An optimization algorithm for RTK integrity monitoring based on solution separation for vehicle applications

doi:10.11947/j.AGCS.2026.20250158

Abstract

Abstract:

Real-time kinematic (RTK) has become a common positioning technique for urban vehicle terminal integrity monitoring algorithms due to its high accuracy and fast convergence. However, due to the differences in application scenarios, terminal equipment, and positioning techniques, the integrity monitoring algorithms in the aviation domain cannot be directly applied to urban vehicle-mounted GNSS terminals. Therefore, this paper optimizes the RTK integrity monitoring algorithm based on the solution separation method, focusing on fault detection and protection level calculation, and verifies its application effectiveness. First, the similarity of the corresponding detection statistics across directions is used to construct a new fault detection statistic, enhancing the algorithm's ability to detect abnormal observations. Then, the nominal bias is extracted from the observation residuals using a two-step Gaussian overbounding method, and the impact of the bias term on the protection level is analyzed to enhance the overbounding effect on positioning errors. Finally, the effectiveness and applicability of the optimized algorithm are validated using urban vehicle datasets. For fault detection, the solution separation method with a two-direction combination is better than that of the single direction, with an average improvement of 21.7%. Compared to the residual detection method, the solution separation method improves the positioning accuracy in the east, north and up directions by 8.3%, 11.5% and 34.2%, respectively, and the correct fix rate of ambiguity is improved by 18.9%. In the protection level calculation, the protection levels of the floating and the fixed solution after considering the nominal bias are 7.273 m and 0.218 m, respectively. The float solution is more significantly affected by the nominal bias, and its missed rate is reduced from 8.8% to 0.3%, reflecting the need to consider the nominal bias term.

Key words: real-time kinematic, integrity monitoring, solution separation, two-direction combination, nominal bias

CLC Number:

P228

Yi LI, Li WANG, Bao SHU, Youjian XU, Mengran LI, Xiaojun LIU, Xin PENG. An optimization algorithm for RTK integrity monitoring based on solution separation for vehicle applications[J]. Acta Geodaetica et Cartographica Sinica, 2026, 55(2): 301-314.

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类型	内容
卫星系统	GPS/BDS
观测频点	L1/B1
截止高度角/（°）	10
定位解模式	动态解+前向滤波
模糊度固定模式	部分模糊度固定+单历元解算
模糊度固定阈值	固定成功率>0.999
先验故障概率^[33]	10^－5
完好性风险^[33]/h	10^－7
连续性风险/h	10^－3

PRN	残差检验法	解分离（单分量）	解分离（双分量）	PRN	残差检验法	解分离（单分量）	解分离（双分量）
G02	18.4（9.9）	10.5（5.3）	8.0（4.1）	C04	9.5（10.0）	5.4（5.8）	4.3（4.6）
G05	9.1（9.4）	4.8（5.0）	3.7（3.8）	C08	5.6（8.8）	3.0（4.8）	2.3（3.7）
G13	7.3（9.2）	4.0（4.9）	3.1（3.7）	C09	6.8（9.6）	3.9（5.5）	3.2（4.4）
G18	6.3（8.5）	3.3（4.4）	2.5（3.4）	C13	6.3（9.3）	3.6（5.3）	2.9（4.2）
G20	11.0（10.7）	6.4（6.2）	5.2（5.0）	C16	5.2（8.5）	2.6（4.5）	2.0（3.4）
G23	10.6（10.0）	5.9（5.6）	4.7（4.4）	C23	10.7（9.9）	6.0（5.7）	4.8（4.6）
G24	8.3（9.7）	4.4（5.3）	3.4（4.1）	C25	7.7（8.5）	3.6（4.0）	2.4（2.8）
G29	8.6（9.2）	4.4（4.7）	3.2（3.5）	C27	6.7（9.3）	3.8（5.3）	3.0（4.2）
C01	7.9（9.9）	4.7（5.8）	3.8（4.7）	C28	11.1（7.8）	5.2（3.3）	3.6（2.1）
C02	6.5（8.7）	3.3（4.6）	2.5（3.5）	C30	9.1（9.9）	4.7（5.2）	3.6（3.9）
C03	6.1（9.0）	3.4（5.0）	2.6（4.0）	均值	8.5（9.3）	4.6（5.0）	3.6（3.9）

方案	RMS/m			模糊度错误固定历元数
方案	东向	北向	高程	模糊度错误固定历元数
无质量控制	0.15	0.15	0.24	17
残差检验法	0.15	0.15	0.24	17
解分离方法	0.01	0.02	0.03	0

方案	RMS/m			模糊度错误固定历元数
方案	东向	北向	高程	模糊度错误固定历元数
无质量控制	2.46	3.98	6.75	1708
残差检验法	0.24	0.26	0.79	111
解分离方法	0.22	0.23	0.52	90

PRN	μ_ob	σ_ob	PRN	μ_ob	σ_ob
G02	0.882（0.014）	0.621（0.017）	C04	0.169（0.008）	0.793（0.023）
G05	0.514（0.013）	0.840（0.024）	C06	0.735（0.018）	0.451（0.018）
G13	0.190（0.006）	0.628（0.025）	C08	0.423（0.008）	0.594（0.017）
G15	0.472（0.004）	0.662（0.005）	C09	0.628（0.012）	0.591（0.021）
G18	0.155（0.009）	0.463（0.021）	C13	0.661（0.004）	0.698（0.008）
G20	1.019（0.013）	0.904（0.020）	C16	0.636（0.016）	0.526（0.018）
G23	0.598（0.009）	1.011（0.021）	C23	1.858（0.015）	1.021（0.025）
G24	0.573（0.011）	0.622（0.020）	C25	1.459（0.015）	1.012（0.022）
G29	0.807（0.006）	1.241（0.025）	C27	0.355（0.014）	0.772（0.025）
C01	0.163（0.008）	0.562（0.021）	C28	0.575（0.017）	0.443（0.027）
C02	1.255（0.009）	0.837（0.018）	C30	0.957（0.026）	1.033（0.022）
C03	0.832（0.013）	0.816（0.020）