1. Preface
Trilateration is a common positioning method that determines the location of a target by measuring the distance or angle between three reference points and the target to be located [1]. This method can be used in scenarios such as radio navigation and WLAN positioning. Radio navigation determines location by measuring the propagation time and strength of radio signals, while WLAN positioning uses the signal strength of a wireless LAN and the distance between multiple access points to achieve positioning.
However, localization methods based on trilateration have some limitations and problems [2]. First, radio navigation is affected by factors such as signal attenuation, multipath effects, and interference, which will lead to measurement errors. Secondly, WLAN positioning depends on the coverage and signal strength of the wireless LAN. If the coverage is insufficient or the signal is blocked, positioning accuracy will decrease. In addition, positioning methods based on trilateration usually require the collection and construction of a location database in advance, which increases the overhead and complexity of the system.
In order to improve positioning accuracy and reliability, integrating trilateration with satellite navigation is a feasible method [4]. Satellite navigation systems such as GPS can provide global positioning services with high accuracy. Integrating trilateration and satellite navigation requires solving issues such as signal fusion, clock synchronization, and error compensation. Through reasonable algorithm design and system optimization, data consistency and accuracy can be achieved. In addition, the fusion method also needs to consider energy consumption management and optimization, as well as real-time and delay issues [6].
In short, it is feasible to integrate trilateration and satellite navigation, which can improve the accuracy and reliability of positioning. With the advancement of technology and in-depth research, positioning methods based on the fusion of trilateration and satellite navigation are expected to be widely used in various application scenarios [7][8].
2. Current research status at home and abroad
2.1 Radio navigation positioning technology
2.1.1 Positioning Features
The concept of radio navigation can be traced back to the early 20th century. The U.S. Navy proposed the idea of using radio signals for navigation positioning in 1904. Among them, the determination of two-dimensional coordinates based on trilateration was the main method at that time. Later, during World War I, radio signals were used for military applications such as navigation, communications, and reconnaissance. Through the transmission, reception and processing of electromagnetic waves, radio navigation equipment can measure navigation parameters such as the direction, distance, distance difference and speed of the carrier relative to the navigation station.
Literature [1] proposed the current radio navigation positioning methods: ρ-θ positioning, θ-θ positioning, hyperbola positioning and distance intersection positioning. The principles of the first three methods do not involve the research content of this article and will not be repeated here. The fourth method, distance intersection positioning, refers to using 2 or 3 ranging platforms to perform ρ-ρ or ρ- ρ–ρPositioning. As shown in Figure 1, the circular position lines of two (or three) ranging systems intersect, and the intersection position is the location of the target.
Figure 1 Schematic diagram of distance interactive positioning[1]
2.1.2 Positioning accuracy
The navigation accuracy of the radio navigation system is not only related to the distance, but also to the relative geometric position of the carrier and the navigation station. That is, the positioning accuracy of users at the same distance may be greatly different. This is determined by the situation and direction of the positioning error in space. of. All navigation and positioning functions are realized directly or indirectly through measurement. Due to the existence of various noise interference and unforeseen factors, there will always be errors in measurement. When the errors are relatively small and there are many influencing factors, according to the central limit theorem, it is assumed that these errors are zero-mean, stationary, and ergodic random processes. In literature [2], the three-dimensional probability density function of user positioning error is obtained as:
Among them,
,δ x is the positioning error in the x direction.
2.1.3 Existing applications
Literature [5] pointed out that satellite navigation represents the development direction of radio navigation in the future, overcoming the defects and shortcomings of traditional navigation, giving the navigation field a new look, and having extremely broad and beautiful development prospects. GPS and GLONASS systems can provide continuous and high-precision position, heading, speed, attitude and time information in real time and conveniently under any climatic conditions; satellite navigation methods provide globally accurate and consistent navigation information, which will improve the world’s land, sea and air transportation. Economy and safety, changing the system of air, maritime and land traffic control and dispatch systems, and contributing to the global economic development and integration process.
At the same time, the application of radio navigation technology is rapidly surpassing the scope of transportation and penetrating into all aspects of the national economy and people’s lives, including industry, agriculture, forestry, fishery, public security, first aid, post and telecommunications, power transmission, geology, and oil extraction. , information network and scientific research, etc. Radio navigation and its application technology will develop into an important high-tech information industry, which will not only promote the development of the national economy, but also continuously improve the quality of people’s lives.
In terms of military applications, satellite navigation, microwave landing, integrated navigation, etc., in addition to being widely used for navigation guidance by military and civilians, also have a wide range of military operations. The Terrain Assisted Navigation System, Joint Tactical Information Distribution System (JTIDS) and Positioning Reporting System (PLRS) are quite different from traditional navigation in terms of system. They generally do not provide services for navigation. They are mainly used as military battlefield applications and provide battlefield information. The required high-precision positioning, anti-interference, anti-destruction, anti-exploitation, anti-deception and other performances have formed a new generation of navigation hybrid, becoming a key link in the development of modern high-tech military, and playing an increasingly important role.
