Total least square algorithm applied in multi-stationintersection of optical theodolite

Yu Guodong; Wu Kexin; Wang Chunyang

doi:10.5768/JAO201738.0602003

Journal of Applied Optics > 2017 > 38(6): 917-922. > DOI: 10.5768/JAO201738.0602003

Yu Guodong, Wu Kexin, Wang Chunyang. Total least square algorithm applied in multi-stationintersection of optical theodolite[J]. Journal of Applied Optics, 2017, 38(6): 917-922. DOI: 10.5768/JAO201738.0602003

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Total least square algorithm applied in multi-stationintersection of optical theodolite

Baicheng Ordnance Test Center of China, Baicheng 137001, China

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Received Date: September 17, 2016
Revised Date: March 26, 2017

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Abstract

Abstract

Horizontal projection method, which is applied in calculating coordinates of aerial bursting points, has major problem in exploiting redundancy observations and in filtrating optimal results from multi-group solutions. Intersection algorithm based on least square, although able to solve the above problems, is influenced by initial value of a larger, iterative slow or even divergent.An intersection algorithm based upon total least square is proposed. In the process of iterative computation, weight matrix is adjusted continuously until a certain precision requirement is satisfied. This algorithm is validated by combining simulation data. Results show that proposed algorithm can obtain better results when initial value is larger, and it is not easy to diverge. It can get better results by 10 iterations or less, and precision can reach 0.3 m when distance from station to target is 1 500 m. This algorithm takes into account both observation error and model linearization error, which greatly reduces influence of initial value and improves convergence speed, and can accurately calculate three-dimensional coordinates of aerial bursting points.
- multi-optical theodolite,
- points of aerial burst,
- total least square,
- intersection

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Total least square algorithm applied in multi-stationintersection of optical theodolite