Closed-form expression of DOP based on effective computation

Jianfeng Cui; Hong Liang

doi:10.1117/12.3026403

9 February 2024 Closed-form expression of DOP based on effective computation

Jianfeng Cui, Hong Liang

Proceedings Volume 13073, Third International Conference on High Performance Computing and Communication Engineering (HPCCE 2023); 130731B (2024) https://doi.org/10.1117/12.3026403
Event: Third International Conference on High Performance Computing and Communication Engineering (HPCCE 2023), 2023, Changsha, China

Abstract

We mainly studied the effective computation method of dilution of precision (DOP). We extended the differential superposition principle and proposed the generalized differential superposition principle (GDSP) method and algebraic cofactor (AC) method for DOP calculation. The methods we proposed are fast algorithms based on effective computation, which avoids matrix inversion. The comparison of the calculation speed and algorithm structure of the definition-expression method, GDSP method, and AC method were conducted: when n=4, the GDSP method has the simplest algorithm structure; when n ≥ 4, the AC method always outperforms the definition expression method, when the complicated computations of the definition method and AC method were decomposed into simple calculations, the difference of the multiplication calculation amount stays at a fixed value. The results validate that the algorithm structure and computing speed of the proposed methods outperform the definition-expression method; the DOP based on our method are fast, general, and accurate analytical solution. The GDSP also applies to positioning performance analysis with complex input error.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Jianfeng Cui and Hong Liang "Closed-form expression of DOP based on effective computation", Proc. SPIE 13073, Third International Conference on High Performance Computing and Communication Engineering (HPCCE 2023), 130731B (9 February 2024); https://doi.org/10.1117/12.3026403

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KEYWORDS

Matrices

Satellites

Error analysis

Mathematical optimization

Satellite navigation systems

Superposition

Chemical elements

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