Research on Position Error of External Radiation Radar Sensor Based on 3D Positioning Algorithm

The paper establishes a measurement-launch station correlation model of a single-frequency off-line radar system, derives the principles of the three-dimensional TOA positioning method and the two-dimensional TOA positioning method to estimate the target height, and gives the analysis of the GDOP positioning accuracy of the corresponding algorithm, and Through the simulation verification of a three-transmission single-receiving external radiation source positioning model, the effects of different algorithms on positioning accuracy and measurement-transmission station correlation are analysed. The results show that using the two-dimensional TOA positioning method to estimate the target height can improve the measurement-transmitting station correlation probability of the single-frequency off-line radiation source radar.


Introduction
The traditional radar is a transceiver, which receives the target echo of its own transmitted signal, analyses the characteristic parameters of the target echo signal, and extracts the relevant information parameters of the target to achieve the positioning and tracking of the target. Because it needs to emit electromagnetic waves by itself, it is easy to be discovered, which greatly reduces its own viability. The external radiation source radar itself does not need to emit an electromagnetic wave signal, and the target can be detected by measuring the direction angle or the time difference of arrival of the third-party radiation source signal and the echo signal reflected by the target. It is difficult to be discovered by reconnaissance and can avoid being attacked, so the external radiation source radar system has a strong survivability.
The single-frequency external radiation source radar refers to an external radiation source radar that uses a single-frequency network radiation source, and belongs to a type of multi-base radar (multitransmission single/multi-reception radar). It not only has the advantages of single-frequency network and traditional external radiation source radar, but also has the following advantages compared to multi-frequency external radiation source radar: 1) The system uses multi-transmission singlereceiving mode and each echo signal is processed at the same time. The frequency network adopts the mode of multi-single-receiving (time-sharing processing) or single-receiving and multi-receiving, which has the advantages of high system performance and low hardware cost; 2) There is only one transmitting station, the equipment is centralized, and the system maintenance is simple and convenient; 3) The received data is centralized In one node, the processing is centralized and the software cost is low; 4) There is less communication between the nodes and higher security (strong anti-radiation missile capability), and the multi-frequency network data is scattered among the nodes, and the needs between the nodes are jointly processed Frequent communication, low security performance. In recent years, digital broadcasting and television signals have gradually replaced analogy signals. The single frequency network technology has been widely used because of its many advantages such as frequency saving and high spectrum utilization. The detection of external radiation sources based on single-frequency network digital broadcast TV signals has also become a research hotspot in recent years. This paper first models the measurement-transmission station correlation problem, then from the perspective of target positioning algorithm selection, analyses the positioning accuracy of different positioning methods and the impact on the measurement-transmission station correlation problem. The external radiation source positioning model was simulated and analysed [1].

Basic principles of three-dimensional scaling technology
The positioning algorithm only needs to obtain the location coordinates of the unknown target in the network based on the network connectivity and other information, which will reduce the requirements of the target hardware and make it more suitable for large-scale WSN. The positioning performance of the positioning algorithm without ranging is hardly affected by the environment. Even if its positioning accuracy will be reduced, it can meet the needs of some applications [2].
The three-dimensional scaling technology TOA is a data analysis technology that converts similar information between entities into spatial geometric information. It is often used in exploratory data analysis or information visualization. It was originally used in data analysis of psychometrics and is now used as a general purpose. The data analysis technology is widely used in various fields. Suppose the dissimilarity between the research subjects i and j is denoted by ij p , and the dissimilarity ij p between the research subjects constitutes the dissimilarity matrix ij p     . The coordinate matrix for constructing points on the three-dimensional space is represented by n m X  , where n is the number of coordinate points, m is the dimension of the coordinate points, the coordinates of the physical objects i and j are K, respectively, and the distance between L and M on the three-dimensional space The Euclidean distance is denoted by ij d . The three-dimensional scaling technique is to use the dissimilarity between the entities to construct the relative coordinate map of the points on the threedimensional space, so that ij p and ij d are as close as possible. In the three-dimensional scale, the closeness is measured by the strength coefficient (STRESS). Define the threat coefficient as: The specific implementation is divided into four steps: (1) construct the dissimilarity matrix ij p     ; (2) multiply each element in matrix ij p     to obtain (2) P ; (3) double-centralize (2) P , that is, both sides of E are multiplied by the centre at the same time See (2) for the calculation formula of matrix J and J. 1 Where E is the identity matrix of order n, J is the full matrix of order, and matrix B after double centralization is shown in equation (3).

TOA positioning algorithm
The specific positioning process of the TOA algorithm is divided into the following stages: (1) Each transmitting station first uses the classic TOA algorithm to construct the initial local coordinate system.
(2) Use the incremental greedy method to convert the initial local coordinates of all targets into global relative coordinates. (3) According to the coordinate information of the beacon transmitting station in the external radiation source radar sensor, convert the global relative coordinates into the initialized global absolute coordinate system. (4) According to the local attributes of the network, let the unknown target select its true 1-hop neighbour target to participate in the positioning solution. (5) Use the Gaussian kernel weighting mechanism to calculate the weight: Where ij d  represents the measured distance (m) between the transmitting station I and the target j; represents the ranging or shortest path between the transmitting station I and the neighbouring target j distance.
With reference to the classic three-dimensional scaling technique, positioning is to locate unknown transmitters by minimizing the threat coefficient. In this paper, the threat coefficient is converted into a target cost function as shown in equation (9), and the target cost function is minimized by solving Conditions to locate unknown targets [3].
Where c is a constant independent of the coordinates of the transmitting station, i S is the local cost function of each unknown target, and its expression is shown in equation (12).
When there is no beacon transmitting station, that is, N=n, the relationship between S and i S is (13).

Conclusions
In this paper, a single-frequency external radiation source radar measurement-transmission station correlation model is established, and the impact of measurement-transmission station correlation problems on subsequent data processing is analysed. Then, from the perspective of target positioning algorithm selection, the positioning accuracy of different positioning methods and the impact on the measurement-transmission station correlation problem are analysed, and simulation verification is carried out through a three-transmission single-receiving single-frequency external radiation source radar positioning model, The comprehensive two-dimensional positioning accuracy, target distance and estimation error of the target can be found. The two-dimensional positioning method for estimating the height of the target is more suitable for the positioning and measurement of the singlefrequency off-line source radar-deblurring of the transmitting station.