High-Accuracy Positioning Algorithm Based on UWB

In the indoor positioning, it proposes a line to approximate hyperbola positioning algorithm based on ultra-wideband (UWB) aiming at the problems of low-accuracy positioning, non-line-of-sight (NLOS) phenomenon and multipath propagation in the precise positioning of mobile tags. The paper a method of using some lines to approximate hyperbola. It can convert quadratic hyperbolic equation into linear equation. Then it can achieve the high-accuracy position combining the time difference of arrival (TDOA) and triangle centroid position algorithm. According to MATLAB simulation, the average distance error of the three-line approximate algorithm is 23.7cm, the average distance error of the three-and-four-line approximate positioning algorithm is 17.7cm, and the average distance error of the five-line approximate positioning algorithm is 12.9cm. In the case of ensuring positioning accuracy, the Chan algorithm runs for a period of 14.5s. The maximum time is 7.9s for the algorithm to run one cycle, and the complexity of the algorithm is greatly reduced.

The positioning principle is divided into two steps: (1) ranging which is measuring the distance between two points; (2) positioning which determines the location of the mobile tag according to the results of the ranging by a specific algorithm. There are four classic positioning methods which include received signal strength [3] (RSS), signal angle of arrival [4] (AOA), time of arrival [5] (TOA) and time difference of arrival [6] (TDOA). The TOA/TDOA scheme is the main ranging scheme for UWB positioning. It can calculate the distance difference from each anchor to a mobile tag by the measured TDOA time. It can establish the plurality of hyperbolic equations according to the distance difference. The Chan algorithm [7] is the classical localization method based on the time difference of arrival. It does not require recursion to give a closed solution to the hyperbolic equation. The Taylor algorithm [8] is a recursive algorithm that requires an estimate of the initial position and solves the partial least squares [9] (LS) solution of the TDOA measurement error in each recursion. The Kalman filter [10] is a linear least-mean-squares estimation algorithm which is the best filter in a linear system. In a variety of sensor measurements, Kalman filtering is widely used for state estimation [11]. Assuming that the experimental process and measurement noises are normally distributed, measurement noise of wireless positioning system is not easy to meet the normal distribution condition due to frequent heavy tailing anomalies value. The Fang algorithm [12] can linearize the TDOA hyperbolic equation and then solve the solution of the hyperbolic equations which is the position of the moving tag. The algorithm is easy to understand and the calculation is simple.
This paper proposes a method of approximating the hyperbolic localization model by subsection approach, which is divided into three-line approximate positioning algorithm, three-and-four-line approximate positioning algorithm, and five-line approximate positioning algorithm. It can use the lines to approximate hyperbola. The quadratic curve model is transformed into a linear model and the intersection point of the line segment can be approximated as the intersection point of the hyperbola. Then it can use the triangular centroid positioning algorithm [13]. The centroid is the positioning result of the mobile tag.
II. TDOA ALGORITHM PRINCIPLE The positioning principle of TDOA [14] is to obtain the distance difference from each anchor to the mobile tag by using a set of TDOA measurement values. It establishes a hyperbolic equation which takes the base station as the focus. The mobile tag that needs to be located is on a certain branch of the hyperbola. The solution of the hyperbolic equations is determined as the position of the estimated moving tag.
Assuming that anchor1 ( 1 The two-point distance equation of the TDOA algorithm is defined as

