A Joint Estimation Method of the Channel Phase Error and Motion Error for Distributed SAR on a Single Airborne Platform Based on a Time-Domain Correlation Method  
[PERSON]  
1 Radar Research Laboratory, School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China; [EMAIL_ADDRESS] (C.Z.); [EMAIL_ADDRESS] (L.L.); [EMAIL_ADDRESS] (S.L.); [EMAIL_ADDRESS] (Z.D.)  
[PERSON]  
1 Radar Research Laboratory, School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China; [EMAIL_ADDRESS] (C.Z.); [EMAIL_ADDRESS] (L.L.); [EMAIL_ADDRESS] (S.L.); [EMAIL_ADDRESS] (Z.D.)  
[PERSON]  
1 China Satellite Network Innovation Co., Ltd., Beijing 100029, China 13 Chongqing Key Laboratory of Novel Civilian Radar, Chongqing  
supersonic fighters or reconnaissance aircrafts. Compared with the spaceborne distributed SAR, the connection between the channels of the distributed SAR on a single airborne platform is rigid, and the motion error is not negligible.  
The HRWS imaging mode is a popular research area of distributed SAR [13; 14; 15; 16; 17]. For single-channel SAR systems, regardless of the operating mode, a high azimuth resolution and a wide swath contradict each other in system design due to the minimum antenna area limitation [18; 19]. Distributed SAR can overcome the minimum antenna area limitation and obtain HRWS imaging by signal reconstruction methods [18; 20; 21; 22; 23]. In addition, compressed sampling has also recently been used to address undersampling SAR [24; 25; 26]. In [11; 17; 27; 28], distributed SAR imaging with TerraSAR-X and Tandem-X was demonstrated. Before signal reconstruction, spaceborne distributed SAR first needs to compensate for channel errors, including channel amplitude phase errors, range sampling delays, and channel errors caused by the cross-track baseline (CTB). The above channel errors lead to amplitude errors, envelope migration, and phase errors between channels. The envelope migration is estimated and compensated by channel coregistration methods in the range time domain [29; 30; 31] or range frequency domain [32]. The amplitude and phase errors can be estimated and compensated by the orthogonal subspace method (OSM) [13], the adaptive weighted least square method (AWLSM) [33], the signal subspace comparison method (SSCM) [14; 34], or the time-domain correlation method (TDCM) [35; 36], among which the first three are more computationally intensive with the TDCM more widely used in real-time processing systems. However, the distributed SAR on a single airborne platform leads to the failure of traditional channel error estimation methods due to the non-negligible coupling of motion error and channel error (collectively referred to as \"signal error\" in this paper). Therefore, the joint estimation method of the channel phase and motion error needs to be studied.  
For the distributed SAR motion error and channel error coupling problem, this paper firstly establishes a signal model of the coupled motion error and channel error of single-platform distributed SAR. Based on this signal model, the phase sequence form of TDCM estimation is then analyzed. A joint estimation method of the channel phase error and motion error for the distributed SAR on a single airborne platform based on the TDCM is also proposed to obtain the acceleration motion error of the platform and the phase error between the distributed channels. The effectiveness of the proposed method is verified through simulation and real data processing.