1. Introduction
A near-space hypersonic vehicle-borne synthetic aperture radar (NS-HSV-SAR), which works at the altitude between 20 and 100 km with a speed of over 5 Mach, bridges the gap between the airborne and space-borne SARs [
1]. The NS-HSV-SAR would initiate a technological revolution to improve the environmental perception ability of radar [
2]. This device is potentially useful for SAR remote sensing applications for two reasons: Firstly, this device is timely, and exhibits a quick response, and high revisiting frequency. The NS-HSV-SAR exhibits a velocity advantage that the airborne SAR cannot match, and a flexibility advantage that the space-borne SAR cannot have. Because this device works in a stable climate environment and smooth airflow disturbance, it flies without constraints through orbital mechanics. Moreover, this device typically works with a squint angle or curvilinear trajectory for flexible and comprehensive detection. These features enable a timely response deployment, and multiple revisers of the detecting and key areas for NS-HSV-SAR, respectively. Secondly, the device exhibits a large footprint and persistent monitoring. Flying between the “sky” and “space” with the same radar system design (e.g., beamwidth) allows NS-HSV-SAR to obtain better performance (e.g., wide-swath) than airborne SAR. Detailed information and the same output signal-to-noise ratio (SNR) can be obtained when flying near the Earth with a lower transmit power than space-borne SAR. Moreover, acquiring long-time monitoring of a specific area is easy for the NS-HSV-SAR given an extensive effective synthetic aperture time (ESAT) and flexible responsiveness.
Although the NS-HSV-SAR is beneficial for remote sensing applications, the corresponding research on theory, method, and system remains in their early stages. Near-space has yet to develop the “vacuum” status, especially for ground moving target indication (GMTI). Several studies have been conducted for the NS-HSV-SAR GMTI [
3,
4]. These studies have mainly discussed clutter suppression issues. Fundamentally, targets may be severely smeared or displaced in a SAR image considering unknown kinematic and positional parameters. This condition makes ground moving target imaging (GMTIm) an interesting research topic, because it can enhance the ability of SAR systems for remote sensing applications [
5]. If a clutter suppression is complete, then the single-channel processing of GMTIm is highly realistic for the NS-HSV-SAR technology (e.g., stratospheric unmanned aerial vehicle-borne SAR) and easy to realize due to its simple construct. Various methods for single-channel GMTIm have been proposed. Several of these methods are evaluated in detail, and categorised into four kinds [
6], namely, keystone transform (KT) [
7,
8], stationary phase [
9,
10], Radon [
11,
12,
13], and joint time-frequency analysis-based methods [
14]. All these methods can perform well under a specific condition, and are designed with a side-looking geometry for a linear trajectory airborne or space-borne SAR. However, the NS-HSV-SAR is preferred when working with a squint angle for flexible and comprehensive detection, to provide further information about the surface structure [
15]. To the best of our knowledge, only parts of the methods have been proposed for traditional SAR/GMTI working with a squint angle [
16,
17,
18,
19]. Xu et al. [
16,
17] focused on multi-channel GMTI, and Garren [
18] mainly concentrated on two-dimensional (2-D) range migration signature analysis of a target. In [
19], the squint angle is only considered to bound the algorithm performance. Thus, this paper mainly discusses the GMTIm for single-channel squint-looking NS-HSV-SAR.
In contrast to the side-looking airborne or space-borne SAR/GMTI, the NS-HSV-SAR/GMTI with a squint angle induces several complicated features in three aspects. The first aspect is range history. The key parameter for the GMTIm is the instantaneous slant range between a radar and a target. A second order range model is typically precisely sufficient for a side-looking system with constant velocity [
20], but this model will cause error to the squint-looking NS-HSV-SAR. A high-order phase error induced by a relative motion between the radar and the target is frequently non-negligible. The second aspect is parameter coupling. Range walk migration (RWM) and Doppler centre are only induced by the radial velocity of the target in a side-looking case [
21], whereas the RWM and Doppler centre shift (DCS) of targets are related to target radial velocity, and the relative velocity and position between the target and the squint-looking NS-HSV-SAR. Moreover, the serious coupling of target and radar parameters for non-negligible high-order terms may cause severe integration loss during the exposure time without compensation. The third aspect is Doppler ambiguity. This aspect is divided into two types for easy distinction and explanation. The first type is a Doppler centre blur caused by the displacement of the Doppler centre, which is discussed in conventional SAR/GMTIs [
6,
10,
22,
23,
24,
25]. The Doppler centre blur may introduce two azimuth spectrum distributions of the signal as follows [
22,
23]: spectrum in a pulse repetition frequency (PRF) band and spanning neighbouring PRF. The second type is a Doppler spectrum ambiguity caused by a high-order Doppler frequency migration (DFM) which rarely occurs in conventional SAR/GMTIs. The Doppler spectrum ambiguity must be considered in the NS-HSV-SAR given the high speed of the radar platform. The Doppler spectrum ambiguity combined with the Doppler centre blur will complicate the echo’s azimuth spectrum distribution and affect the performance of GMTIm.
