BAYESIAN-ESTIMATION OF SOIL PARAMETERS FROM RADAR BACKSCATTER DATA

Given measurements m(1), m(2),...,m(j) representing radar cross-sectio ns of a given resolution element at different polarizations and/or dif ferent frequency bands, we consider the problem of making an ''optimal '' estimate of the actual dielectric constant epsilon and the rms surf ace height h that gave rise to the particular {m(j)} observed, To obta in such an algorithm, we start with a data catalog consisting of caref ul measurements of the soil parameters epsilon and h, and the correspo nding remote sensing data {m(j)}. We also assume that we have used the se data to write down, for each j, an average formula which associates an approximate value of m(j) to a given pair (epsilon, h), Instead of deterministically inverting these average formulas, we propose to use the data catalog more fully and quantify the spread of the measuremen ts about the average formula, then incorporate this information into t he inversion algorithm, This paper describes how we accomplish this us ing a Bayesian approach, In fact, our method allows us to 1) make an e stimate of epsilon and h that is optimal according to our criteria; 2) place a quantitatively honest error bar on each estimate, as a functi on of the actual values of the remote sensing measurements; 3) fine-tu ne the inital formulas expressing the dependence of the remote sensing data on the soil parameters; 4) take into account as many (or as few) remote sensing measurements as we like in making our estimates of eps ilon and h, in each case producing error bars to quantify the benefits of using a particular combination of measurements.