Expression for Doppler Shift in Two-Dimensional Plane

When the radial distance's direction between target and radar detection station changes unceasingly, Doppler shift in fact has the nonlinear acceleration item owing to contained the rotary motion effect. The analysis by utilizing separately the radial motion equation and the trigonometric function expansion proves that the Doppler shift about changing radius vector in two-dimensional plane can be always resolved into two terms. The first term is only associated with radial velocity and second term is associated with radial acceleration. The analysis result also indicated that the Doppler shift has the recursion nature, that is, the current Doppler shift can be derived from foregoing moment information of Doppler shift as well as its changing rate. The analog calculation result has verified that the derived recursion formula has quite accuracy.