III. LINE TO APPROXIMATION HYPERBOLA ALGORITHM
In an ideal situation, if there are no obstacles and non-line-of-sight (NLOS) in the room, the four anchors in the four corners of the room will be considered as the focuses of the hyperbola respectively. The hyperbolas will intersect one point which is the coordinates of the mobile tag. However, because of problems such as indoor blocking, NLOS phenomenon and multipath propagation in the actual environment, the hyperbolas do not intersect one point and form a common overlapping area which can be considered as the possible existing area of a mobile tag.
The basic principle of triangle centroid positioning algorithm is to calculate the coordinates of the three intersections of the common overlap of the three hyperbolas. These three intersections form the vertices of the triangle. The centroid of the triangle is the coordinate of the estimated moving tag.
The triangle centroid formula is defined as 3 y y y y (2) Where ( 1 We propose a line to approximate the hyperbola method and the nodes of the three piecewise functions are the nodes of three hyperbolas. The core idea of the line to approximate the hyperbola method is to use three lines, three-and-four lines and five lines respectively to approximate hyperbola. According to the positive or negative distance difference obtained by the TDOA measurement value, it is simple to determine the position of mobile tag on the hyperbolic branch, the judgment rules shown in Table .   TABLE I. JUDGMENT RULE TABLE   upper down left In Table ,  When we use three lines to approximate hyperbola, the first line and the third line are hyperbolic asymptote lines respectively, and the second line is the vertical line of the hyperbolic apex. When it is judged that the mobile tag is on one side of the hyperbola, we can use three lines to approximate hyperbolas. When we use five lines to approximate hyperbola, the first line and the fifth line are respectively the asymptotes of which the original hyperbola is moved some distances. The moved distance formula is shown in (3). The third line is the vertical line of hyperbolic focus which translates by L1 (5cm). The nodes of the vertical line and the hyperbola are ( 8 y ,) and ( 9 x , 9 y ). Then the nodes are translated by L2 (25cm) and the coordinates of nodes are ( 8 x , 8 y +L2) and ( 9 x , 9 y +L2).
The second line is the connected line of ( 8 asymptote. The fourth line is the connected lines of ( 9 x , 9 y +L2) and asymptote.
The localization results are shown respectively in From this, the time taken for the Chan algorithm to run one cycle is 14.5s, and the time taken by the five-line segment approximation algorithm to run one cycle is 7.9s.

A. Experimental Environment
The experimental site is a 9.8×7.8×3.

B. Experimental results
In order to verify the feasibility and correctness of the algorithm, the same mobile tag is placed in different positions in the classroom at different time. Then we use the three-line segmental approximate positioning algorithm, the three-and-four-line segmental approximate positioning algorithm and the five-line segmental approximate positioning algorithm respectively to conduct comparative experiments. The simulation results are shown from Table to   Table .   The experimental results are shown in Fig. 4 by using the same mobile tag to collect TDOA data walking along the preset route in the classroom. The dynamic positioning error is shown in Table . There are three paths for walking in the classroom. The first path is which the range of the y-axis is (500.8, 500.8) and the range of x-axis is (103.1, 980.2). The second path is which the range of the y-axis is (139.1, 500.8) and the range of x-axis is (103.1, 103.1). The third path is which the range of the y-axis is (139.1, 139.1) and the range of x-axis is (103.1, 980.2).
It can be clearly seen that the five-line approximate positioning algorithm has better positioning accuracy than the other positioning methods. It can be well adapted to the environment and meet the requirements of general indoor positioning, such as construction sites, chemical plants, prisons and other scenes.

V. CONCLUSIONS AND PROSPECTS
The paper proposes a positioning algorithm that uses line to approximate the hyperbola based on UWB. It is seen from static positioning results that the accuracy of five-line approximate positioning algorithm is improved by 4.8cm compared with the three-and-four-line approximate positioning algorithm. The accuracy of the three-and-four-line approximate positioning algorithm is improved by 6cm compared with the three-line approximate positioning algorithm. It is seen from dynamic positioning results that the accuracy of the five-line approximate positioning algorithm is improved by 7.9cm compared with the three-and-four-line approximate positioning algorithm. The accuracy of the three-and-four-line approximate positioning algorithm is improved by 20.1cm compared with the three-line segmental approximate positioning algorithm. While continuing to increase the number of approximate line segments, the positioning accuracy is limited, and the upper limit of accuracy performance has been basically achieved. Therefore, five-line segmental approximate positioning is adopted.  In addition, NLOS is one of the main factors affecting the ranging accuracy in a multi-path environment. We identify the NLOS and detect the direct path in the received signal correctly. Then we add the identification result to the positioning algorithm to further improve the ranging positioning performance. This is the next job.