A New Hybrid Positioning Method by Fusion of BDS and 5G Signal Using the Particle Swarm Method

Abstract

In recent years, with the vigorous construction of 5G networks, the high-density deployment, low delay, and high bandwidth of 5G network systems have enabled high-precision positioning services. By integrating the BeiDou Navigation Satellite System (BDS) and 5G systems, more reliable positioning services can be provided, and BDS–5G signal integrated positioning has become a new research hotspot. However, BDS–5G signal fusion positioning faces the problems of how to build an effective fusion positioning model between heterogeneous systems and the high complexity of multiobjective function positioning solutions. Therefore, this paper constructs a TOA/TDOA fusion positioning model of BDS–5G signals and introduces the multiobjective particle swarm optimization positioning solution method (MOPSO) to realize the reliable positioning of BDS and 5G signal system fusion (MOPSO-TOA/TDOA). The experimental results show that compared with the traditional BDS–5G signal fusion positioning algorithm based on a Kalman filter, the positioning accuracy of the BDS–5G signal joint solution system based on a multiobjective particle fusion algorithm is 24.8% higher than that of the Kalman filter in terms of positioning convergence time, 18.9% higher in terms of system positioning accuracy, and 50–80% higher than that of the BDS positioning system alone, and the reliable positioning ability in complex environments is effectively enhanced.

1. Introduction

The BeiDou satellite navigation system (BDS) is a Global Satellite Navigation Satellite System (GNSS) independently developed and operated by China. By receiving satellite signals, the BeiDou satellite positioning receiver can obtain pseudorange (the measured distance between the satellite and the receiver) and ephemeris data. The satellite’s real-time position can be solved through the satellite ephemeris. Due to the existence of a satellite clock error, we need at least four observable satellites to calculate the exact position of the receiver. However, in a complex urban environment, there is the problem that buildings block visible satellites, resulting in poor satellite geometry. At the same time, buildings on both sides of a roadblock will also lead to poor signal continuity. These problems will seriously affect the performance of the satellite navigation system, resulting in reduced positioning accuracy or even an inability to locate [1,2,3,4,5]. The 5G system has the characteristics of large bandwidth, dense networking, and multiple antennas and can achieve high-precision positioning under indoor sheltered conditions. With the maturity of 5G-related systems and the development of high-precision time synchronization technology, the application of 5G technology in life is becoming increasingly important. The 5G system is characterized by large bandwidth, dense networking, and multiple antennas. The maximum distance between 5G base station sites is less than 200 m, characterized by ultra-dense heterogeneous networks. Considering the 5G base station signal during satellite positioning can supplement the geometric configuration of satellite positioning and reduce the system position accuracy factor value (PDOP, the smaller the value, the higher the positioning accuracy). Therefore, the 5G base station signal can effectively improve the number of visible satellites and the positioning performance of the system in complex environments [6,7,8]. The high-precision positioning technology of BeiDou–5G fusion based on 5G signals has increasingly become the focus of academic and industrial circles.

Many scholars have studied the integration and positioning of GNSS and 5G. Jue et al. (2017) [9] combined the network density of 5G deployment with the visibility of GNSS satellites. Studying and establishing the model of 5G network deployment and satellite visibility was helpful to achieve better positioning switching. However, it is still necessary to further study the design of 5G networks and consider accurate vehicle positioning in the case of multipaths. Bai et al. (2021) [10] studied GNSS equipment failure and skyscraper blocking in bad weather and proposed a GNSS-free emergency location service based on 5G internet of vehicles using fog computing. Through simulation verification, this paper preliminarily discusses the fog computing architecture design of emergency location services. Destino et al. (2018) [11] studied theoretically deriving the Fisher information matrix (FIM) and the lower limit of position and rotation errors of 5G–GNSS hybrid positioning estimation. Then, they used a two-step method, first calculating the FIM of position-related parameters and then calculating the rotation equivalent Fisher information matrix (EFIM) of position information for fusion positioning, which improved the positioning accuracy to a certain extent and reduced the number of satellites needed. Causa et al. (2018) [12] studied fusing the positioning results of cellular networks and GNSS through an extended Kalman filter (EKF) or particle filter to filter the observation noise of cellular networks. However, the disadvantage is that if the terminal was close to the base station, the performance gain was not very high, and the improvement of satellite positioning accuracy was limited. John et al. (2018) [13] proposed a location algorithm that integrated GNSS data and 4G long-term evolution (LTE) system data. It used channel deviation distribution estimation (H-BLADE) to integrate the time difference of arrival (TDOA) measurements of GNSS and LTE. It improved the location performance in harsh environments, such as urban canyons and indoor environments, through cellular location systems.

