﻿ 一种顾及有色噪声的四星座GNSS动态导航滤波算法
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 大地测量与地球动力学  2019, Vol. 39 Issue (6): 625-629  DOI: 10.14075/j.jgg.2019.06.014

### 引用本文

SUN Qingfeng, CAI Changsheng, CUI Xianqiang, et al. A Filtering Algorithm for Quad-Constellation GNSS Kinematic Navigation with Consideration of Colored Noise[J]. Journal of Geodesy and Geodynamics, 2019, 39(6): 625-629.

### Foundation support

National Key Research and Development Program of China, No. 2016YFB0501803; National Natural Science Foundation of China, No. 41674039, 41674012.

### 文章历史

1. 中南大学地球科学与信息物理学院，长沙市麓山南路932号，410083

1 函数模型拟合滤波有色噪声处理算法

 $\left. \begin{array}{l} {P^{\rm{G}}} = {\rho ^{\rm{G}}} + c{\rm{d}}t - c{\rm{d}}{T^{\rm{G}}} + d_{{\rm{orb}}}^{\rm{G}} + d_{{\rm{trop}}}^{\rm{G}} + d_{{\rm{ion}}}^{\rm{G}} + b_P^{\rm{G}} + \varepsilon _P^{\rm{G}}\\ {P^{\rm{R}}} = {\rho ^{\rm{R}}} + c{\rm{d}}t + c{\rm{d}}t_{{\rm{sys}}}^{{\rm{R}}, {\rm{G}}} - c{\rm{d}}{T^{\rm{R}}} + d_{{\rm{orb}}}^{\rm{R}} + d_{{\rm{trop}}}^{\rm{R}} + d_{{\rm{ion}}}^{\rm{R}} + b_P^{\rm{R}} + \varepsilon _P^{\rm{R}}\\ {P^{\rm{E}}} = {\rho ^{\rm{E}}} + c{\rm{d}}t + c{\rm{d}}t_{{\rm{sys}}}^{{\rm{E}}, {\rm{G}}} - c{\rm{d}}{T^{\rm{E}}} + d_{{\rm{orb}}}^{\rm{E}} + d_{{\rm{trop}}}^{\rm{E}} + d_{{\rm{ion}}}^{\rm{E}} + b_P^{\rm{E}} + \varepsilon _P^{\rm{E}}\\ {P^{\rm{C}}} = {\rho ^{\rm{C}}} + c{\rm{d}}t + c{\rm{d}}t_{{\rm{sys}}}^{{\rm{C}}, {\rm{G}}} - c{\rm{d}}{T^{\rm{C}}} + d_{{\rm{orb}}}^{\rm{C}} + d_{{\rm{trop}}}^{\rm{C}} + d_{{\rm{ion}}}^{\rm{C}} + b_P^{\rm{C}} + \varepsilon _P^{\rm{C}} \end{array} \right\}$ (1)

 $\left. {\begin{array}{*{20}{l}} {{\mathit{\boldsymbol{L}}_k} = {\mathit{\boldsymbol{A}}_k}{\mathit{\boldsymbol{X}}_k} + {\mathit{\boldsymbol{e}}_k}}\\ {{{\bf{X}}_k} = {\mathit{\boldsymbol{ \boldsymbol{\varPhi} }}_{k \cdot k - 1}}{\mathit{\boldsymbol{X}}_{k - 1}} + {\mathit{\boldsymbol{W}}_k}} \end{array}} \right\}$ (2)

 $\left. {\begin{array}{*{20}{l}} {{\mathit{\boldsymbol{e}}_k} = {\mathit{\boldsymbol{B}}_{k,k - 1}}{\mathit{\boldsymbol{e}}_{k - 1}} + {\mathit{\boldsymbol{\eta }}_k}}\\ {{\mathit{\boldsymbol{W}}_k} = {\mathit{\boldsymbol{C}}_{k,k - 1}}{\mathit{\boldsymbol{W}}_{k - 1}} + {\mathit{\boldsymbol{\xi }}_k}} \end{array}} \right\}$ (3)

 $\left. \begin{array}{l} {{\mathit{\boldsymbol{\bar e}}}_k} = a \times \sum\limits_{j - m}^{j - 1} \mathit{\boldsymbol{V}} /m\\ {\mathit{\boldsymbol{\overline W}} _k} = b \times \sum\limits_{k - m}^{k - 1} {{\mathit{\boldsymbol{V}}_{\bar X}}} /m \end{array} \right\}$ (4)

 $\left. \begin{array}{l} {\mathit{\boldsymbol{L}}_k} + {{\mathit{\boldsymbol{\bar e}}}_k} = {\mathit{\boldsymbol{A}}_k}{\mathit{\boldsymbol{X}}_k} + {\mathit{\boldsymbol{\eta }}_k}\\ {\mathit{\boldsymbol{X}}_k} = \left( {{\mathit{\boldsymbol{ \boldsymbol{\varPhi} }}_{k, k - 1}}{\mathit{\boldsymbol{X}}_{k - 1}} + {{\mathit{\boldsymbol{\bar W}}}_k}} \right) + {\mathit{\boldsymbol{\xi }}_k} \end{array} \right\}$ (5)

 图 1 基于有色噪声函数模型拟合的Kalman滤波位置解算算法流程 Fig. 1 Process of Kalman filtering algorithm for position calculating based on the color noise function model fitting
2 实验结果与分析

 图 2 KIRU测站3个方向定位误差对比 Fig. 2 Comparison of positioning errors in three directions at KIRU station

 图 3 使用函数模型拟合滤波算法的MGEX测站单点定位精度改善程度 Fig. 3 Improvement of accuracy of single point positioning accuracy at MGEX station by using function model fitting filtering

 图 4 动态定位中2颗不同GPS、GLONASS和BDS卫星的观测残差序列对比 Fig. 4 Comparison of observation residual sequences for two different GPS, GLONASS and BDS satellites kinematic positioning

 图 5 动态定位状态预测残差序列对比

3 结语

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A Filtering Algorithm for Quad-Constellation GNSS Kinematic Navigation with Consideration of Colored Noise
SUN Qingfeng1     CAI Changsheng1     CUI Xianqiang1     YI Zhonghai1
1. School of Geosciences and Info-Physics, Central South University, 932 South-Lushan Road, Changsha 410083, China
Abstract: Classic Kalman filtering requires noise to be Gaussian white noise. However, the observation error and the state prediction error in GNSS kinematic positioning are colored noise. This paper establishes the colored noise model by using past observation residuals and state residuals in order to weaken the effects of colored noise on kinematic navigation solutions. Quad-constellations GNSS receiver measurements are used for a kinematic navigation experiment, and the results show that the algorithm can effectively improve positioning accuracy, as compared with the classic Kalman filtering algorithm with no consideration of the colored noise. The improvement rate of three-dimensional position accuracy is over 9%.
Key words: colored noise; kinematic navigation; filtering algorithm; GNSS