###### Abstract
Equipped with rubidium clock USOs disciplined by the Global Navigation Satellite System (GNSS), the LT-1 system limits the time synchronization error to 60 ns at the time of 600 s data acquisition, and the frequency stability can be up to \(10^{-11}\)[9]. The problem of phase synchronization refers to the fact that the demodulation frequency of the receiver is hard to be consistent with the modulation frequency of the transmitter, which originates from the difference of USOs on the two satellites and results in additional phase modulation in the demodulated signal [21; 22]. The random phase error can be divided into three components: linear phase error, quadratic phase error, and higher-order phase error, which will cause linear displacement, main lobe dispersion, and side lobes increase, respectively [23; 24]. In addition, the phase error will eventually be transferred to the interference phase, resulting in the decline of the accuracy of interferometric height measurement. Therefore, highly accurate phase compensation must be implemented in BiSAR/MultiSAR system. In order to ensure the consistency of transmitter and receiver over a long period of time, many phase synchronization methods have been proposed, such as ultra-high stability frequency source [25], direct pulse synchronization [26], self-synchronization [27], continuous duplex inter-satellite link [28], simplex communication [29; 30], and alternate pulse synchronization scheme [21; 31]. As a proven BiSAR synchronization technology, the alternate pulse scheme is successfully applied to the TanDEM-X system, and its long-term operation performance is evaluated and verified in [32]. However, in order to exchange the synchronization pulse, the BiSAR data acquisition is interrupted [32]. The quality of SAR images and interferometric products suffer from periodic data loss. Thus, acquisition cannot be interrupted frequently. A tradeoff between the proper sampling of the random phase error and the quality of SAR images leads to the synchronization frequency equal to 5 Hz [33], which limits the accuracy of phase synchronization. As an evolutionary version of the alternate pulse scheme, a non-interrupted phase synchronization scheme is designed for the LT-1 mission [9; 34; 35]. With intelligent use of the duration between the end of the echo receiving window and the start of the next pulse repetition time (PRT) to exchange synchronization pulse, the LT-1 system avoids interrupting the normal BiSAR data acquisition and increases the maximum synchronization frequency to PRF/2. Generally, the phase synchronization accuracy meets the design requirements of the LT-1 system. However, the thermal noise and signal attenuation are inescapable, and there may be potential multipath effects and radio frequency interference in the transmission link [36]. The synchronization phase will be disturbed by the noise. Under the framework of the non-interrupted synchronization scheme, the phase synchronization accuracy can be further improved by coherent integration [9]. However, when the synchronization frequency decreases, the synchronization accuracy will be reduced due to the decoherence of signals. In addition, the number of averages should be chosen carefully due to compromise between the coherence and the number of averages [24]. [PERSON] et al. [37] proposed a phase compensation method based on Kalman filtering (KF) to improve the accuracy of phase synchronization. However, Kalman filter estimates the current state by combining the observed values and the predicted values. The predicted values come from the estimation of the previous state. Therefore, a hysteresis phenomenon occurs in the estimated result, which limits the further improvement of synchronization accuracy. Compressive sensing (CS) provides a newly developed theoretical framework for information acquisition and signal processing, which is widely applied in information theory, image processing, optical/microwave imaging, wireless communication [38].