Keating et al. (2019) [14] presented a representative method to simulate and evaluate the hybrid positioning capabilities of GNSS and 5G networks in outdoor urban, suburban, and rural scenes. A new scenario definition was proposed that combined the network density of 5G deployment with the visibility mask of GNSS satellites. Maymo-Camps et al. (2018) [15] proposed a new 5G–GNSS hybrid positioning scheme that combined the angle of arrival (AOA) estimates from 5G base stations and time of arrival (TOA) measurements from GNSS satellites. The TOA measurement value of 5G base stations was not used to avoid the time synchronization error of 5G networks. In [16], a multirate adaptive Kalman filter was proposed to solve the problem of nonstationarity of 5G measurement noise in GNSS–5G hybrid positioning. However, the above GNSS–5G hybrid positioning methods were based on Newton iterative LS (least square) or Kalman filter positioning methods. When there were few visible satellites and base stations, the positioning results were difficult to converge, the convergence time was too long to locate in real-time, and the positioning accuracy was poor [17,18,19,20,21].

Aiming at the problem of multisource fusion, Wang et al. (2021) [22] proposed a new data heterogeneous fusion method by using improved particle filter fusion technology to optimize the model for the problem of multisource heterogeneous fusion of GNSS and environmental data in landslides and other environments. Aiming at the problems of slow convergence speed of data fusion in the network, sensitivity to initial values, and ease of falling into local optimal solutions, Xin et al. (2020) [23] proposed a BP neural network WSN data fusion algorithm based on improved particle swarm optimization, which effectively improved the accuracy and convergence speed of data fusion. The particle swarm optimization algorithm is an effective method to solve the problem of data fusion optimization. The particle swarm optimization algorithm is widely used in multisource data fusion [24,25,26,27,28,29].

This paper, starting with integrating BDS and the 5G signal layer, proposes a joint positioning model (MOPSO-TOA/TDOA) of BDS and 5G TOA/TDOA. Aiming at the difficulty of solving the multiobjective function in the colocalization model, we use the joint solution method of multiobjective particle swarm (MPSO), and the general algorithm flow is shown in Figure 1. The overall algorithm is divided into two parts. One is the model building part, in which the TOA data of the BDS satellite signal received by the receiver and the TDOA data of the 5G base station are used to build the system model. The second part is the model solution part, which converts multiple observation equations into multiple objective cost functions. The multiobjective particle filter algorithm is used to solve the multiobjective cost functions. The optimal solution satisfying the minimum overall function is the optimal positioning result. To verify the effectiveness of this algorithm, this paper first analyzed the convergence of the algorithm. Then, we compared the convergence and positioning accuracy of the BeiDou–5G multitarget particle fusion algorithm and Kalman filter fusion algorithm in the actual scene. Finally, we selected several scenes with the poor positioning effect of single BeiDou to carry out joint positioning experiments, including real environments, such as buildings on one side, under bridges, and between buildings. By analyzing the geometric distribution of base stations and satellites and the positioning accuracy of the joint solution, the results show that the joint solution algorithm proposed in this paper can effectively improve the reliability of positioning in occluded scenes. Finally, the fusion test results and shortcomings were analyzed, and the future development direction of BDS–5G signals was proposed.

The structure of the paper is as follows: Section 2 describes the mathematical model of BDS–5G fusion, Section 3 introduces the multiobjective particle filter algorithm for the model solution, Section 4 describes our experimental methods and results in detail, and Section 5 provides a conclusion and plan for future work.

