﻿ 基于TDOA系统的高精度软时钟同步方法 High Precision Soft Clock Synchronization Method Based on TDOA System

Hans Journal of Wireless Communications
Vol. 09  No. 06 ( 2019 ), Article ID: 33689 , 14 pages
10.12677/HJWC.2019.96024

High Precision Soft Clock Synchronization Method Based on TDOA System

Ge Yan, Hongwei Hou, Yifan Luo, Tianhao Fang, Wenjin Wang, Chi Wu

National Mobile Communications Research Laboratory, Southeast University, Nanjing Jiangsu

Received: Dec. 5th, 2019; accepted: Dec. 23rd, 2019; published: Dec. 30th, 2019

ABSTRACT

Based on the clock synchronization problem in TDOA (Time Difference of Arrival) real-time positioning system, a cross-recognition synchronization method is proposed. The soft clock synchronization design of TDOA positioning system is implemented on the DW1000 module provided by Decawave. Considering the transceiver characteristics of the module, only one signal can be transmitted in space at the same time. The method includes the communication protocol between the primary base station, the secondary base station and the user tag. The communication time slots between the modules are arranged to solve the problem of interference. At the same time, the method analyzes the communication process between modules to derive the linear equations that are satisfied between time stamp, clock frequency drift and time axis deviation. The least squares solution is substituted into the TDOA positioning algorithm to complete a clock synchronization and positioning with the user tag. The method proposed in the paper fully considers the requirements of TDOA real-time positioning system, and has the advantages of low delay, simple implementation and easy analysis.

Keywords:Indoor Positioning, TDOA System, Soft Clock Synchronization, Least Squares

1. 引言

2. TDOA定位

TDOA定位原理

${t}_{i}=\frac{1}{c}\sqrt{{\left(x-{x}_{i}\right)}^{2}+{\left(y-{y}_{i}\right)}^{2}+{\left(z-{z}_{i}\right)}^{2}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,N$ (1)

${\stackrel{˜}{t}}_{i}={t}_{i}+{n}_{i},\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,N$ (2)

${\stackrel{˜}{d}}_{ij}=c{\stackrel{˜}{t}}_{ij}=c\left({\stackrel{˜}{t}}_{i}-{\stackrel{˜}{t}}_{j}\right)$ (3)

${d}_{i}^{2}-{d}_{1}^{2}=-2{x}_{i,1}x-2{y}_{i,1}y-2{z}_{i,1}z+{K}_{i}-{K}_{1}$ (4)

${d}_{i}^{2}-{d}_{1}^{2}={\left({d}_{i,1}+{d}_{1}\right)}^{2}-{d}_{1}^{2}={d}_{i,1}^{2}+2{d}_{i,1}{d}_{1}$ (5)

${d}_{i,1}^{2}+2{d}_{i,1}{d}_{1}=-2{x}_{i,1}x-2{y}_{i,1}y-2{z}_{i,1}z+{K}_{i}-{K}_{1}$ (6)

$\varphi =h-{G}_{a}{p}_{a}$ (7)

$h=\frac{1}{2}\left[\begin{array}{c}{\stackrel{˜}{d}}_{2,1}^{2}-{K}_{2}+{K}_{1}\\ {\stackrel{˜}{d}}_{3,1}^{2}-{K}_{3}+{K}_{1}\\ ⋮\\ {\stackrel{˜}{d}}_{N,1}^{2}-{K}_{N}+{K}_{1}\end{array}\right]$

${G}_{a}=-\left[\begin{array}{cccc}{x}_{2,1}& {y}_{2,1}& {z}_{2,1}& {\stackrel{˜}{d}}_{2,1}\\ {x}_{3,1}& {y}_{3,1}& {z}_{3,1}& {\stackrel{˜}{d}}_{3,1}\\ ⋮& ⋮& ⋮& ⋮\\ {x}_{N,1}& {y}_{N,1}& {z}_{N,1}& {\stackrel{˜}{d}}_{N,1}\end{array}\right]$

${\stackrel{^}{p}}_{a}={\left({G}_{a}^{\text{T}}{\Phi }^{-1}{G}_{a}\right)}^{-1}{G}_{a}^{\text{T}}{\Phi }^{-1}h$ (8)

${\stackrel{^}{p}}_{a}={\left({G}_{a}^{\text{T}}{Q}^{-1}{G}_{a}\right)}^{-1}{G}_{a}^{\text{T}}{Q}^{-1}h$ (9)

$\phi ={h}_{b}-{G}_{b}{\stackrel{^}{p}}_{b}$ (10)

