Sun; nc.ude.aaub@gnipnijnus

Received 2 December 2017; Accepted 4 April 2018; Published 10 May 2018

Academic Editor: Wanquan Liu

Copyright © 2018 Xuwang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes a spectrum zoom processing based target detection algorithm for detecting the weak echo of low-altitude and slow-speed small (LSS) targets in heavy ground clutter environments, which can be used to retrofit the existing radar systems. With the existing range-Doppler frequency images, the proposed method firstly concatenates the data from the same Doppler frequency slot of different images and then applies the spectrum zoom processing. After performing the clutter suppression, the target detection can be finally implemented. Through the theoretical analysis and real data verification, it is shown that the proposed algorithm can obtain a preferable spectrum zoom result and improve the signal-to-clutter ratio (SCR) with a very low computational load.

#### 1. Introduction

The existing radar systems are mainly designed to detect the high-speed military targets such as the fighter plane, missile, and armed helicopter. These targets usually fly at a high altitude with a high speed so that it is very easy to separate the target echo and ground/sea clutter in the frequency domain. In this case, the target detection process of radar systems can be simply described as follows: firstly perform the coherent accumulation and then detect the targets with some traditional constant false alarm rate (CFAR) detection algorithms [1–4]. In practice, the coherent accumulation pulse number is small such that the detection result can be updated quickly with a low computational complexity.

In recent years, there are various types of aircraft, such as the paraglider, light helicopter, and rotorcraft emerging quickly in the market. These aircraft usually fly under 1000 meters with a speed lower than 200 km/h and a radar cross section (RCS) smaller than 2 m^{2}. Therefore, these aircraft are mostly called the low-altitude and slow-speed small (LSS) targets, and they have the common characteristics: simple manipulation, easy accessibility, and excellent concealment. Nowadays, the LSS target detection and tracking has become an important research direction in the field of radar signal processing and has a great significance in protecting the safety of major events and maintaining the order of airport flights. For a LSS target, the small RCS signifies that the target echo is very weak, and the low flying height usually results in the mixture of the target echo and heavy ground clutter. In the time domain, the ground clutter has a noticeable mask effect on the target echo. Meanwhile, the Doppler frequency of ground clutter is very close to that of target echo when the target speed is slow. Therefore, it is also difficult to separate the target echo and ground clutter in the frequency domain. All these factors make the LSS target detection very challenging. Unfortunately, the existing radar systems cannot be competent for this problem. Consequently, it is necessary to retrofit the existing radar systems such that they can obtain the LSS target detection ability but also keep the high-speed target detection ability.

There have been already many studies in the literatures focusing on the problem of detecting LSS targets under the background of sea clutter. For example, a short-time fractional Fourier transform based detection algorithm was proposed in [5] by investigating the micro-Doppler effect of the targets at the sea surface. In order to improve the detection performance, an adaptive waveform was designed dynamically in [6], where the expectation-maximization algorithm is used to estimate the time-varying parameters of the compound-Gaussian sea clutter. For the maneuvering target detection, two algorithms which apply the adaptive Chirplet decomposition and spectral subtraction, respectively, were proposed in [7]. A time-frequency iteration decomposition method was proposed in [8] by focusing on the nonstationarity of scattered echo from the slow moving weak target at the sea surface. Meanwhile, a time-frequency method was also applied to detect the small accelerating target in the background of sea clutter [9]. In addition, Fourier-Bessel transform was combined with time-frequency analysis to decompose the nonstationary echo of the maneuvering target into multiple components [10]. Besides the method of time-frequency analysis applied in maneuvering target detection problems, the effectiveness of track-before-detect (TBD) method in suppressing the sea clutter was assessed with the real data [11]. Furthermore, a polynomial fitting based signal phase training structure was studied in [12] for the LSS target detection in the sea clutter.

In fact, it is also very significant to study the LSS target detection problem under the background of the ground clutter especially in the complex urban environment. With the fast development of the technology and reduction of the price of aircraft, a large number of paragliders and rotorcrafts appear in the people’s daily life. These cheap aircraft mainly fly on the ground and the illegal manipulation on these aircraft can result in serious security issues. However, there are few literatures focusing on the slow moving target detection in the ground clutter [13–17]. A space-time adaptive processing method was proposed to detect the ground moving target with range migration (RM) [14]. In order to reduce the amount of echo data and achieve a wide observation swath, a parametric sparse representation method was used for the motion parameter estimation of the ground target in [15]. In particular, some spectrum zoom algorithms provide a new path for the LSS target detection. For example, the chirp-Z transform (CZT) which can be used to obtain an arbitrary frequency resolution was introduced in [18]. Based on the CZT, an interlaced CZT was proposed in [19] and this transform can produce a spectrum with denser frequency samples at any required place. Furthermore, the warped discrete Fourier transform which can produce inhomogeneous frequency samples was studied in [20, 21]. These algorithms may have some value in the LSS target detection, but the computational complexity is very high. More seriously, the above methods do not consider the characteristics of existing radar systems and the convenience of retrofitting process.

A new detection algorithm based on spectrum zoom processing is proposed in this paper according to the characteristics of LSS targets. By retrofitting the existing radar systems with some simple operations, the proposed algorithm can make the radar systems obtain an excellent LSS target detection ability. Meanwhile, the high-speed target detection ability is still retained. With the available range-Doppler frequency image in the existing radar systems, the proposed algorithm firstly concatenates the data from the same low Doppler frequency slot of different images and then performs the spectrum zoom processing on the obtained data. Finally, the clutter suppression and target detection are performed on the spectrum zoom result. Spectrum zoom processing is the key step which can effectively separate the target echo and ground clutter in the frequency domain and significantly improve the signal-to-clutter ratio (SCR).