2. System Model

The BDS is based on the satellite receiver receiving the satellite position and the pseudorange for the operation to determine the user’s position. In general, three formulas based on the distance between satellite stations can be formed using three satellites, and the spatial position of the user observation station can be calculated by forming an equation. In the process of real positioning, there is also a deviation between the satellite clock and the receiver clock. It is necessary to introduce the error into the equation group as an unknown quantity and calculate it together. Therefore, the pseudorange value $\rho$ received by the BDS receiver (which corrects the measured range value of the process and ionospheric delay) is equal to the true range value $r$ plus the error value caused by the receiver clock error $\delta$, with $\rho =r+\delta +\mathsf{\epsilon }$, $r$ as the Euclidean distance between the receiver position $\left(x,y,z\right)$ and the satellite position $\left(x_s,y_s,z_s\right)$, and $\mathsf{\epsilon }$ as the pseudorange measurement error, which determines the variance of the positioning error [30]. Thus, there is the following Formula (1):

$$\{\begin{array}{c}{\rho }_1=\sqrt{{\left(x_{s1}-x\right)}^2+{\left(y_{s1}-y\right)}^2+{\left(z_{s1}-z\right)}^2}+\delta +{\mathsf{\epsilon }}_{s1}\\ {\rho }_2=\sqrt{{\left(x_{s2}-x\right)}^2+{\left(y_{s2}-y\right)}^2+{\left(z_{s2}-z\right)}^2}+\delta +{\mathsf{\epsilon }}_{s2}\\ {\rho }_3=\sqrt{{\left(x_{s3}-x\right)}^2+{\left(y_{s3}-y\right)}^2+{\left(z_{s3}-z\right)}^2}+\delta +{\mathsf{\epsilon }}_{s3}\\ ⋮\\ {\rho }_n=\sqrt{{\left(x_{sn}-x\right)}^2+{\left(y_{sn}-y\right)}^2+{\left(z_{sn}-z\right)}^2}+\delta +{\mathsf{\epsilon }}_{sn}\end{array}$$

(1)

where ${\rho }_i$ is the space pseudorange from the satellite to the receiver; $\left(x,y,z\right)$ is the coordinate of the satellite receiver to be obtained; $\delta$ is the product of the error and speed between the satellite clock and the receiver clock; $\left(x_{si},y_{si},z_{si}\right)$ is the spatial coordinate of the BDS satellite; and $i$ is the serial number of the observed satellite.

In 5G positioning theory, the TDOA measurement method is often used to locate users. The TDOA-based positioning method, also known as hyperbolic positioning, is based on the principle of measuring the difference in the propagation time of the signal from the tag to the two base stations to obtain the fixed distance difference between the label and the two base stations. The TDOA algorithm is an improvement of the TOA algorithm, which does not directly use the signal arrival time but uses the time difference between the signals received by multiple base stations to determine the location of the moving target. Therefore, compared with TOA, there is no need to add a unique timestamp for clock synchronization, and the positioning accuracy is relatively improved. Assuming that base station 1 is taken as the benchmark and the distance between the receiver and base station 1 is $d_1$, there is

$$\{\begin{array}{c}{d}_1=\sqrt{{\left(x_{b1}-x\right)}^2+{\left(y_{b1}-y\right)}^2+{\left(z_{b1}-z\right)}^2}+{\mathsf{\epsilon }}_{b1}\\ d_2-d_1=\sqrt{{\left(x_{b2}-x\right)}^2+{\left(y_{b2}-y\right)}^2+{\left(z_{b2}-z\right)}^2}-d_1+{\mathsf{\epsilon }}_{b2}\\ d3-d_1=\sqrt{{\left(x_{b3}-x\right)}^2+{\left(y_{b3}-y\right)}^2+{\left(z_{b3}-z\right)}^2}-d_1+{\mathsf{\epsilon }}_{b3}\\ ⋮\\ d_n-d_1=\sqrt{{\left(x_{bn}-x\right)}^2+{\left(y_{bn}-y\right)}^2+{\left(z_{bn}-z\right)}^2}-d_1+{\mathsf{\epsilon }}_{bn}\end{array}$$

(2)

where $d_k\left(k=1,2\dots ,n\right)$ represents the distance from the receiver to base station $k$, $\left(x_{bk},y_{bk},z_{bk}\right)$ represents the position coordinate of base station $k$, $\left(x,y,z\right)$ represents the position of the receiver, and ${\mathsf{\epsilon }}_{bi}$ is the measurement error. The measurement error is a random variable whose value affects the variance of the positioning result, which is temporarily not considered in the model analysis.