${h}_{b}=\left[\begin{array}{c}{\left({\stackrel{^}{p}}_{a,1}-{x}_{1}\right)}^{2}\\ {\left({\stackrel{^}{p}}_{a,2}-{y}_{1}\right)}^{2}\\ {\left({\stackrel{^}{p}}_{a,3}-{z}_{1}\right)}^{2}\\ {\stackrel{^}{p}}_{a,4}^{2}\end{array}\right]$

${G}_{a}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\\ 1& 1& 1\end{array}\right]$

${\stackrel{^}{p}}_{b}={\left({G}_{b}^{\text{T}}{\psi }^{-1}{G}_{b}\right)}^{-1}{G}_{b}^{\text{T}}{\Psi }^{-1}{h}_{b}$ (11)

3. 交叉验证的时钟同步

3.1. 时钟误差模型

Figure 1. Schematic diagram of single transceiver communication process

${N}_{i}={N}_{i}^{0}+t{f}_{i}$ (12)

${N}_{j}={N}_{j}^{0}+t{f}_{j}$ (13)

${N}_{i}^{s}={N}_{i}^{0}+t{f}_{i}$ (14)

${N}_{j}^{r}={N}_{j}^{0}+\left(t+\frac{{d}_{ij}}{c}+\tau \right){f}_{j}$ (15)

$\frac{{N}_{j}^{r}}{{f}_{j}}-\frac{{N}_{i}^{s}}{{f}_{i}}-{\epsilon }_{ij}-\tau =\frac{{d}_{ij}}{c}$ (16)

${\epsilon }_{ij}=\frac{{N}_{i}^{0}}{{f}_{i}}-\frac{{N}_{j}^{0}}{{f}_{j}}$ (17)

3.2. 时钟同步过程

Figure 2. Temporal logic

3.3. 通信协议设计

Figure 3. Communication protocol

Table 1. Description of the protocol field

3.4. LS同步

${F}_{n}=2n+\underset{i=1}{\overset{n}{\sum }}\left(i-1\right)=\frac{n}{2}\left(n+3\right)$ (18)

${V}_{n}=\left(n+1\right)+n+1=2n+2$ (19)

${N}_{{F}_{n}×{V}_{n}}{\Phi }_{{V}_{n}×1}=\frac{1}{c}d$ (20)

${n}_{1×{V}_{n}}^{ij}=\left[0,\cdots ,0,{N}_{j}^{r},0,\cdots ,0,-{N}_{i}^{s},0,\cdots ,0,-1,0,\cdots ,0,1,0,\cdots ,0,-1\right]$ (21)

${\Phi }_{{V}_{n}×1}={\left[\frac{1}{{f}_{0}},\cdots ,\frac{1}{{f}_{j}},\cdots ,\frac{1}{{f}_{i}},\cdots ,\frac{1}{{f}_{n}},{\epsilon }_{01},\cdots ,{\epsilon }_{0i},\cdots ,{\epsilon }_{0j},\cdots ,{\epsilon }_{0n},\tau \right]}^{\text{T}}$ (22)

${\Phi }_{{V}_{n}×1}=\frac{1}{c}{\left[{N}_{{F}_{n}×{V}_{n}}^{\text{T}}{N}_{{F}_{n}×{V}_{n}}\right]}^{-1}{N}_{{F}_{n}×{V}_{n}}^{\text{T}}d$ (23)

${\delta }_{ij}=\frac{{N}_{j}^{r}-{N}_{j}^{0}}{{f}_{j}}-\frac{{N}_{i}^{r}-{N}_{i}^{0}}{{f}_{i}}=\frac{{N}_{j}^{r}}{{f}_{j}}-\frac{{N}_{i}^{r}}{{f}_{i}}-{\epsilon }_{ij}$ (24)

(25)

${n}_{\text{TDOA}}^{0i}=\left[{N}_{0}^{r},0,\cdots ,0,-{N}_{i}^{r},0,\cdots ,0,-1,0,\cdots ,0,1,0,\cdots ,0\right]$ (26)

4. 基于实测数据的仿真验证

4.1. 实物测量

4.1.1. 定位模块

4.1.2. 可行性分析

Table 2. Relationship between sending frequency and packet loss rate

$B+R\cdot L\le M$ (27)

4.1.3. 噪声测量分析

4.2. 仿真设置

Table 3. Simulation parameter setting

4.3. 仿真结果与分析

Figure 4. Cumulative probability distribution curve of synchronization parameter error

Figure 5. Cumulative probability distribution curve of TDOA positioning errors

5. 结论

High Precision Soft Clock Synchronization Method Based on TDOA System[J]. 无线通信, 2019, 09(06): 185-198. https://doi.org/10.12677/HJWC.2019.96024

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