### GPS

#### Brief description of GPS

As a new generation of precise satellite positioning system, GPS system represents the cutting-edge technology and is the crystallization of the development of contemporary science and technology. Initially, GPS was originally developed for military applications, such as positioning and navigation of military vehicles, aircraft, and ships [5, 6]. Because of its ranging and timing functions, GPS can provide global users with high-precision, all-weather, and large-scale position and time information, which can well meet the military and civilian positioning and navigation needs. The composition of the GPS system is shown in Fig. 1.

As can be seen from Fig. 1, the GPS system is mainly composed of three parts: the space satellite part, the ground monitoring part, and the user receiving part [7].

(1) Space satellite part

The space satellite part is mainly composed of 24 satellites distributed in 6 elliptical orbital planes of the earth, including 21 working satellites and 3 standby satellites in orbit. These satellites are 17,700 km away from the earth and the satellite operating cycle is 1.58 h. Four satellites are deployed on the plane, and the coverage angle is 55 degrees [8, 9]. In actual use, the GPS system receiver can capture more than 4 satellites. At this time, in order to improve the positioning accuracy, the receiver divides the captured satellites into several groups according to the constellation distribution, with 4 satellites in each group. After calculation and analysis, the group with the smallest error is selected for positioning calculation.

(2) Ground monitoring part

The ground monitoring part is mainly composed of a main control station, 3 ground control stations and 5 global monitoring stations [10]. The main control station is located in Colorado, the United States mainland. The five monitoring stations distributed around the world under the direct control of the master control station are the data collection centers of the GPS system. Among them, the monitoring stations are equipped with receivers that can continuously measure visible satellite data and cesium clocks with precise time measurement. The main function of the monitoring station is to obtain satellite observation data including ionospheric and meteorological data and send it to the main control station. Then the main control station analyzes these data, calculates the clock parameters and satellite orbits, and sends the analysis results to three ground control stations.

(3) User receiving part

The user receiving part is mainly composed of GPS signal receiver [11]. The main function is to collect satellite signals. Through the collection and calculation of parameters such as the satellite orbit, the distance between the satellite and the receiver, the current position information of the user is obtained, including latitude and longitude, altitude, and speed of movement. GPS receiver is mainly composed of antenna and receiver. The receiver is powered by a DC power source inside and outside the machine. Generally, the power is supplied by an external power source and the battery is charged. After the power is turned off, the internal battery powers the memory to ensure data storage.

#### GPS positioning principle

GPS positioning methods are divided into two methods: absolute positioning and relative positioning. The former is used to determine the position of the moving carrier in the earth reference frame in real time. The positioning accuracy is within 100 m. The latter uses multiple machines to determine the mutual relationship between measurement stations. After a certain period of observation, the data is processed by data post-processing software, and its relative accuracy reaches nanometer level [12, 13].

(1) Absolute positioning principle

The basic principle of the so-called absolute positioning is to use only one receiver to observe satellite signals and determine itself independently.

The position of the antenna phase center in the coordinate system is called absolute positioning because this position is the only absolute.

Positioning can be divided into dynamic absolute positioning and static absolute positioning [13, 14]. The former is mainly used for flying because of its low positioning accuracy.

Navigation is required for machines, vehicles, and ships that require less precision. The latter can continuously measure the pseudo-range from the satellite to the observation station and improve the positioning accuracy through data processing, so it can be used for observation or navigation in some fine industries with high accuracy requirements [15].

GPS observation can get the position of the satellite and the distance from the satellite to the ranging point, and then use the satellite as the center and the distance as the radius to make a spherical surface. If three satellites are observed at the same time, we will get three spherical surfaces. It is the position of the measurement point that is required to be solved. Of course, in the actual measurement, due to the factor of the clock difference, the pseudo range measured by the receiver includes three coordinate component unknowns and one clock difference unknown, so if you want to solve these four unknowns, you must observe at least four satellites to establish The equations are used to settle the station coordinates corresponding to the user's receiver antenna. Let P be the pseudo-range observation, R be the true distance from the receiver to the satellite, C be the speed of light, and T be the difference in the reception clock, then the observation equation is:

$$\rho = R + c + \tau = \sqrt {\left( {x_{s} - x_{r} } \right)^{2} + \left( {y_{s} - y_{p} } \right)^{2} + \left( {z_{s} - z_{p} } \right)^{2} } + c \times \tau$$

(1)

(2) Relative positioning principle

The accuracy of absolute positioning is often inaccurate, which is mainly affected by factors such as satellite orbit errors, clock synchronization errors, and errors generated during propagation in the atmosphere. Although we can eliminate the errors caused by weakening some systems through methods such as mathematical modeling, its positioning accuracy can only reach meters, which is difficult to meet the needs of high precision [16]. Relative positioning is also called differential positioning. The basic principle is to use multiple receivers to observe GPS satellites simultaneously to determine the mutual relationship between the stations where each receiver is located in the earth coordinate system. Therefore, within a certain distance range, the orbit error of the satellite, the satellite clock error, the receiver clock error, and the refraction errors of the ionosphere and troposphere have a certain correlation with the impact on the observations. Use different combinations of these observations for relative positioning., The influence of the above errors can be eliminated or reduced, thereby improving the positioning accuracy.