For TDOA receivers, we can measure the difference between the transmission time of the ranging signal between the receiver and the two base stations. Assuming that the transmission time of the ranging signal between the receiver and base station is $t$, we have

$$d_k-d_1=c\left(t_k-t_1\right)=c\mathsf{\Delta }{t}_k$$

(3)

where $c$ is the signal propagation speed 299,792,458 m/s, and $\mathsf{\Delta }{t}_k$ is the time difference between the time from the 5G base station signal to the receiver measured for the kth measurement and the time between the 5G base station signal and the receiver measured for the first time. From Formula (2), we obtain:

$$\{\begin{array}{c}0=\sqrt{{\left(x_{b1}-x\right)}^2+{\left(y_{b1}-y\right)}^2+{\left(z_{b1}-z\right)}^2}-d_1\\ c\mathsf{\Delta }{t}_2=\sqrt{{\left(x_{b2}-x\right)}^2+{\left(y_{b2}-y\right)}^2+{\left(z_{b2}-z\right)}^2}-d_1\\ c\mathsf{\Delta }{t}_3=\sqrt{{\left(x_{b3}-x\right)}^2+{\left(y_{b3}-y\right)}^2+{\left(z_{b3}-z\right)}^2}-d_1\\ ⋮\\ c\mathsf{\Delta }{t}_n=\sqrt{{\left(x_{bn}-x\right)}^2+{\left(y_{bn}-y\right)}^2+{\left(z_{bn}-z\right)}^2}-d_1\end{array}$$

(4)

Simultaneous Equations (1) and (4) can be obtained:

$$\{\begin{array}{c}{\rho }_1=\sqrt{{\left(x_{s1}-x\right)}^2+{\left(y_{s1}-y\right)}^2+{\left(z_{s1}-z\right)}^2}+\delta \\ {\rho }_2=\sqrt{{\left(x_{s2}-x\right)}^2+{\left(y_{s2}-y\right)}^2+{\left(z_{s2}-z\right)}^2}+\delta \\ {\rho }_3=\sqrt{{\left(x_{s3}-x\right)}^2+{\left(y_{s3}-y\right)}^2+{\left(z_{s3}-z\right)}^2}+\delta \\ ⋮\\ \begin{array}{c}{\rho }_n=\sqrt{{\left(x_{sn}-x\right)}^2+{\left(y_{sn}-y\right)}^2+{\left(z_{sn}-z\right)}^2}+\delta \\ 0=\sqrt{{\left(x_{b1}-x\right)}^2+{\left(y_{b1}-y\right)}^2+{\left(z_{b1}-z\right)}^2}-d_1\\ c\mathsf{\Delta }{t}_2=\sqrt{{\left(x_{b2}-x\right)}^2+{\left(y_{b2}-y\right)}^2+{\left(z_{b2}-z\right)}^2}-d_1\\ c\mathsf{\Delta }{t}_3=\sqrt{{\left(x_{b3}-x\right)}^2+{\left(y_{b3}-y\right)}^2+{\left(z_{b3}-z\right)}^2}-d_1\\ ⋮\\ c\mathsf{\Delta }{t}_n=\sqrt{{\left(x_{bn}-x\right)}^2+{\left(y_{bn}-y\right)}^2+{\left(z_{bn}-z\right)}^2}-d_1\end{array}\end{array}$$

(5)

multiple measurements can solve the above equation to obtain accurate positioning coordinates, and due to the advantages of the particle filter algorithm in solving nonlinear equations, the particle filter (PF) is used to calculate it, which is an approximate Bayesian filtering algorithm based on Monte Carlo simulation. Its core idea is to use some discrete random sample points (particles) to approximate the probability density function of the system random variables and replace the integral operation with the sample mean to obtain the minimum variance estimation of the state.

3. BDS–5G Signal Fusion Location Algorithm

3.1. Multiobjective Particle Swarm Optimization (MOPSO)

The particle swarm optimization algorithm solves complex optimization problems by simulating the group behavior of birds, such as foraging and migration. The particle swarm optimization algorithm randomly distributes a certain number of particles in the feasible area of the problem space, and each particle flies at a certain speed. During flight, the particles adjust their state by combining the current best position and the best position of the population to flee to a better area. The optimization process of the particle swarm optimization algorithm is similar to that of birds foraging. Using this information-sharing mechanism, the group’s movement evolves from disorder to order and finally achieves the purpose of searching for the optimal solution.

