## 5 Data Fusion Processing Method of Target Coordinates on Multi-Acoustic Basic Arrays  
It is assumed that the test data have no deviation and obey a normal distribution. That is to say, the observed values \(C_{A}\), \(C_{B}\), and \(C_{C}\) of the target position coordinates obtained by the basic arrays A, B, and C obey a normal distribution, the mean value of which represents the true values \(C_{A}\)\({}^{\prime}\), \(C_{B}\)\({}^{\prime}\), and \(C_{C}\)\({}^{\prime}\) of the target position coordinates. The standard deviation results of basic array test data are denoted as \(\sigma_{A}\), \(\sigma_{B}\), and \(\sigma_{C}\), respectively, which are obtained by accepting the target's spread range. The probability density function of \(C_{A}\), \(C_{B}\), and \(C_{C}\) is as follows:  
\[\left\{ \begin{array}{l}f(C_{A}\ ^{\prime})=\frac{1}{\sigma_{A}\sqrt{2\pi}} \exp\left\{-\frac{(C_{A}-C_{A}\ ^{\prime})}{2\sigma_{A}^{2}}\right\}\\ f(C_{B}\ ^{\prime})=\frac{1}{\sigma_{B}\sqrt{2\pi}}\exp\left\{-\frac{(C_{B}-C_{B}\ ^{ \prime})}{2\sigma_{B}^{2}}\right\}\\ f(C_{C}\ ^{\prime})=\frac{1}{\sigma_{C}\sqrt{2\pi}}\exp\left\{-\frac{(C_{C}-C_{C}\ ^{ \prime})}{2\sigma_{C}^{2}}\right\}\\ \end{array} \right. \tag{12}\]  
In general, the target position coordinates have theoretical value. However, there is a certain deviation between the actual target position in a set of tests and the theoretical value, which makes the uncertainty great. Therefore, it is difficult to obtain valid prior information about \(C_{A}\), \(C_{B}\), and \(C_{C}\) before the test. One basic array can only test one target explosive position once, making the target position test non-repeatable. The obtained test results are denoted as \(C_{A}^{s}\), \(C_{B}^{s}\), and \(C_{C}^{s}\), respectively; \(C_{A}\ ^{\prime}\), \(C_{B}\ ^{\prime}\), and \(C_{C}\ ^{\prime}\) are estimated with the observed values \(C_{A}^{s}\), \(C_{B}^{s}\), and \(C_{C}^{s}\) by applying the conventional point estimation theoretical approach. Subsequently, the probability density function of the true values \(C_{A}^{s}\), \(C_{B}^{s}\), and \(C_{C}^{s}\) of the target position is as follows:  
\[\left\{ \begin{array}{l}f(C_{A}\ ^{\prime}\bigg{|}C_{A}^{s})=\frac{1}{\sigma_{A} \sqrt{2\pi}}\exp\left\{-\frac{C_{A}\ ^{\prime}-C_{A}^{s}}{2\sigma_{A}^{2}}\right\}\\ f(C_{B}\ ^{\prime}\bigg{|}C_{B}^{s})=\frac{1}{\sigma_{B}\sqrt{2\pi}}\exp\left\{-\frac{C _{B}\ ^{\prime}-C_{B}^{s}}{2\sigma_{B}^{2}}\right\}\\ f(C_{C}\ ^{\prime}\bigg{|}C_{C}^{s})=\frac{1}{\sigma_{C}\sqrt{2\pi}}\exp\left\{-\frac{ C_{C}\ ^{\prime}-C_{C}^{s}}{2\sigma_{C}^{2}}\right\}\\ \end{array} \right. \tag{13}\]Formula (13) delineates the probability density function acquired for \(C_{A}\) ', \(C_{B}\) ', and \(C_{\text{C}}\)'given the test values \(C_{A}^{s}\), \(C_{B}^{s}\), and \(C_{\text{C}}^{s}\). This formula encompasses not only the information derived from the actual measured values but also incorporates prior information. In contrast, conventional data processing methods narrow their focus solely to the actual measured values, neglecting considerations for the accuracy of the test equipment. Consequently, the aforementioned representation of test data is considered more scientifically sound. From the perspective of probability theory, when evidence is acquired, there necessarily exists a probability density distribution function for the target position under this circumstance, and we denote probability density distribution function as \(f(x,y,z|C_{A},C_{B},C_{\text{C}})\). The optimal estimate for the target coordinate is determined by the spatial position associated with the maximum value of \(f(x,y,z|C_{A},C_{B},C_{\text{C}})\). Because the three-dimensional coordinate's data of the low-altitude target are independent of each other in three basic arrays, the traditional probability of the low-altitude target gained by each basic array is as follows:  
\[\left\{