## 2 System Modeling  
The system is constructed on the basis of DILL structure like shown in the Figure 1. The front-end receiver carries space sampling of different DOA signals and then transforms them into baseband signals by down-conversion. The signals are spatially filtered in the filter rejector to judge, recognize the users' signals and restrain some noises. The signal received by the antenna is transmitted to the DOA estimator and used to estimate the DOA information. Finally, the estimating signals are processed by the UKF algorithm and the state distribution of the exact approximated signals is realized by recursion Bayes estimation. We can attain many approximations of the actual values, improving the update processing and tracking efficiency and accuracy to make the system more stable and efficient. In the tracking model, the spatial signal filter is a beam space matrix made up of a baseband low-pass filter and a group of orthogonal weighing coefficients. The scene of judge original signals by the beam space matrix is shown in Figure 2, where the abscissa axis denotes the multiple orthogonal beam space confined to 0-360\({}^{\circ}\). A half beam width of the adjacent two beams is overlapped and we call it the power beam device. We select the baseband signals by passing different power beam devices. If we can get a relatively large power output, this implies that the signal is between the two space angles formed by the power beam device. Then we can attain the distribution interval of the signal DOA and further can judge and recognize the distribution of the mobile signal source DOA, providing the initial data for the subsequent extract location in the DILL. The tracking device of the DILL is similar to the phase-lock loop as it is modified from the later one. Like the tracking device of the phase-lock loop shown in Figure 3, we replace the phase discriminator by the angle detector, the loop filter and digital-controlled oscillator. The angle detector is made up of two angular deflection correlators and an array vector generator to convert the related angles [11,12]. The rough estimated signal \(r_{k}(i)\) is transmitted to the angular detector in the DILL, and then we carry out angular deflection related operations of the \(r_{k}(i)\) and \(a(\hat{\theta}(i)\pm\Delta\theta)\) produced from the array vector generator. Then we update the error signal by subtracting the square of their molds to make a more exact approximation to the actual signal. We already did a DOA rough estimation of the signal source by spatial filter in the forepart process, making the receipt signal in the pull-in range in the estimation stage. Figure 1: Locating and tracking model. Figure 3: Tracking device in the Direction Lock Loop (DILL). Figure 2: Beam space matrix. In the whole feedback regulation process, we transmit the \(e_{k}(\hat{\theta_{i}})\) through a loop filter to control the digital-controlled oscillator, realizing the self-adapting real-time locating and tracking in the pull-in range. The estimated signal by the DOA algorithm is not very exact due to the various Gaussian noises in the loop output signal and t the nonlinear influence on the communication system. At the same time, the number of estimated signals in the loop out is larger than the sampling number, so we should do more sampling to estimate filtering processing. The filtering based on the UKF can remove the nonlinear influence and restrain the noise efficiently, so this paper adopts the UKF filtering tracking algorithm  
\[G(\theta_{k}(i)\,|\,\theta_{k})=\left|R(\theta_{k},\hat{\theta_{k}}(i)+\Delta \theta)\right|^{2}-\left|R(\theta_{k},\hat{\theta_{k}}(i)-\Delta\theta)\right|^{2} \tag{7}\]  
\(\
u_{ke}(i)\) can be expressed as:  
\[ \begin{array}{l}\
u_{ke}(i)=\left|\
u_{ik}(i)\right|^{2}-\left|\
u_{ik}(i) \right|+\\ 2\,\mathrm{Re}\left\{d(i)(R(\theta_{k},\hat{\theta_{k}}(i)+\Delta\theta)\
u_{ k}{}^{*}(i)-R(\theta_{k},\hat{\theta_{k}}(i)-\Delta\theta)\
u_{k}{}^{*}(i))\right\} \end{array}