## 5 Evaluation of the Fusion Effect of Semi-Physical Simulation and Field Data  
For the fusion of the abovementioned semi-physical simulation landing point data that do not pass the integrity detection but complete the supplementation with the field test data, the empirical distribution function (EDF) image in Definition 1 is drawn. At the same time, the semi-physical simulation data that have not passed the integrity detection and have not been supplemented are directly fused with the field test data, and the empirical distribution function image is drawn as a control group. Considering the utilization of semi-physical simulation data information, the Bayesian fusion method is selected. The idea of Bayesian methods for solving statistical problems is different from classical statistical methods. One of their distinguishing features is using all possible information as much as possible while ensuring that the decision-making risk is as small as possible. This is not only the field test information but also the information before the field test, such as the useful information of the aircraft system during development, the information of the simulation test, and the test information of similar weapon equipment systems. The actual number of field trials can be small. Therefore, in the presence of the abovementioned prior information, as a data fusion method, the Bayesian method can be used for small sample test analysis. Generally, Bayesian fusion easily obtains an explicit expression in the case of a normal distribution. The specific fusion process is described below. Let the external field sample data be \(X^{B}=\left\{X_{i}^{B},i=1,2,\cdots,N_{B}\right\}\). Each test sample datapoint is an \(M\)-dimensional vector, and the \(i\)-dimensional vector is denoted as \(Y_{i}^{B}=\left\{x_{1i}^{B},x_{2i}^{B},\cdots,x_{N_{B}i}^{B}\right\}\). The semi-physical simulation sample data are \(X^{A}=\left\{X_{i}^{A},i=1,2,\cdots,N_{A}\right\}\). Each test sample is an \(M\)-dimensional vector, and the \(i\)-dimensional vector is denoted as \(Y_{i}^{A}=\left\{x_{1i}^{A},x_{2i}^{A},\cdots,x_{N_{A}i}^{A}\right\}\). We use the semi-physical simulation data source as the prior information and the field test data source as the field sample for data fusion. **Definition 2**. : The observed sample \(X=\left(X_{1},X_{2},\cdots,X_{n}\right)\) is the overall sample. The density function of \(X\) is \(p(x;\theta)\) and the parameter to be estimated is \(\theta\). The Bayesian academics treat \(\theta\) the same as a random variable \(X\) and treat \(p(x;\theta)\) as a conditional probability density in classical statistics \(p(x|\theta)\). Under the prior distribution \(\pi(\theta)\), for \(\theta\) to generate a new understanding, the posterior density is obtained as  
\[h(\theta\mid x_{1},x_{2},\cdots,x_{n})=\frac{\pi(\theta)p_{X}(x_{1},x_{2}, \cdots,x_{n}\mid\theta)}{\int\pi(\theta)p_{X}(x_{1},x_{2},\cdots,x_{n}\mid \theta)d\theta} \tag{9}\]  
where \(\pi(\theta)\) is the prior distribution, \(p_{X}(x_{1},x_{2},\cdots,x_{n}|\theta)\) is the maximum likelihood function of the sample, and the distribution type of \(\theta\) is only determined by \(\pi(\theta)p_{X}(x_{1},x_{2},\cdots,x_{n}|\theta)\). Therefore, the Bayesian statistical model can be simplified as \(h(\theta|x)\propto\pi(\theta)p_{X}(x|\theta)\). The data \(Y_{i}^{B}\) of the \(i\)-th dimension of the field test data source obey a normal distribution \(N(\mu_{i},\sigma_{i}^{2})\), where \(\sigma_{i}^{2}\) is known as the sample variance of \(Y_{i}^{B}=\left\{x_{1i}^{B},x_{2i}^{B},\cdots,x_{N_{B}i}^{B}\right\}\).