The present paper addresses the NS-HSV-SAR and presents the GMTIm for a squint-looking geometry by considering the aforementioned issues. The effects of the high-order terms are discussed, and a precise range model is presented on the basis of the phase error analyses. In contrast to previous methods that only consider the Doppler centre blur of the echo signal, we discuss the Doppler ambiguity of the squint-looking NS-HSV-SAR (i.e., the coexistence of the Doppler centre blur and spectrum ambiguity). All potential distributions of echo’s azimuth spectrum are derived. Then, a GMTIm method is proposed on the basis of the detailed analyses of the signal characteristics. The proposed method has three main steps. Firstly, a pre-processing function is developed to solve the Doppler spectrum ambiguity problem and eliminate most Doppler centre blur effects. In contrast to the deramp function in [
3,
23,
24], the proposed function is developed on the basis of a prior information, and does not require any parameters search. Moreover, the proposed function can correct the range curvature migration (RCM) and most RWMs. Then, a blur matched KT (BM-KT) is proposed to correct the residual RWM. The KT can simultaneously achieve RWM corrections of different targets at a lower SNR than the Hough transform utilized in [
6,
24,
25]. Moreover, the BM-KT can prevent the inapplicability of KT to the case of Doppler ambiguity [
7,
8,
26]. The first two steps can ensure a range dimension focusing of the target at a low SNR, regardless of any target parameter. Finally, in each focused range cell, a new chirp Fourier transform (CFT) with a time-saving searching strategy (TS-CFT) is developed for azimuth focusing. In addition, several other aspects, such as the generalisation of the proposed method for the NS-HSV-SAR with curvilinear trajectory, implementation of the method for multiple target imaging, and applicability and discussion of the method, are also included.
This paper is organised as follows. In
Section 2, the signal model and characteristics are established and analysed, respectively. Then, the proposed GMTIm method is introduced in
Section 3. Certain implementation considerations are given in
Section 4, and the numerical simulation results are analysed in
Section 5. The discussion of the proposed method is presented in
Section 6. Finally, conclusions are drawn in
Section 7.
7. Conclusions
This paper focuses on GMTIm and analysis for a squint-looking NS-HSV-SAR. A precise range model is firstly utilized on the basis of the phase error analysis considering the complex range history, parameter coupling, and Doppler ambiguity of the echo signal. Then, all potential distributions of echo’s azimuth spectrum are derived, and a GMTIm method is proposed in accordance with the detailed analysis of the signal characteristics. The properties of the proposed GMTIm method are as follows: considers the simultaneous existence of the Doppler centre blur and spectrum ambiguity; convenient unified process of range focusing for multiple targets without any target knowledge; and the TS-CFT method suitable for the cubic chirp-type signal with a low complexity searching strategy. The implementation considerations, including the generalisation of the proposed method for the NS-HSV-SAR with a curvilinear trajectory, implementation of the proposed method for multiple target imaging, and applicability and limitation of the proposed method, are also discussed. Validity and performance were investigated through theoretical analysis and numerical experiments.
However, clutter suppression is not fully considered in this method, and the target indication in the BM-KT is the direct use of amplitude detection. The proposed method does not consider the existence of interference in practice. Besides, this paper mainly considers GMTIm and disregards target parameter estimation and relocation. Furthermore, the target is focused on range time and azimuth Doppler frequency domain through the proposed method. Although this result is suitable for professionals to analyse the characteristics of the targets in different dimensions, this result cannot intuitively facilitate the radar operator in obtaining the target position and motion information as range time and azimuth time domain. The abovementioned problems will be investigated in the future.