﻿ 基于智能手机自设基站的相对定位分析
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 大地测量与地球动力学  2024, Vol. 44 Issue (5): 468-472, 478  DOI: 10.14075/j.jgg.2023.09.131

### 引用本文

LAN Minyi, GAO Chengfa. Analysis of Relative Positioning Based on Self-Established Base Station Using Smartphones[J]. Journal of Geodesy and Geodynamics, 2024, 44(5): 468-472, 478.

### Foundation support

Research Fund of Ministry of Education and China Mobile, No.MCM20200J01.

### 第一作者简介

LAN Minyi, postgraduate, majors in multi-source fusion localization, E-mail: lmyseu@163.com.

### 文章历史

1. 东南大学交通学院，南京市东南大学路2号，211189

1 相对定位模型 1.1 观测模型

 \begin{aligned} \varPhi_i^p= & \rho_i^p+c \cdot \mathrm{d} t_i-c \cdot \mathrm{d} T^p+\left(d_{\text {orb }}\right)_i^p+ \\ & \left(d_{\text {trop }}\right)_i^p-\left(d_{\text {ion }}\right)_i^p+\widetilde{N}_i^p+\varepsilon \end{aligned} (1)
 \begin{aligned} \varPhi_j^p= & \rho_j^p+c \cdot \mathrm{d} t_j-c \cdot \mathrm{d} T^p+\left(d_{\text {orb }}\right)_j^p+ \\ & \left(d_{\text {trop }}\right)_i^p-\left(d_{\text {ion }}\right)_j^p+\widetilde{N}_j^p+\varepsilon \end{aligned} (2)

 $\begin{array}{c} \nabla \varPhi_{i j}^p=\left(\rho_j^p-\rho_i^p\right)+\nabla(c \cdot \mathrm{d} t)_{i j}+\nabla\left(d_{\text {orb }}\right)_{i j}^p+ \\ \nabla\left(d_{\text {trop }}\right)_{i j}^p-\nabla\left(d_{\text {ion }}\right)_{i j}^p+\nabla \widetilde{N}_{i j}^p+\varepsilon \end{array}$ (3)

 $\begin{array}{c} \mathit{\Delta} \nabla \varPhi_{i j}^{p q}=\left(\rho_j^q-\rho_i^q-\rho_j^p+\rho_i^p\right)+\left(d_{\text {orb }}\right)_{i j}^{p q}+ \\ \;\;\;\mathit{\Delta} \nabla\left(d_{\text {trop }}\right)_{i j}^{p q}-\mathit{\Delta} \nabla\left(d_{\text {ion }}\right)_{i j}^{p q}+\mathit{\Delta} \nabla \widetilde{N}_{i j}^{p q}+\varepsilon \end{array}$ (4)

1.2 Kalman滤波模型

Kalman滤波算法是通过一系列线性系统状态方程，利用系统观测数据对系统状态进行估计的一种最优估计算法，广泛应用于导航、监测、控制等领域。本文采用的参数估计方法为Kalman滤波，其数学模型可表示为：

 $\boldsymbol{X}_k=\boldsymbol{\varPhi}_{k / k-1} \boldsymbol{X}_{k-1}+\boldsymbol{\varGamma}_{k-1} \boldsymbol{W}_{k-1}$ (5)
 $\boldsymbol{Z}_k=\boldsymbol{H}_k \boldsymbol{X}_k+\boldsymbol{V}$ (6)