The definition of the multiobjective optimization problem is described as follows: We need to find the optimal location to minimize the overall cost function:

$$minF\left(x,y,z\right)=min\left(f_1\left(x,y,z\right),f_2\left(x,y,z\right),\dots ,f_n\left(x,y,z\right)\right)$$

(6)

where $F\left(x,y,z\right)$ represents the overall cost function in the multiobjective optimization process and $f_k\left(x,y,z\right)$ is the error of a single objective function. PSO initializes a uniformly distributed particle randomly within a specified range. All particles in the group have an image effect, each particle has its position and speed, and the particles are driven by the global optimal particle ($g_{best}$) and the individual optimal particle ($p_{best}$) to find the optimal solution. In the single objective particle swarm optimization algorithm, $g_{best}$ and $p_{best}$ can be uniquely determined by comparing their fitness values since there is only one objective function. In the multiobjective particle swarm optimization algorithm, for selection $p_{best}$, the particle is better if the particle can minimize each cost function. If you cannot strictly compare who is better, randomly select one of them as the individual best. For choosing $g_{best}$, many noninferior solutions can be used as the global optimal individual. However, in PSO, each particle can only choose one as the global optimal individual. Therefore, preserving these noninferior solutions and selecting a better noninferior solution is the core of the particle swarm optimization algorithm in dealing with multiobjective optimization problems. The velocity and position update equations of particles are as follows:

$$\upsilon \left(t+1\right)=\omega \upsilon \left(t\right)+c_1{r}_1\left(p\left(t\right)-x\left(t\right)\right)+c_2{r}_2\left(g\left(t\right)-x\left(t\right)\right)$$

(7)

$$x\left(t+1\right)=x\left(t\right)+\upsilon \left(t+1\right)$$

(8)

where $\omega$ is the inertia weight, and its size controls the size of the search ability; $c_1$ and $c_2$ are the individual experience coefficient and social experience coefficient, respectively; r₁ and r₂ are random numbers between ranges $\left[0, 1\right]$; and $p$ and $g$ are the individual optimal solution and the global optimal solution, respectively.

In each iteration of the multiobjective particle swarm optimization algorithm, many noninferior solutions will be generated. Because they are not dominant, it is difficult to select the optimal particle, so we need to consider ensuring the diversity of the noninferior solutions. Based on the above reasons, the PSO algorithm selected by the optimal solution evaluation is used to search the noninferior optimal solution set of the multiobjective optimization problem. The algorithm initializes a particle swarm in the decision variable space. It guides the particles to fly in the decision variable space through each objective function in the multiobjective optimization problem to finally fall into the noninferior optimal solution set. Reflected in the objective function space, the particles will fall into the noninferior optimal objective domain. Specifically, this is achieved in the following ways: First, use each objective function in the multiobjective optimization problem to find the global extremum $g_{best}\left[i\right]\left(i=1,2\dots n\right)$ and individual extremum $p_{best}[i,j]\left(j=1,2\dots n\right)$ of each particle corresponding to each objective function. Second, when updating the speed of each particle, use the “mean” of each $g_{best}\left[i\right]$ as the global extremum. The $p_{best}\left[i,j\right]$ of each particle is determined by judging the dispersion degree of $p_{best}\left[i,j\right]$ relative to $g_{best}\left[i\right]$ to decide whether to take the mean value of $p_{best}\left[i,j\right]$ or randomly select in $p_{best}\left[i,j\right]$.

3.2. BDS–5G Signals Joint Solution and MOPSO-TOA/TDOA Model Algorithm

The objective function of the BDS–5G signal joint solution is constructed from Equation (5) as follows:

$$\{\begin{array}{c}{f}_{n1}\left(x,y,z\right)=\left|\left|{\rho }_n-\sqrt{{\left(x_{sn}-x\right)}^2+{\left(y_{sn}-y\right)}^2+{\left(z_{sn}-z\right)}^2}-\delta \right|\right|\\ f_{n2}\left(x,y,z\right)=\left|\left|c\mathsf{\Delta }{t}_n-\sqrt{{\left(x_{bn}-x\right)}^2+{\left(y_{bn}-y\right)}^2+{\left(z_{bn}-z\right)}^2}-d_1\right|\right|\end{array}$$

(9)

The algorithm flow is as follows:

• Initialize particle swarm: given the population size N, randomly generate the position $X_i$ and speed $V_i$ of each particle;
• Calculate the fitness value of each particle with the objective function $f_{n1}\left(x,y,z\right)$, $f_{n2}\left(x,y,z\right)$;
• Calculate the individual extreme value of each particle and the global extreme value of the objective function;
• Calculate the mean value $g_{best}$ and distance $d_{g_{best}}$ of the global vector;
• Calculate the distance $d_{p_{best}}\left[i\right]$ between each particle $g_{best}\left[n,i\right]$;
• Calculate the individual extreme value $p_{best}\left[i\right]$ to be used when updating the position and speed $V_i$ for each particle $X_i$;
• Update the position $X_i$ and velocity $V_i$ of each particle with the results $g_{best}$ and $p_{best}\left[i\right]$ of (3) and (6).

