Positional Error Model of Line Segments with Modeling and Measuring Errors Using Brownian Bridge

doi:10.11947/j.JGGS.2023.0201

Abstract

Abstract:

Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science. There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features. This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors. First, the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment. Second, an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed. Third, a comprehensive error band of the line segment is constructed, wherein both the modeling and measuring errors are contained. The proposed error model can be used to evaluate line segments’ overall accuracy and trustability influenced by modeling and measuring errors, and provides a comprehensive quality indicator for the geospatial data.

Key words: spatial data; line segment; modeling error; measuring error; Brownian bridge

Xiaohua TONG, Lejingyi ZHOU, Yanmin JIN. Positional Error Model of Line Segments with Modeling and Measuring Errors Using Brownian Bridge[J]. Journal of Geodesy and Geoinformation Science, 2023, 6(2): 1-10.

Figures/Tables 4

Fig.1

Tab.1

Original data of line segments and derived error parameters in Case 1"

Line No.	x₁ /m	δ /m²	d /m	a /m	Tr $d 2$ /m²	g $d 2$ /m	p
1	25	1	25	5.000	7.000	5.613	0.871
2	30	1	30	5.477	7.477	5.801	0.934
3	35	1	35	5.916	7.916	5.986	0.990
4	40	1	40	6.325	8.325	6.121	1.040
5	45	1	45	6.708	8.708	6.260	1.087
6	50	1	50	7.071	9.071	6.389	1.828

Tab.1

Tab.2

Original data of line segments and derived error parameters in Case 2"

Line No.	x₁ /m	δ /m²	d /m	a /m	Tr $d 2$ /m²	g $d 2$ /m	p
1	40	0.5	40	6.325	4.162	4.328	1.040
2	40	1	40	6.325	8.325	6.121	1.040
3	40	1.5	40	6.325	12.487	7.496	1.040
4	40	2	40	6.325	16.649	8.656	1.040
5	40	2.5	40	6.325	20.811	9.677	1.040
6	40	3	40	6.325	24.974	10.601	1.040

Tab.2

Fig.2

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