IDENTIFIABILITY IN WIND ESTIMATION FROM SCATTEROMETER MEASUREMENTS

In this paper we consider the problem of identifiability of a wind vector that is estimated from wind scatterometer measurements of the radar backscatter of the ocean's surface. The traditional wind estimation approach produces multiple estimates of the wind direction. A second processing step, known as "dealiasing" or "ambiguity removal" is used to select a single wind estimate from these multiple solutions. Dealiasing is typically based on various ad hoc considerations. The traditional wind estimation approach results in multiple solutions associated with local minima in an objective function formed from the noisy backscatter measurements. We address the question of the uniqueness of the wind vector estimates resulting from this intuitive approach. We show that wind vector estimation using scatterometer measurements is set-wise or system identifiable; i.e., we provide mathematical proof that there is a unique set of wind vectors that could have given rise to the observed backscatter values, and that the set of wind vector estimates is consistent. The fact that the wind vector estimate is a set arises from the nature of the relationship between the backscatter and wind vector. Within this set there is no way to select a unique wind vector estimate from the measurements at a single sample point; hence, we establish a theoretical reason for dealiasing.