【正文】 ns are carried out at the cluster head before transferring pressed data to the base station or end user. We will call this a centralized processing scheme. A specific application such as target localization using conventional methods, however, requires a circumspect design in order to obtain an accurate and costeffective system. The main reason is that the observation at each sensor is monly time series data. To individually transmit such data from all cluster members to be processed at cluster head entails a large amount of overall munication cost particularly when the cluster is designed to be large to reach the localization accuracy requirement. An alternative is to apply distributed processing by some means depending upon the characteristics of the utilized methods for a particular application. We exploit a wellknown scheme, the range difference based localization, for distributed processing in sensor works and demonstrate that the system performance can be improved when pared with the centralized method. Ⅲ . RANGE DIFFERENCE BASED LEAST SQUARE LOCALIZATION Range Differences (RD) can be derived from Time Difference of Arrival (TDOA) estimation through the relationship between distance and traveling speed of the signal over a medium. Time delay estimation technique [10] is the fundamental tool used to determine TDOAs. We will assume the existence of an optimal time delay estimator producing estimated TDOA perturbed by additive noise to model uncertainty. There have been a number of RDbased approaches proposed in the past 15 [11], [12]. We focus on a closedform least square method proposed in [11] since it was reported to be more efficient than the other schemes and was shown to approach the Cramer Rao Bound (CRB) in high Signal to Noise Ratio (SNR) environments. Let N sensors be assigned to participate in the localization process located at coordinates ? ? ? ?? ?NN yxyx ,....., 11 . Assuming the target is located at ? ?sss yxZ ,? , the differences of the distance between sensors i and j where i, j = 1, . . . , N and the source denoted by dij can be obtained by the basic relation: jiij DDd ?? where iD = ? ? ? ?22 isis yyxx ??? . RDs with respect to one arbitrary reference sensor are typically used. Without the loss of the generality, we select ? ?11,yx to be the location of reference sensor. The time series data collected from the other sensors together with the received signal at the reference sensor can produce the TDOA estimates and RDs can be derived from TDOAs using the knowledge of signal traveling speed. In the real application, however, the actual RDs are not available since there are some errors from TDOA estimation. Consequently, We have ?1id = 11 ii nd ? , i = 1. . . N. The TDOA estimate obtained by generalized cross correlation with Gaussian data is asymptotically normally distributed in high SNR environment [13]. Therefore, the RD estimate is also Gaussian and we assume 1in ～ N? ?21,0 i? . The Localization problem can be formulated as a linear least squares problem, bA ?? , where ???????????11222NNN dyxdyxA ??? ，???????????sssRyx? ，?????????????2122122121NN dRdRb ? ，? ? ? ?2121 yyxxR iii ???? These linear least square equations can be solved by a batch approach and the solution, ? ? bAAA TT 1?? ?? . However, we can update ?? without having to resolve the linear equations by a sequential least squares procedure [14] which can be described by letting ??nA = ? ? ? ?? ?TT nanA 1? and ??nb = ? ? ? ? ? ?? ?Tnbbb ?21 . The sequential least square estimator bees ? ? ? ? ? ? ? ? ? ? ? ??????? ?????? ??? 11 nnanbnnn T ??? （ 1 ）， ? ? ? ? ? ?? ? ? ? ? ??? ?? ??? nanna nann T 11 1，? ? ? ? ? ?? ? ? ?? ? ????? 1nnann T（ 2） and index n corresponds to the thn sensor. Ⅳ . DATA MODEL 16 A static acoustic target generating a WSS Gaussian random observation process, ??ts , is assumed where the intensity attenuates at the rate that is inversely proportional to the distance from the target. Perturbed by additive Gaussian measurement noise ??ti? , the received signal at thi sensor is given by ??txi = ? ? ? ?tDts ii i ?? ??. The energy can be calculated by averaging over a time window T =sfM where M is the number of samples and sf is the sampling frequency as ??kyi = ? ?? ?? ???kM Mkj i jxM 11 21 . Assuming ??ts and ??t? are independent, we get ??? ?kyi? = ? ?? ? ? ?? ?tD tsi222 ???? (3) ? ?? ?kyivar =? ?? ? ? ?? ?MtD tsi22222???????? ??? ? (4) ， Let ??ts ～N ? ?2,0 s? and the noise at each sensor has the same distribution so that ??ti? ～ N ? ?2,0 ?? . The signal PSD ? ?? ?fGs , the noise PSD ? ?? ?fGs , and the coherence are assumed to be flat over a bandwidth Δ f z? centered at frequency 0f . The SNR at each sensor, ? ?? ?222,???isiwis DfG fG ? .According to [10], CRB of the TDE estimate is the following 130302222138 ??????????????????? ?????? ???????? ???????????ffffCCTijijij ?? where ijC = ? ?? ?? ?? ? ???????? ????????? ? ??fGfGfGfGjjsiis,1,1, 111?? It is simple to derive that the variance of the estimate can be in the form, 212121 Di ??? ?? , where03030221212283S N RffffTD???????? ?????? ????????? ????? 17 03030202122813S N RffffTS N RD?????????????? ????????? ?????????? ???? (5) and 0SNR denotes 22???s . Please note that 21i? is the variance of TDE between thi sensor and the reference sensor as assumed in the previous section. Such variance is proportional to 2iD where the constants, 21? and ? are functions of 21D . Therefore,