2.2 WLAN positioning technology
2.2.1 Positioning Principle
WLAN positioning is a technology that uses WLAN signals for positioning. It analyzes the signal’s strength, arrival time, and other characteristics to determine the device’s location. Literature [3] points out that technology based on RSSI (Received Signal Strength Indication) is the main research method for indoor wireless positioning in WLAN networks. Indoor positioning technology based on RSSI technology can be divided into distance-based methods and non-distance calculation methods. Among the distance-based wireless positioning methods, the trilateral positioning method and the triangulation positioning method are the most commonly used, while non-distance calculation methods generally use the fingerprint matching method. Since the triangulation method and fingerprint matching method do not involve the research content of this article, they will not be introduced in detail here. The schematic diagram of the three-sided positioning method is shown below.
Figure 2 Schematic diagram of three-sided positioning method[4]
2.2.2 Positioning accuracy
As shown in Figure 2, it is known that the distance between the terminal to be located and the signal source APi,i=1,2,3 is di,i=1,2,3, according to geometric principles, the terminal to be located must be located at the center of the circle with the position of the AP as the center, corresponding to At the intersection of three circles whose distance is radii. Assume that the coordinates of the terminal are (x,y), and the labels of the three APs are xi,yi,i=1,2,3, then the terminal coordinates (x, y):
For the accuracy of WLAN positioning technology, mean square error (MSE) and root mean square error (RMSE) are commonly used to evaluate the dispersion of positioning errors:
? ? 
?
In the formula: (x,y) represents the actual position of the mobile handheld terminal, 
? represents the estimated position. As a good supplementary positioning method for GPS, WLAN network provides sufficient technical support. In dense urban areas and indoor environments, WLAN network has wide coverage, convenient access, and easy expansion. At the same time, more and more smart devices All support WLAN networks, giving them a sufficient hardware environment foundation.
2.2.3 Satellite navigation integration
Because WLAN positioning technology has better accuracy and coverage in indoor environments, satellite navigation positioning technology has higher accuracy and positioning coverage in outdoor environments. Therefore, WLAN positioning technology and satellite navigation positioning technology have complementary advantages. The integration of the two can make up for the differences between indoor and outdoor environments and provide more comprehensive and accurate positioning services.
Satellite navigation and positioning technology (such as GPS) has problems such as signal attenuation and multipath effects in indoor environments, resulting in low indoor positioning accuracy. WLAN positioning technology can provide precise indoor location information. By integrating the two, WLAN indoor positioning information can be used to correct satellite navigation positioning errors, thereby improving the overall positioning accuracy [8].
3. Future research directions
In response to the above problems and the increasing demand for indoor location services in emergency rescue, personal applications, and other government and industry applications, the current development trend of integrated navigation and positioning technology is mainly reflected in the following three directions.
- Improve indoor positioning accuracy. Due to the complex indoor environment, there are serious non-line-of-sight (NLOS) propagation multipath conditions such as reflection, diffraction and diffraction. The movement of people will also bring unpredictable changes to the electromagnetic propagation environment. The above situations have brought huge challenges to indoor high-precision positioning, and are currently technical problems that need to be researched and solved [10].
- Improve indoor positioning efficiency. In order to overcome errors caused by non-line-of-sight, current indoor positioning systems mostly use grid positioning technology, which performs feature matching and positioning by pre-storing grid feature information. If you want to use this method to achieve high-precision positioning, you need to create and store a large number of feature grids and increase the density of node layout. How to further improve indoor positioning efficiency and achieve accurate indoor positioning with smaller feature information has become a research hotspot in current indoor positioning technology.
- Integrated outdoor positioning system. Location services are developing from outdoor services to indoor and outdoor integrated services. Integrating outdoor positioning systems to achieve seamless indoor and outdoor positioning has become an inevitable trend in the development of indoor positioning technology. In my country, with the construction of my country’s independently developed Beidou system, the integration of indoor positioning systems and Beidou systems is becoming an important direction for the development of my country’s navigation and positioning systems [11].
4. Simulation verification
In this section, some matlab simulation experiments are carried out based on the principle of trilateration. The main purpose is to verify the accuracy of trilateration, realize some functions of trilateration, and enhance the intuitive understanding of trilateration. The following figure shows The positioning situation of 15 random positions at a certain point
? 
- Random move 1 (b) Random move 2
Figure 3 Trilateration verification
As can be seen from the figure above, trilateration can achieve high-precision positioning for nodes at different locations, with a positioning error of about 10-6, but the assumption at this time is that the target is relatively stationary. In order to further understand the principle of trilateration, we continue to carry out some mobile node position measurements. When the node movement step is short, trilateration can theoretically accurately describe the movement trajectory of the node. The following figure shows a more complex Mobile trajectory positioning map.
? 
- Random move 1 Random move 2
Figure 4 Trilateration path verification
As can be seen from the figure above, for slowly moving units, trilateration using three base stations can achieve high-precision positioning of two-dimensional coordinates and depict a more accurate node movement path. However, this simulation experiment did not consider the effects of delay and Doppler. In reality, it is also necessary to consider the impact of various interferences on the positioning results, and errors and deviations will increase.