In relative positioning, at least two GPS signal receivers are required, which are respectively set at the two ends of the baseline. One of the endpoints is a known coordinate point. The same set of GPS satellites are simultaneously observed, and the difference between the coordinate components between the two points and the baseline are measured. Length, the relative position of the baseline endpoint or the baseline vector is calculated, and the exact coordinates of the other point can also be calculated. Relative positioning can also be divided into static and dynamic positioning methods. The static relative positioning method is currently the most accurate of all GPS positioning methods, but the measurement time is relatively long, and generally takes one to three hours [17]. The dynamic relative positioning method is to press one receiver on a moving carrier and install the other receiver at a known point (reference station). The former is called a dynamic GPS signal receiver, while the latter is called a reference GPS signal receiver. These two receivers simultaneously observe a group of GPS satellites in sight, and the reference receiver provides differential correction numbers for the dynamic receiver, which is called GPS differential positioning data [18]. The dynamic receiver uses its own GPS observations and differential correction data from the reference receiver to accurately calculate the user's 3D coordinates.

### GPS multi-antenna detection system for wireless network communication

(1) GPS one-machine multi-antenna monitoring system

The GPS one-machine multi-antenna monitoring system aims to give full play to the advantages of GPS measurement technology in automated real-time deformation monitoring and reduce the cost of purchasing GPS receivers. The design idea is: a GPS receiver is connected to multiple antennas, so that each Only GPS antennas are installed on the monitoring points, and no receivers are installed. Multiple monitoring points share a GPS receiver, which can greatly reduce the cost of the monitoring system without reducing the accuracy of conventional GPS measurements. Based on this idea, a GPS multi-antenna control switch can be designed so that one GPS receiver connects to multiple antennas, and these antennas work automatically in sequence by software control.

(2) Multi-antenna controller

The multi-antenna controller includes software and hardware, and is one of the core parts of a multi-antenna system. The hardware part is composed of multi-channel microwave switch and corresponding control circuit, a GPS receiver and corresponding processing chip; the off-state of several signal channels in the microwave switch is controlled by the switch control circuit in real time. The software part mainly realizes the functions of controlling the multi-channel working mode, setting the observation time of the measuring point, real-time communication with the GPS receiver and data transmission. The newly developed GPS multi-antenna controller, the field computer uses an embedded industrial control computer, and integrates the control circuit board and the dual-frequency GPSOEM board, and is equipped with an LCD liquid crystal display, which can intuitively monitor the situation of the multi-antenna data collection site.

The key technical problem to be solved in the hardware part of the GPS multi-antenna controller is the high isolation of the GPS signals of each channel in the microwave switch. The key technical problem to be solved in the software part is to realize real-time precise positioning, so that the positioning accuracy reaches mm level.

(3) Design of data transmission system

The data transmission from the GPS antenna to the multi-antenna controller can only be transmitted through a wired medium, so the coaxial cable or optical fiber can be used for data transmission. Coaxial cable is only suitable for short-distance data transmission; however, regardless of the distance of optical fiber, the quality and reliability of data transmission are guaranteed, but its cost is relatively high. The coaxial cable consists of a layer of mesh copper conductor and a copper conductor located on the central axis. Compared with the ordinary twisted pair, the coaxial cable has strong anti-interference ability and good shielding performance, and is often used for connection between devices. If a repeater (signal amplifier) is used, the length of the network connected by the coaxial cable can be increased up to several kilometers.

Data transmission from field data to the monitoring center. Since the monitoring site is generally located in a remote mountainous area, the field data received by the receiver adopts wireless transmission mode, GPRS and GSM are both good choices. Here we use the GPRS communication method. The specific method is to connect the GPS multi-antenna controller through the RS-232 serial port on the controller and the GPRS terminal RS-232 serial port through a patch cord to transmit the original GPS data to GPRS terminal, and then continuously send to the monitoring center through the terminal wireless mode.

(4) Data processing system

The data processing system is responsible for the entire process of transmitting, storing, analyzing, calculating and displaying the original data of the receiver. First, the data of the multi-antenna receiver and the reference station are transmitted to the GPRS transmitter through the RS-232 serial port, and then the data is sent to the monitoring center through the wireless network long-distance transmission, and the monitoring center data processing software classifies and analyzes the multi-site data. Converted into location information. Through the process of comparing the position information of the reference station and the measuring point, and time sequence analysis, the predicted deformation trend curve can be generated, as shown in Fig. 2 [19].

