Velocity and acceleration estimation of Doppler weather radar/lidar signals in colored noise

We are interested in estimating the Doppler shift occurred in weather radar returns, which yields precipitation velocity information. Conventional techniques including the pulse pair processor rely heavily on the assumption that the additive noise is white and hence their performance degrades when the noise color is unknown. Because the data length for a given range gate is usually small, we employ the high resolution MUSIC algorithm to estimate the Doppler shift. The challenge lies not only in proving that MUSIC is applicable to weather radar signals which are affected by multiplicative noise, but also in showing that MUSIC is robust when the additive noise is colored. The resulting algorithm can also be used to infer wind speed from a small number of lidar observations where the velocity is approximately constant. Assuming linear shear over a longer range, we employ the ambiguity function to estimate the acceleration and instantaneous wind velocity. Real weather radar and lidar data as well as simulated examples are provided to illustrate the performance of the algorithms.