5. Code implementation
% ----------------Use the trilateral positioning method to locate unknown nodes-------------------------- ----------
%{
The clc command is used to clear the contents of the command window. No matter how many applications are opened, there is only one command window.
Therefore, whether clc is called in a script m file or a function m file, the clc command will clear the contents of the command window.
The clear command can be used to clear the contents of the workspace. MATLAB has a basic workspace, identified by base.
Additionally, when opening a function m-file, a lot of workspace may be generated. Each function corresponds to a workspace.
%}
clear;
maxx = 800;% maximum abscissa of reference node distribution
maxy = 800;% maximum ordinate of reference node distribution
%---------------------- Randomly initialize three known reference points [cx, cy]------------- ----
%{
rand() generates uniformly distributed random numbers between 0 and 1
rand(m) generates a m*m matrix. Of course, the values of the matrix are uniformly distributed random numbers between 0 and 1.
rand(m,n) or rand([m,n]) generates an m*n matrix
randn() generates normally distributed random numbers with mean 0 and variance 1. Usage is similar to rand.
%}
cx = maxx*rand(1,3);
cy = maxy*rand(1,3);
plot(cx,cy,'k^','MarkerSize',8);%Reference node diagram
% Given starting point and end point
x0=0;
yo=0;
sx=500;
sy=500;
L_total=sqrt(sx^2 + sy^2);% total straight line distance
mx=0;% initialize node position
my=0;
l=10;%Set the step size
%%
%-------- Randomly initialize an unknown node (mx, my) -----------
for ii=1:30 % number of walks
lx=mx;%Save the last coordinates
ly=my;
L_now=sqrt((sx-lx)^2 + (sy-ly)^2);
while 1
mx = lx + 20*cos(rand()); %next coordinate
my = ly + 20*sin(l*rand() + 1);
%forward distance
L_next=sqrt((mx-sx)^2 + (my-sy)^2);
if L_next<L_now
break
end
end
hold on;
% Blind node graph
ifii>1
x=[lx,mx];
y=[ly,my];
plot(x,y,'b-o','Linewidth', 0.7);
end
% text(mx + 10,my,num2str(ii))
da = sqrt((mx-cx(1))^2 + (my-cy(1))^2);
db = sqrt((mx-cx(2))^2 + (my-cy(2))^2);
dc = sqrt((mx-cx(3))^2 + (my-cy(3))^2);
% Calculate positioning coordinates
[locx,locy] = triposition(cx(1),cy(1),da,cx(2),cy(2),db,cx(3),cy(3),dc);
plot(locx,locy,'r + ', 'Linewidth', 1);
legend('Location base station','Location label','Blind node','Location','SouthEast');
title('Positioning by trilateration');
xlabel('X/m')
ylabel('Y/m')
grid on
derror = sqrt((locx-mx)^2 + (locy-my)^2);
disp(derror);
end
References
- Huang Zhigang, editor; Sun Guoliang, Feng Wenquan, Chen Jinping, Zheng Yugui, editors. Radio Navigation Principles and Systems [M]. Beijing: Beihang University Press , 2007.
- Dong Mei, Yang Zeng, Zhang Jian, et al. Wireless LAN positioning technology based on signal strength [J]. Computer Applications 2004, 24(12):49 -52.
- Compiled by Deng Zhongliang, Yu Yanpei, Xu Lianming, etc. Indoor and outdoor wireless positioning and navigation [M]. Beijing: Beijing University of Posts and Telecommunications Press, 2013.
- PRATT T, BOSTIAN C. Satellite Communications[M].2nd ed. Beijing: Publishing House of Electronics Industry, 2003.
- Yang Zhanglin, Research and Implementation of WLAN Positioning System Based on RSSI [D]. Dalian: Dalian University of Technology, 2009.
- Zhao Jun, Zero-configuration indoor positioning system based on radio frequency signal strength [D]. Hangzhou: Zhejiang University, 2007.
- Fan Luhong, Pi Yiming, Li Jin. Beidou Satellite Navigation Principles and Systems [M]. Beijing: Electronic Industry Press, 2021.
- Dias, Ryan, Abdulhayan, Sayed, S. B., Vinay Kumar. Localized Positioning Systems using Trilateration Algorithm. [J]. Journal of Pharmaceutical Negative Results, 2022, vol .13: 508-516.
- Qinghua Luo, Kexin Yang, Xiaozhen Yan, Jianfeng Li, Chenxu Wang, Zhiquan Zhou. An Improved Trilateration Positioning Algorithm with Anchor Node Combination and K-Means Clustering[ J]. Sensors (Basel, Switzerland),2022, vol. 22(16): 6085.
- Mahmoud F Mosleh, Mohammed J Zaiter, Ali H Hashim. Enhanced Distance Utilized ToA/RSS to Estimate Position using Trilateration in Outdoor[J]. IOP Conference Series: Materials Science and Engineering, 2021, vol. 1105: 012023.
- Irwan Hadi Saputra, Gede Putra Kusuma. Indoor Positioning System Using Combination of Trilateration and Fingerprinting Methods[J]. International Journal of Advanced Trends in Computer Science and Engineering, 2020, vol.9(4): 6331-6339.