# Wake-Independent Velocity Estimation and Motion Compensation for SAR Moving Target Based on Time–Frequency Analysis

## TL;DR

This paper introduces a new method for estimating the velocity and compensating the motion of moving targets in SAR imaging, without relying on wake features, validated using simulations and real Sentinel-1 data.

## Contribution

A wake-independent velocity estimation and motion compensation framework using time–frequency analysis for SAR moving targets.

## Key findings

- Estimated velocity errors remain below 0.1 m/s (radial) and 0.5 m/s (azimuthal) in simulations.
- Motion compensation effectively corrects azimuthal displacement, restoring target positions in SAR images.
- The method was successfully validated using real Sentinel-1 SAR data.

## Abstract

What are the main findings?
A wake-independent velocity estimation and motion compensation framework based on time–frequency analysis is proposed, where the beam center crossing time is determined by detecting abrupt intensity transitions.The method is verified using both simulation results and Sentinel-1 data.

A wake-independent velocity estimation and motion compensation framework based on time–frequency analysis is proposed, where the beam center crossing time is determined by detecting abrupt intensity transitions.

The method is verified using both simulation results and Sentinel-1 data.

What are the implications of the main findings?
It provides a more general motion compensation technique for sea surface ship targets, especially for targets without significant wake.The successful application on Sentinel-1 data validates its feasibility for maritime mobile target monitoring.

It provides a more general motion compensation technique for sea surface ship targets, especially for targets without significant wake.

The successful application on Sentinel-1 data validates its feasibility for maritime mobile target monitoring.

Imaging moving targets in synthetic aperture radar (SAR) remains a significant challenge due to the defocusing and azimuthal displacement caused by target motion. To address this, this paper proposes a velocity estimation and motion compensation technique to mitigate the impact of moving targets on SAR imaging quality. The core innovation of this study lies in a wake-independent method for determining the radar beam center crossing time. Unlike traditional approaches that rely on wake features, our proposed method determines the crossing time by detecting the abrupt change in echo intensity along the time axis (i.e., the azimuth direction) of the time–frequency spectrum. Using this estimated timing, the target’s radial and azimuthal velocities are estimated. Subsequently, using the estimated velocity, the motion compensation of the moving target echoes is carried out through phase correction. Due to the difficulty in obtaining AIS data strictly synchronized with real SAR acquisitions, simulation data are initially utilized to verify the proposed method. The simulation results of moving ships with different velocities under three incidence angles demonstrate that the estimated errors of the radar radial and the azimuthal velocities generally remain below 0.1 m/s (2% relative error) and 0.5 m/s (5% relative error), respectively. Furthermore, after motion compensation, the azimuthal displacement caused by radial velocity is effectively corrected, restoring targets to their actual positions. Finally, the Level-0 raw data of ships acquired by Sentinel-1 SAR are applied to further verify the effectiveness of the method proposed in this paper.