### Inter sequence analysis

For a long time, deformation analysis and processing methods have assumed that the observed data are statistically independent or uncorrelated, such as regression analysis methods. This kind of statistical method is a static data processing method, which cannot realize dynamic prediction of variables. However, whether it is observation data arranged in time series or observation data arranged in spatial order, there is more or less statistical autocorrelation between the data. With the development of modern science and technology and the improvement of computer application, various theories and methods have provided a wide range of research methods for deformation analysis and deformation prediction.

(1) Definition of stochastic process and time series

A stochastic process is a (family of) random variable that depends on a parameter. For example: the terminal voltage of an electronic component or device due to the random thermal disturbance of internal micro-particles is called thermal noise voltage, and its value at any given moment is a random variable; the temperature at each moment of the day is a random variable, which Sets constitute a random process. The definition of a stochastic process is: let E be a random test and S = (P) be its sample. If for each e ∈ s, there is always a real-valued function X (e, t)Corresponding to this, the function of the parameter t of this family is called a random process, and each function in the family is called a sample function of the random process, and T is the variation range of the parameter t, called a parameter set. Random processes can be divided into continuous random processes and discrete random processes according to whether they are continuous random variables or discrete random variables at any time. The specific value obtained by the random process in the test results is called the "implementation" of the random process, or the sample function, also called the sample observation. Time series are random sequences, that is, random sequences with discrete parameters.

(2) Time series modeling method

The key of time series analysis is to establish an appropriate mathematical model based on a reasonable analysis of observation results.

The general steps for modeling are:

(1) Preparation stage. The acquisition of initial data requires that the data can accurately and truly reflect the behavioral state of the modeling system. First, the data needs to be analyzed and tested, including the elimination of glitches and compensation data. The zero-mean test requires data preprocessing for sequences that do not meet the stability requirements. The processing methods mainly include differential processing or trend item extraction, and digital signal processing methods can process data flexibly.

(2) Preliminary determination of model structure and category. To determine the structure and category of the model, you need to choose a modeling method.

(3) After the structure of the model is determined, the appropriate method for selecting the model parameters should be estimated according to certain principles; then the model suitability test of the model is performed to determine the final appropriate model.

(3) The mathematical foundation of the model

Auto-covariance function of random variables:

$$D\left( {X_{t} ,X_{s} } \right) = {\text{Cov}}\left( {X_{t} ,X_{s} } \right) = E\left\{ {\left[ {X_{t} - E\left( {X_{t} } \right)} \right]\left[ {X_{s} - E\left( {X_{s} } \right)} \right]} \right\}$$

(2)

Autocorrelation function and autocorrelation coefficient of random variables:

$$R_{X} \left( {t,s} \right) = E\left( {X_{t} ,X_{s} } \right)$$

(3)

Initial estimation of model parameters:

$$X_{t} = \phi_{1} X_{t - 1} + \phi_{2} X_{t - 2} + \cdots + \phi_{p} X_{t - p} + a_{t}$$

(4)

Test of time series stationarity: According to the definition of stationary time series, the mean and variance of stationary time series are constant; the interval between self-coordinates is related to the breakpoint of this interval. The relevant formula for the test of time series stationarity is as follows:

$$\overline{X}_{i} = \frac{1}{M}\sum\limits_{j = 1}^{M} {X_{ij} }$$

(5)

$$\hat{\sigma }^{2}_{i} = \frac{1}{M}\sum\limits_{j = 1}^{M} {\left( {X_{{_{i} }}^{j} - \overline{X}_{i} } \right)}^{2}$$

(6)

$$r_{\tau } \left( i \right) = \frac{1}{M}\sum\limits_{j = 1}^{M - \tau } {\left( {X_{ij} - \overline{X}_{i} } \right)} {{\left( {X_{i,j + \tau } - \overline{X}_{i} } \right)} \mathord{\left/ {\vphantom {{\left( {X_{i,j + \tau } - \overline{X}_{i} } \right)} {\hat{\sigma }_{{_{t} }}^{2} }}} \right. \kern-\nulldelimiterspace} {\hat{\sigma }_{{_{t} }}^{2} }}$$

(7)

(4) Model establishment

According to the stationarity formula of the time series, the parsed data is firstly discretized, and then substituted into formula 5 to obtain the parameter mean value, the mean value is substituted into formula 6 to obtain the data variance, and finally substituted into formula 7 for stationarity analysis. After the above series of processing, Judging whether there is a trend of deformation according to the size of the difference.