Correcting Spatial Variance of RCM for GEO SAR Imaging Based on Time-Frequency Scaling

Abstract

Compared with low-Earth orbit synthetic aperture radar (SAR), a geosynchronous (GEO) SAR can have a shorter revisit period and vaster coverage. However, relative motion between this SAR and targets is more complicated, which makes range cell migration (RCM) spatially variant along both range and azimuth. As a result, efficient and precise imaging becomes difficult. This paper analyzes and models spatial variance for GEO SAR in the time and frequency domains. A novel algorithm for GEO SAR imaging with a resolution of 2 m in both the ground cross-range and range directions is proposed, which is composed of five steps. The first is to eliminate linear azimuth variance through the first azimuth time scaling. The second is to achieve RCM correction and range compression. The third is to correct residual azimuth variance by the second azimuth time-frequency scaling. The fourth and final steps are to accomplish azimuth focusing and correct geometric distortion. The most important innovation of this algorithm is implementation of the time-frequency scaling to correct high-order azimuth variance. As demonstrated by simulation results, this algorithm can accomplish GEO SAR imaging with good and uniform imaging quality over the entire swath.

Squint Mode GEO SAR Imaging Using Bulk Range Walk Correction on Received Signals

“…To avoid the requirement for conducting sub-band synthesis, Chen et al [15] combined singular value decomposition and azimuth nonlinear scaling, and obtained a 20-m resolution within a 150 × 130 km swath. Yu et al [16] proposed a time-frequency scaling algorithm to correct linear and quadratic variances in the azimuth direction and obtained well-focused results. Ding et al [17] modified the quadratic term in the azimuth direction and obtained a 20-m resolution within a 400 × 200 km swath under conditions where the Doppler rate was zero or approximately zero.…”

“…where t and τ denote the slow time in the azimuth direction and the fast time in the range direction, respectively; σ is the radar cross-section of P c ; rect(·) is the rectangle function; T s is the synthetic aperture time; R(t) represents the slant range history between the beam center and P c ; c is the speed of light; T p is the pulse width of the transmitted chirp signal; K r is the frequency modulation rate; and λ is the wavelength of the beam. As previously reported [16], R(t) can be described by a polynomial expression of order N, as follows:…”

“…where r n is the nth polynomial coefficient that can be obtained by fitting based on ephemeris data and geographic information specific to the target zone. A value of N = 5 has been demonstrated to be sufficiently large for GEO SAR imaging [16], and that value is assumed hereafter. However, because R(t) varies for different target zones at different locations, the coefficients r n are spatially variant, and can be expressed as functions of ∆R = R c − R re f and ∆t = t c − t re f , as follows:…”

“…where the auxiliary coefficients r n,ref , k n,m,r , and k n,m,a | ∆R , where k n,m,a | ∆R denotes the spatially variant coefficient k n,m,r at ∆R, can be calculated as presented previously in Yu et al [16]. As Figure 3 shows, echoes usually contain range walk ∆R W and range curvature ∆R B .…”

“…In order to correct the squint effect, the linear residual terms k 1,1,r · ∆R and k 1,1,a | ∆R · ∆t c in Equation (3) were removed since these two terms depend on the locations of targets. Segmentation was adopted by applying Equations (16) and (25). After segmentation, each sub-block corresponds to an area of ∆R seg × (1 − χ)T s , as shown in Figure 19.…”