4. Performance Analysis

4.1. Algorithm Simulation Performance Test

To verify the performance of the MOPSO-TOA/TDOA algorithm in the BDS–5G joint solution system, the convergence of the algorithm in the X, Y, and Z directions was verified using BDS satellite data and 5G base station data. In the selection of the initialization parameters, since the coordinates of the 5G base station are known, 5G base station position coordinates were selected for the initial position of iteration so that the algorithm could reach the convergence state faster. The test platform was MATLAB 2019 (a). Considering the complex environment and the insufficient number of visible satellites, at least four objective function equations were required to solve the position. The target equation set composed of two satellites and two 5G base stations were selected for testing. The four objective equations are as follows:

$$\{\begin{array}{c}{f}_1\left(x,y,z\right)=\Vert {\rho }_1-\sqrt{{\left(x_{s1}-x\right)}^2+{\left(y_{s1}-y\right)}^2+{\left(z_{s1}-z\right)}^2}-\delta \Vert \\ f_2\left(x,y,z\right)=\Vert {\rho }_2-\sqrt{{\left(x_{s2}-x\right)}^2+{\left(y_{s2}-y\right)}^2+{\left(z_{s2}-z\right)}^2}-\delta \Vert \\ f_3\left(x,y,z\right)=\Vert c\mathsf{\Delta }{t}_n-\sqrt{{\left(x_{b3}-x\right)}^2+{\left(y_{b3}-y\right)}^2+{\left(z_{b3}-z\right)}^2}-d_1\Vert \\ f_4\left(x,y,z\right)=\Vert c\mathsf{\Delta }{t}_n-\sqrt{{\left(x_{b4}-x\right)}^2+{\left(y_{b4}-y\right)}^2+{\left(z_{b4}-z\right)}^2}-d_1\Vert \end{array}$$

(10)

Through a parameter modification test, when the number of particles of the multiobjective particle filter algorithm is set to 100, the inertia factor is set to 0.8, and the speed factor is set to 0.1, the algorithm can converge quickly and obtain the optimal result.

The value of the objective function changed with the number of iterations, as shown in Figure 2. The figure contains four objective functions. In the early iteration process, the particles were in the search state, and the results of each objective function changed significantly. When iterating to 50 values approximately 100 times, each objective function converged, and the error of the calculated position result is shown in Figure 3. When iterating 100 times, the multiobjective particle positioning algorithm obtained the optimal solution.

4.2. Algorithm Simulation Performance Test

To compare the performance of the proposed MOPSO-TOA/TDOA algorithm and the traditional Kalman filtering fusion algorithm, outdoor field tests were used to verify the performance. The main streets in an urban environment were selected, and BeiDou satellite signals and 5G base station signals were received simultaneously. The two algorithms were used to calculate the location of the received data, and the algorithm convergence time and location accuracy were compared. The test terminal adopted the BDS–5G signal positioning terminal jointly developed by the Beijing University of Posts and Telecommunications and Hwa Create Corporation, which can simultaneously receive satellite pseudorange, coordinates, 5G ranging, and other observation information for joint positioning real-time solutions. The receiving terminal is shown in Figure 4a. Two hundred complex environment test sites near a city street were selected as test sites. The test route is shown in Figure 4b. The red location mark represents the test point. The Sinan k708 full-frequency high-precision positioning GNSS board and CTI E91 are the reference real coordinates to provide the authority positioning truth value. The convergence time and accuracy of the algorithm were compared and analyzed.

As shown in Figure 4c,d, 200 test points on urban roads were measured. The red curve represents the error between the position calculated by the MOPSO-TOA/TDOA algorithm and the real position, and the blue curve represents the error between the position calculated by the Kalman filtering fusion algorithm and the real position. The experiment shows that the average convergence time of the MOPSO-TOA/TDOA algorithm is 0.124 s, and the average positioning error is 2.65 m. The average convergence time of the positioning algorithm based on the extended Kalman filter is 0.165 s, and the average positioning error is 3.27 m. The BDS–5G signal fusion positioning algorithm based on MOPSO-TOA/TDOA improves the convergence time by 24.8% compared with the fusion positioning algorithm based on the Kalman filter. The positioning accuracy is improved by 18.9%, and the system’s robustness and real-time positioning ability are improved.

