The Analysis of the Ratio between VDOP and HDOP

Yi-Hsueh Tsai, Jie-Shan Lin, Fan-Ren Chang, and Li-Sheng Wang

Abstract:	The DOP (Dilution of Positioning) value is used to describe the multiply between positioning errors and pseudorange errors. It is well known that the V(Vertical)DOP value is always greater than H(Horizontal)DOP value under the same geometric distribution of navigation satellites. Although some intuitive explanations are discussed in many references, the systematic analysis of the ratio between VDOP and HDOP is still lacking. In the linearized measurement equations, the influences of the pseudorange errors will be on the accuracy of positioning and receiver’s clock bias. The covariance matrix associated to the positioning error can be obtained via the formula of the inverse of a block-partitioned matrix. From that, we see that a slightly modified “directional cosine matrix” is the key to investigate VDOP vs HDOP. Since the directional cosine matrix, which depends on the locations of those visible satellites, is changed from time to time, in order to obtain the expectation value of the ratio between VDOP and HDOP, we have assumed that the satellites in view are uniformly distributed in the upper sphere relative to the local tangent plane centered at the user. In the derivation, we find several factors affecting the ratio between VDOP and HDOP. The ratio will go up as the mask angle increases. The ratio will go down if one pseudolite is added. The values of VDOP/HDOP are reduced as one pseudolite is installed, especially when the number of visible satellites is small.
Published in:	Proceedings of the 2002 National Technical Meeting of The Institute of Navigation January 28 - 30, 2002 The Catamaran Resort Hotel San Diego, CA
Pages:	205 - 211
Cite this article:	Tsai, Yi-Hsueh, Lin, Jie-Shan, Chang, Fan-Ren, Wang, Li-Sheng, "The Analysis of the Ratio between VDOP and HDOP," Proceedings of the 2002 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2002, pp. 205-211.
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