A theoretical analysis is done to arrive at expressions for quick estimation of the leakage noises due to jitter and drift motions in a surveillance sensor system. The expression for the mean square clutter leakage started out in an integral form, involving pixel footprint size, background spatial distribution density, optical parameters of the telescope, observation range, detector transfer function, and the filter function. The filter is assumed to be an Nth order temporal differencing type, and the background scene has a Cauchy type distribution with specific standard deviation and correlation length. Then the integral expression is reduced to a simplified case where the system motion is assumed to be one dimensional, consisting of a linear combination of a uniform drift motion and a sinusoidal jitter vibration. For both the jitter and the drift dominant case the integrations are reduced to the summing of sine and cosine integral functions. Asymptotic expansions are then used to express the clutter leakage in terms of sine and log functions. The resulting expressions are simple enough to be rapidly used with a desk-top calculator. The results are compared with curves generated by a digital computer using a more exact numerical integration method and agrees well except for the values at the jitter vibrational peaks where the approximation method over estimates.