This paper is organized as follows. In Section 2, the basic theory of spectrum zoom processing is introduced. In Section 3, the spectrum zoom processing based LSS target detection algorithm is proposed. In Section 4, the performance of the proposed algorithm is theoretically analyzed in terms of the SCR improvement and computational load. In Section 5, we verify the theoretical analysis in Section 4 with some real data. Finally, conclusions are drawn in Section 6.

#### 2. Basic Theory of Spectrum Zoom Processing

##### 2.1. Signal Model

Let , be a continuous time complex signal with a finite length, where and are positive integers and . Dividing into signals with the length of , we can getwhereShifting the signal to along the time axis, we haveCombining (1) with (3), we can obtain

After sampling the continuous time signal and with a period of , respectively, the resulting discrete time sequences areObviously, is just the arrangement of with the sequential order.

According to [22], the Fourier transform (FT) of can be written asMeanwhile, the discrete time Fourier transform (DTFT) of can be written asand the discrete Fourier transform (DFT) of can be written aswhere and .

Obviously, the sequence is just the sample of at the frequency ; that is,where . Assume that the whole energy of is concentrated in . Therefore, the sampling process of obeys Nyquist’s law, and is the extension of with the period of . In this case, is also the sample of at ; that is,

Similar to (6)–(10), the FT of can be written asMeanwhile, the DTFT and DFT of can, respectively, be written aswhere and . We also havewhere .

In addition, taking the FT on both sides of (4), we arrive atwhich shows the relationship between and in the frequency domain.

##### 2.2. Spectrum Zoom Processing

The sequence , , shows the whole spectrum information of in . However, only partial spectrum information of is necessary in some applications. Consider a specific problem. Assume that the sequence ,, is known. Then, divide the frequency range into bands with equal lengths. In this case, how to obtain the spectrum information of at the band, that is, ,?

An obvious method is as follows: firstly calculate the sequence , , according to (8), and then select out . Here, we introduce a fast method for obtaining with ,, as follows. This method will be applied to retrofit the existing radar systems in Section 3.

For simplicity, letwhere and . According to (10), we haveSubstituting (15) into (17), we can getwhere . It can be seen that is just the DFT of . Therefore, it is very easy to obtain by applying the sequence .

Since includes the variable , we need to calculate a new sequence for a given , which can result in a high computational load. Instead, we can approximate as follows:Equation (18) can be approximated asAccording to (14), we can getSubstituting (21) into (20), we can getHence, can be approximated as the DFT of . Since the variable is not contained in the sequence , for a given , only the same sequence needs to be calculated when takes all the . This way can significantly reduce the computational load. In the case when , , is known, a fast way for obtaining the spectrum information of at the band (i.e., ) is to select out the sequence from the known information and then perform the DFT.

According to (10) and (14), , is the sample of with the period of , whereas , , is the sample of with the period of . From (22), we know that the frequency spectrum sample with a short sampling period can be obtained from the frequency spectrum sample with a relative longer sampling period by DFT, which is the so-called spectrum zoom processing. According to the above analysis, we can summarize the spectrum zoom processing as follows: (i) sample the continuous time complex signal whose frequency spectrum locates in with a period of , and obtain sequences , with the length ; (ii) write the DFT of , as , ; (iii) for an arbitrary , the DFT of sequence can be approximately regarded as the spectrum sampling result of in with a period of or can be equivalently regarded as the DFT of the sequence ,, where is the sequential arrangement of the sequences ,, in the frequency range (i.e., ). It can be seen that the spectrum zoom processing provides a simple and fast approach for obtaining the refined spectrum from the coarse spectrum, which is very significant in the applications where only the refined spectrum on a partial band is necessary.

#### 3. Spectrum Zoom Processing Used for the LSS Target Detection

The existing radar systems are mainly designed for high-speed targets. Considering the facts that the instantaneous position of the high-speed target varies quickly and the Doppler frequency of target echo varies in a board range, the detector usually takes a small coherent accumulation pulse number. Such an operation can obtain a high frame rate to update the target state quickly with a low computational complexity. Meanwhile, the resulting range-Doppler frequency image has a large spectrum interval. However, as a large number of LSS targets appear in recent years, the existing radar systems cannot perform an effective detection on these targets. The main reasons are as follows: the echo of LSS target is very weak, and more coherent pulses are necessary to accumulate the target energy; the Doppler frequency of LSS target echo is very close to that of the ground clutter, and the spectrum should be refined enough to separate them. Therefore, the existing radar systems should be retrofitted properly.

Based on the spectrum zoom processing introduced in Section 2, a simple and feasible scheme is designed for retrofitting the existing radar systems in this section. This scheme applies the available range-Doppler frequency image in the existing radar systems to obtain the refined spectrum information of the observation data in the low Doppler frequency band, which can effectively separate the target echo and ground clutter in the frequency domain and improve the accumulation effect of the target energy. Next, this retrofitting scheme will be introduced in detail.

##### 3.1. Whole Retrofitting Scheme

A typical model of the pulse Doppler radar observation data is shown in Figure 1. The horizontal axis represents the fast time dimension, containing range gates in total. The vertical axis represents the slow time dimension, containing pulses in total. Each sequential pulses are regarded as a frame of the observation data, and it contains frames of the observation data in Figure 1. Write the pulse as , where represents the sample of the range gate in the pulse, ,. Define matrixwhich represents the frame of the observation data, .