Correlation and covariance of satellite scatterometer measurements

Capable scatterometer designs have been developed that seek improved resolution through the use of higher pulse sampling rates. The high sampling rates bring the traditional scatterometry assumption of measurement independence into question. This paper uses fundamental scattering theory to derive general expressions for correlation and covariance between scatterometer measurements and provides practical analysis using current and future instruments as examples. The paper derives expressions for the measurement variance parameter K_p when measurement correlation due to Rayleigh fading effects is present and relates K_p to the statistics of multiple pulse measurements. A function of the transmit signal modulation and receive processing, the measurement correlation is zero for nonoverlapping measurements but can become significant for overlapping measurements at high pulse sampling rates. The paper discusses the effects of correlation on the accuracy of scatterometer measurements and evaluates tradeoffs between spatial overlap, levels of additive noise, and measurement precision.