Radial Velocity Retrieval for Multichannel SAR Moving Targets With Time–Space Doppler Deambiguity

Abstract

In this paper, with respect to multichannel synthetic aperture radar (SAR), we first formulate the problems of Doppler ambiguities on the radial velocity (RV) estimation of a ground moving target in range-compressed domain, range-Doppler domain and image domain, respectively. It is revealed that in these problems, cascaded time-space Doppler ambiguity (CTSDA) may arise, i.e., time domain Doppler ambiguity (TDDA) in each channel arises first and then spatial domain Doppler ambiguity (SDDA) among multi-channels arises second. Accordingly, the multichannel SAR systems with different parameters are investigated in three cases with different Doppler ambiguity properties. Then, a multi-frequency SAR is proposed for RV estimation by solving the ambiguity problem based on Chinese remainder theorem (CRT). In the first two cases, the ambiguity problem can be solved by the existing closed-form robust CRT. In the third case, it is found that the problem is different from the conventional CRT problem and we call it a double remaindering problem in this paper. We then propose a sufficient condition under which the double remaindering problem, i.e., the CTSDA, can also be solved by the closed-form robust CRT. When the sufficient condition is not satisfied, a searching based method is proposed. Finally, some results of numerical experiments are provided to demonstrate the effectiveness of the proposed methods.

On the Foundation of Sparse Sensing (Part I): Necessary and Sufficient Sampling Theory and Robust Remaindering Problem

“…Proof. With the fact that, r − c = Γ−r + c , it is clear that {r + c , r − c } must fall into one of the following four cases, 1) r + c ∈ [Γ/4, Γ/2) and r − c ∈ (Γ/2, 3Γ/4] 2) r + c ∈ [Γ/2, 3Γ/4) and r − c ∈ (Γ/4, Γ/2] 3) r + c ∈ [0, Γ/4) and r − c ∈ (3Γ/4, Γ] 4) r + c ∈ [3Γ/4, Γ) and r − c ∈ (0, Γ/4] Recall (22), to ensure robustness, we consider applying τ + l ∈ {0, 1} to determine the order of l such that ∆ + l are in ascending order, i.e., r+ c,l = r + c,l − τ + l Γ are sorted in the order of ∆ + l . Here, we use r + c,l = r + l Γ , the noisy observation of common residue from the l-th sampler.…”

“…This idea is further generalized to other parameter estimations, such as phase unwrapping [20] with applications in synthetic aperture radar (SAR) [21], [22].…”

Beamforming in SAR satellites for nadir echo suppression

“…Furthermore, in [5], the nadir echo interference is mitigated by proper design of PRF in high‐squint spotlight SAR imaging. However, lack of freedom in choosing PRF degrades the performance, since PRF plays a key role in the performance of SAR satellites [6].…”

Statistical Robust Chinese Remainder Theorem for Multiple Numbers: Wrapped Gaussian Mixture Model

“…For example, in a pulse repetition frequency (PRF) radar [9], when the distance exceeds the wavelength of transmit pulses, the raw signal from a reflection is the distance modulo the used wave length. As two fundamental tasks, frequency and phase estimation have a wide range of applications, such as localization in wireless sensor networks [9] [15] and imaging of moving targets in synthetic aperture radar (SAR) [16], [7], [8] [29].…”