4.3. Test of the BDS–5G Signal MOPSO-TOA/TDOA Algorithm in the Complex Environment

To verify the ability of the BDS–5G signal fusion positioning algorithm based on MOPSO-TOA/TDOA to improve the localization of a single BDS in complex scenes, such as occlusion, test experiments were carried out in actual scenes (city urban canyon, unilateral buildings, and under the bridge). The control group (single BDS positioning test) and the experimental group (BDS–5G signals MOPSO-TOA/TDOA test) were set up to conduct a comparative analysis of the positioning experiments in three environments. The test scenario is shown in the following Figure 5a,c,e. The blue square represents the 5G base stations distribution, the red pentagram represents the distribution of the BeiDou satellites, and the light blue rectangular area is the building sheltered area. Two hundred positioning experiments were carried out in these three scenarios. The cumulative distribution of errors of positioning results and real positions is shown in Figure 5b,d,f. Red represents the results of the BDS–5G MOPSO-TOA/TDOA algorithm, and blue represents the BDS positioning results. The 1σ value of the overall error is shown in

Table 1. Outdoor BDS–5G signals joint positioning test results/m (1σ).

Complex Scenes	Conditions	Error
canyon	Single BDS	12.3993
	BDS–5G	3.1342
Unilateral building	Single BDS	30.816
	BDS–5G	10.0659
Under the bridge	Single BDS	6.0791
	BDS–5G	3.7049

.

Through the analysis of the above results, BDS–5G signal particle filter fusion positioning is improved in all scenarios compared with single BDS positioning. In the three occluded scenes, the MOP-SO-TOA/TDOA algorithm has greatly improved the positioning accuracy compared to the single BDS. The positioning accuracy has been improved by 50–80%, and the overall average positioning errors are 5.63 m and 16.43 m, respectively, which increased by 65.7%. BDS–5G signal integrated positioning technology can effectively improve the positioning ability of BDS, which is more significant in sheltered environments.

5. Conclusions

This paper proposes a new solution model based on TOA measurements of BDS satellites and TDOA measurements of 5G base stations. The solution efficiency of the model is improved by using a multiobjective particle filter algorithm, which provides a new method (MOPSO-TOA/TDOA) for data fusion of BDS–5G signals. Compared with the traditional Kalman filtering fusion algorithm, the BDS–5G signal fusion method based on the MOP-SO-TOA/TDOA algorithm can effectively improve the positioning accuracy and convergence time of the system and determine the target position in real-time in complex environments. The MOPSO-TOA/TDOA algorithm and KF algorithm perform real-time location calculations in complex urban environments. The convergence times of the MOPSO-TOA/TDOA algorithm and KF algorithm are 0.124 s and 0.165 s, respectively. The MOPSO-TOA/TDOA algorithm reduces the time by 24.8%, the positioning accuracies of the algorithm are 2.65 m and 3.27 m, respectively, and the positioning accuracy of the MOPSO-TOA/TDOA algorithm is improved by 18.9%. We also compared the performance of the MOPSO-TOA/TDOA algorithm and separated the BDS into three complex environments. The average errors of the MOPSO-TOA/TDOA algorithm and single BDS algorithm were 5.63 m and 16.43 m, respectively, with an overall increase of 65.7%.

To build a seamless indoor and outdoor positioning system, the BDS network should be more closely integrated with the 5G communication network under construction. Through the introduction of a 5G communication network, the BDS is used for positioning in outdoor open areas, BDS–5G is used for fusion positioning in complex environments or indoor and outdoor boundaries, and 5G signal positioning is used indoor areas where it is difficult to receive satellite signals. Under the condition of ensuring the regular switching of the positioning signal, the BDS–5G fusion positioning system can achieve the effect of uninterrupted accurate positioning, thus providing the essential support of entire scene high-precision space-time perception for future intelligent society. In this regard, it is necessary to further carry out BDS–5G signal integration technology tests in different industry application scenarios, analyze and optimize the performance of BDS–5G signal technology under various conditions, and lay the foundation for the comprehensive promotion of BDS–5G signal technology.