k－1历元到k历元卡尔曼滤波器更新过程分为状态更新和量测更新，可表示为：

 $\left\{\begin{array}{l} \hat{\boldsymbol{X}}_{k, k-1}=\boldsymbol{\varPhi}_{k, k-1} \hat{\boldsymbol{X}}_{k-1} \\ \boldsymbol{P}_{k / k-1}=\boldsymbol{\varPhi}_{k / k-1} \boldsymbol{P}_{k-1} \boldsymbol{\varPhi}_{k / k-1}^{\mathrm{T}}+\boldsymbol{\varGamma}_{k-1} \boldsymbol{Q}_{k-1} \boldsymbol{\varGamma}_{k-1}^{\mathrm{T}} \\ \boldsymbol{K}_k=\boldsymbol{P}_{k / k-1} \boldsymbol{H}_k^{\mathrm{T}}\left(\boldsymbol{H}_k \boldsymbol{P}_{k / k-1} \boldsymbol{H}_k^{\mathrm{T}}+\boldsymbol{R}_k\right)^{-1} \\ \hat{\boldsymbol{X}}_k=\hat{\boldsymbol{X}}_{k / k-1}+\boldsymbol{K}_k\left(\boldsymbol{Z}_k-\boldsymbol{H}_k \hat{\boldsymbol{X}}_{k / k-1}\right) \\ \boldsymbol{P}_k=\left(\boldsymbol{I}-\boldsymbol{K}_k \boldsymbol{H}_k\right) \boldsymbol{P}_{k / k-1} \end{array}\right.$ (7)

 $\boldsymbol{X}_k=\left[\boldsymbol{r}_r, \mathit{\Delta} \nabla N\right]$ (8)

 $\boldsymbol{X}_k=\left[\boldsymbol{r}_r, \boldsymbol{v}_r, \boldsymbol{a}_r, \mathit{\Delta} \nabla N\right]$ (9)

2 实验及分析 2.1 实验设计

 图 1 自设基站安装示意图 Fig. 1 Installation diagram of self-installed base station

2.2 自设基站坐标标定

 图 2 自设基站定位误差序列 Fig. 2 Positioning error sequence of self-established base station

2.3 智能手机与自设基站差分定位

2.3.1 静态实验

 图 3 静态实验华为Mate40定位误差序列 Fig. 3 Positioning error sequence of Huawei Mate40 in static experiment

2.3.2 动态实验

 图 4 行人动态实验华为Mate40定位误差序列 Fig. 4 Positioning error sequence of Huawei Mate40 in pedestrian dynamic experiment

 图 5 骑车动态实验华为Mate40定位误差序列 Fig. 5 Positioning error sequence of Huawei Mate40 in cycling dynamic experiment

3 结语

1) 在静态实验中，CORS基准站同智能手机华为Mate40差分的平面和高程定位精度分别为0.089 m、0.025 m；自设基站同智能手机华为Mate40差分的平面和高程定位精度分别为0.092 m、0.006 m。智能手机华为Mate40同CORS基准站和自设基站能够获得cm级定位精度，且两者差异较小。

2) 在行人动态实验中，自设基站同智能手机华为Mate40差分的平面和高程定位精度分别为0.591 m、0.957 m；CORS基准站同智能手机华为Mate40差分的平面和高程定位精度分别为0.511 m、1.099 m。在骑车动态实验中，自设基站同智能手机华为Mate40差分的平面和高程定位精度分别为0.631 m、1.182 m；CORS基准站同智能手机华为Mate40差分的平面和高程定位精度分别为0.467 m、0.629 m。智能手机华为Mate40同CORS基准站和自设基站的差分结果均能获得dm级平面定位精度，表明基于智能手机的自设基站能同CORS基准站一样提供基准站服务。

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Analysis of Relative Positioning Based on Self-Established Base Station Using Smartphones
LAN Minyi1     GAO Chengfa1
1. School of Transportation, Southeast University, 2 Dongnandaxue Road, Nanjing 211189, China
Abstract: Aiming at the problems of low positioning accuracy and poor reliability in areas without CORS services, we propose a method for differential positioning using a self-established base station with smartphone. The method uses an external antenna to improve the quality of GNSS observation data and uses devices such as RF shielding boxes to set up a self-established base station. The Huawei Mate40 smartphone is used as a mobile station, and RTK positioning is performed with both traditional CORS base station and self-established base station. Static, walking, and cycling experiments are designed to evaluate the service capability of self-established base station. The experimental results show that in the static experiment, the RTK positioning accuracy of Huawei Mate40 smartphone with self-established base station can reach centimeter-level accuracy. In the dynamic experiment, the RTK positioning accuracy of Huawei Mate40 smartphone with both self-established base station and CORS reference station can reach decimeter-level accuracy, with a difference in planar positioning accuracy of about 0.1 m between the two methods. The self-established base station based on a smartphone can provide stable reference station services and meet the needs of surveying and mapping work in specific scenarios.
Key words: smartphone; self-established base station; relative positioning; accuracy analysis