Doppler Frequency Estimation of Point Targets in the Single-Channel SAR Image by Linear Least Squares

Abstract

This paper presents a method and results for the estimation of residual Doppler frequency, and consequently the range velocity component of point targets in single-channel synthetic aperture radar (SAR) focused single-look complex (SLC) data. It is still a challenging task to precisely retrieve the radial velocity of small and slow-moving objects, which requires an approach providing precise estimates from only a limited number of samples within a few range bins. The proposed method utilizes linear least squares, along with the estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, to provide optimum estimates from sets of azimuth subsamples that have different azimuth temporal distances. The ratio of estimated Doppler frequency to root-mean square error (RMSE) is suggested for determining a critical threshold, optimally selecting a number of azimuth subsample sets to be involved in the estimation. The proposed method was applied to TerraSAR-X and KOMPSAT-5 X-band SAR SLC data for on-land and coastal sea estimation, with speed-controlled, truck-mounted corner reflectors and ships, respectively. The results demonstrate its performance of the method, with percent errors of less than 5%, in retrieved range velocity for both on-land and in the sea. It is also robust, even for weak targets with low peak-to-sidelobe ratios (PSLRs) and signal-to-clutter ratios (RCSs). Since the characteristics of targets and clutter on land and in the sea are different, it is recommended that the method is applied separately with different thresholds. The limitations of the approach are also discussed.

Two-Dimensional Ship Velocity Estimation Based on KOMPSAT-5 Synthetic Aperture Radar Data

“…Thus, the most robust and precise approach for the range velocity estimation of a moving vessel would be a direct estimation of the residual Doppler frequency given by Equations (1), (2), and (4). However, it is often difficult to estimate the central frequency in the Doppler frequency domain directly, mainly because of noise [8]. This study uses the method proposed by [8]; where further details of the method used can be found.…”

“…However, it is often difficult to estimate the central frequency in the Doppler frequency domain directly, mainly because of noise [8]. This study uses the method proposed by [8]; where further details of the method used can be found. The method adopted is to estimate α defined by the Equation 2via linear least squares instead of direct estimation of residual Doppler frequency, which provides optimum estimates from sets of azimuth subsamples that have different azimuth temporal distances [8].…”

“…This study uses the method proposed by [8]; where further details of the method used can be found. The method adopted is to estimate α defined by the Equation 2via linear least squares instead of direct estimation of residual Doppler frequency, which provides optimum estimates from sets of azimuth subsamples that have different azimuth temporal distances [8]. The accuracy of estimating residual Doppler frequencies depends on factors including the SCR and the speed, size, and roll and pitch the target ship.…”

“…While these features distort SAR images, they have been exploited as ground moving targets indicators (GMTIs) and to retrieve the velocity of a target [7]. The velocity of vessels can be measured from SAR signals by measuring the residual Doppler frequency components directly [2,8]. The characteristics of the targets and clutter in these residual Doppler frequency estimations of vessels at sea would be very different from those of vehicles on land in terms of the following: (1) The size of the target; a ship is usually larger than an object on land; (2) the SCR at sea, which is generally larger than that on land, although the latter depends greatly on the state of the sea and system parameters including frequency and polarization; (3) the wake produced by the movement of a ship or boat across the surface of water, which helps to detect it and determine its heading [3].…”

“…These three features make it easier to detect and estimate the residual Doppler frequency of moving targets at sea. However, there are some negative features to consider, including the following: (1) The forward speed of a ship, which is generally lower than that of land vehicles, implies that the residual Doppler frequency associated with the target motion is relatively small and difficult to discriminate from the clutter bandwidth; and (2) the roll and pitch motions of a ship, which make scattering centers move continuously during the SAR observation [8].…”