In this paper we consider the problem of estimating a vector source in a sensor network, where each sensor in the network makes a local observation of this vector source. We assume that the local observations are distorted and noise corrupted versions of the original signal source, i.e., the observation of m-th sensor ym and the signal source x are related through y m = Hmx + nm where the matrix Hm represents the distortion (filtering) effect and nm denotes the additive noise. Each sensor encodes its observation separately and sends the encoded message to a central processor (CP), whose task is to form an estimate of source x. Our objective is to design quantizers such that the distortion in the source estimate formed by the CP is minimized, subject to the sum quantization rate constraint. Realizing the resemblance of this problem to the classical CEO problem  in multiterminal source coding, and inspired by the work in , we propose a successive coding and decoding strategy, based on Wyner-Ziv coding concept. Numerical evaluation of the sum rate-distortion performance of the proposed algorithm reveals an interesting trade off between sum rate, target distortion, and number of sensor nodes which are participating in the sequential coding.