【正文】 ?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, with a fixed reference sensor, TDE with respect to the farther sensors from the target is less accurate. Ⅴ . DISTRIBUTED LOCALIZATION From the description of the range difference based localization method, we can note that there are two key steps which are TDOA estimation and target localization obtained by solving least square equations. In a Centralized scheme, both steps take place at the cluster head. The cluster head should be a reference sensor and TDOAs with respect to the cluster members can be obtained through time delay estimation. The distributed localization concepts can be adopted by enabling some processes to occur at each participating sensor, not just at the cluster head. If time series data collected at the cluster head is transmitted to the participating sensors, time delay estimation can be operated there. Broadcasting the data from one reference sensor to many participating sensors is expected to require less total munication overhead than in the opposite direction. Solving least square equations enpasses two mechanisms depending on whether batch or sequential procedure is applied. Batch estimator requires all measurements available at the same time whereas sequential estimator needs only the estimate obtained from the (n?1)th sensor and a TDOA corresponding to the nth sensor. The latter, however, demands less putational plexity as it does not have to deal with matrix inversion which might be burdensome when the matrix is large due to a large number of participating sensors. Another advantage is that the current estimate can be used as the prior information to properly select the next participating sensor. According to the data model that the variance of time delay estimation is proportional to the square distance between the sensor and the target, the preferred sensors can be simply selected by considering the nearest sensors to the current estimate. Consequently, bining the ideas of distributed processing for time delay estimation and sequential least square localization is expected to improve the localization performance in terms of both munication cost savings and accuracy. By using the notations defined in the previous section, we propose the following algorithm: 1) The sensor which receives the highest average signal energy in a certain time window is selected to be an initial sensor. Please note that the term “initial sensor” is used to call the sensor that starts the process instead of “cluster head”. 18 2) The initial sensor broadcasts collected time series data to at most k nearest neighbors within the maximum radio range where k is the initial expected number of participating sensors. There might be a possibility that less than k sensors can be reached depending on the coverage of the radio range and the density of the sensor field. 3) Each neighbor operates time delay estimation using time series data collected at the sensor and the one sent from the initial sensor to estimate TDOAs. 4) The initial estimate is obtained by using batch estimator based on TDOAs puted by the three nearest neighbors. The neighbor might be requested to broadcast time series data received from the initial sensor if there are less than three sensors that have already received it. 5) k4 nearest sensors to the initial estimate achieved from the batch estimator are expected to participate in the sequential least square method. It bees k?i nearest sensors for the following estimate where i is a number of sensors that are already included in the localization process. The route of s