Improved Analytical Formula for the SAR Doppler Centroid Estimation Standard Deviation for a Dynamic Sea Surface

Abstract

The existing formulas for the synthetic aperture radar (SAR) Doppler centroid estimation standard deviation (STD) suffer from various limitations, especially for a dynamic sea surface. In this study, we derive an improved version of these formulas through three steps. First, by considering the ocean wavenumber spectrum information, a new strategy for determining the number of independent samples of the sea wave velocity field is adopted in the new formula. This is contrary to the method used in the existing formulas, where the number of SAR geometric resolution cells is taken as the number of samples assuming that adjacent SAR resolution cells are statistically uncorrelated. Second, the pulse repetition frequency and Doppler bandwidth are decoupled in the new formula, unlike in the existing formulas where they are unchangeably related to each other. Third, the effects of thermal noise and Doppler aliasing are jointly quantified in a mathematically exact manner instead of being treated separately, as in the existing formulas. Comprehensive SAR raw data simulations for the ocean surface show that the new formula has a better performance in predicting the Doppler centroid estimation STD than the existing formulas.

How to Obtain a Detailed SAR Pattern of Currents on the Ocean Surface

“…Thus, having the values 𝑣̅ 𝑟𝑎𝑑 obtained through the Doppler centroid with an average accuracy of ƒ 𝑆𝑇𝐷 /2𝑘 , where ƒ 𝑆𝑇𝐷 is the Doppler centroid standard deviation, one can determine the shift (𝑅/𝑉) 𝑣̅ 𝑟𝑎𝑑 at each image point, and then to shift it to its real place, i.e., to restore the real picture of currents with average accuracy of (𝑅/𝑉)(ƒ 𝑆𝑇𝐷 /2𝑘 ). The issue of ƒ 𝑆𝑇𝐷 , taking into account also other factors besides the orbital velocities, was considered in detail in [3], where, by means of numerical simulation, an estimate was obtained at SAR working frequency 9.6 GHz and a wide range of near-surface wind speeds: ƒ 𝑆𝑇𝐷 ≈ 3𝐻𝑧. Note that it is generally possible to determine the current velocity and perform the procedure for reconstructing the real pattern of currents on the ocean surface without resorting to the Doppler centroid.…”