考量Generalized Mixed Pixels Effect之雷射測距修正

Laser Ranging Modeling under Generalize Mixed Pixels Effect

張家綿(Chia-Mien Chang)

指導教授 ： 趙鍵哲

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202003773

摘要

具定心定平的脈衝式飛行時間雷射測距技術為廣泛使用之高精度目標距離測量工具，然而當目標點位於幾何邊緣處，測距儀獲致來自不同物距的光跡反射資訊，此變異量即會反映至測距品質，而該類具系統性的混合距離變異量即為所謂mixed pixels effect。在此效應下所對應的為單一光跡涵蓋多重物距資訊，儘管mixed pixels effect對幾何邊緣目標點具較顯著的影響，入射角因子於測距任務執行時也同樣涉及物距變異導致之光跡變形，故於本研究中將入射角效應以及mixed pixels effect延伸定義為「廣義mixed pixels effect」。不同的雷射測距儀具備不同的觀測量參數及回波處理方式，故對應於此類系統誤差模式亦不盡相同且難以估計。基於物理推導並搭配函數模式及隨機模式，本研究提出一套涵蓋五個步驟的雷射測距修正策略，建構有效的廣義mixed pixels effect修正函式。首先，mixed pixels effect可藉本文所提出之發散角估算實驗，並搭配偏心觀測進行消除，然而偏心觀測會附帶生成相應系統誤差，包含入射角效應、偏心誤差及中心軸線偏移誤差。入射角效應可模式化並透過觀測量收集與最小二乘平差求解模式化參數；同時，考量上述修正函式中入射角參數於實務上常屬未知，本研究設計一組迭代精化流程以估算入射角最佳解。最後，偏心誤差與中心軸線偏移誤差的修正函式則可透過角邊關係三角幾何推導獲致。本研究共試驗兩台具脈衝式飛行時間雷射測距技術之全測站，分別為Trimble M3 DR2”以及Topcon GPT-3002LN，實驗成果顯示依據所提出之雷射測距修正策略，兩台測距儀可分別消除99%及97%的測距誤差，有效地保障幾何邊緣目標點之測距品質。

關鍵字

精度分析 ； 發散角 ； 光跡 ； 廣義mixed pixels effect ； 入射角 ； 幾何邊緣目標點

並列摘要

The pulsed time-of-flight laser ranging technique with centering and horizontalization has been widely applied to acquire high quality ranges of interest. However, when a target lies on discontinuous surfaces, the footprint of a laser rangefinder covers multiple ranges, which is called mixed pixels effect and will systematically distort the ranging quality. Meanwhile, the ranging error of incidence angle effect is triggered by a deformed footprint containing various ranges as well. Although the mixed pixels effect has a greater effect on targets at discontinuous surfaces than incidence angle effect, based on the commonality of causing ranging errors within one footprint, this study proposed a “generalized mixed pixels effect” to embrace the ranging errors involving in deformed footprint cases. Errors caused by generalized mixed pixels effect vary in rangefinders and are difficult to be uniformly treated. A correction model was formulated through integrating individual effects by considering the physical and geometrical aspects of laser ranging. An adjustment procedure was followed to estimate the parameters of the correction equation by taking all observation uncertainties into account. To analyze the individual effects and eventually combine them into a complete model, a five-step workflow has been developed. Firstly, a divergence angle estimation method was presented to avoid the mixed pixels effect by a decentering approach. Yet, while eliminating the mixed pixels effect, the incidence angle effect, an offset error, and an axis offset error are accompanied by such an operation. Incidence angle effect was modeled and the parameter was estimated by adjustment techniques. Particularly, since incidence angles are usually unknown in field surveys but needed in the proposed correction strategy, an iterative estimation procedure was designed to obtain the optimal incidence angle of the target point. Finally, by the derivation of basic trigonometric functions, a correction for compensating the offset error and the axis offset error was formulated. Through the experimental tests on Trimble M3 DR 2” and Topcon GPT-3002LN, it is confirmed that the proposed method effectively resolves 99 percent and 97 percent, respectively, of the ranging errors for the two instruments, and preserves the ranging quality under the generalized mixed pixels effect.

並列關鍵字

Accuracy analysis ； Divergence angle ； Footprint ； Generalized mixed pixels effect ； Incidence angle ； Target at discontinuous surfaces

參考文獻

Abshire, J. M., J. F. McGarray, L. K. Pacini, J. B. Blair, and C. G. Elman, 1994. Laser Altimetry Simulator version 3.0, User’s Guide, NASA Technical Memorandum 104588, 66 p.

Adams, M. D., 1993. Amplitude modulated optical range data analysis in mobile robotics, IEEE International Conference on Robotics and Automation, pp. 8-13.

Adams, M. D., P. J. Probert, 1996. The interpretation of phase and intensity data from AMCW light detection sensors for reliable ranging, The International Journal of Robotics Research, 15(5): 441-458.

Baltsavias, E. P., 1999. Airborne laser scanning: basic relations and formulas, ISPRS Journal of Photogrammetry and Remote Sensing, 54(2-3): 199-214.

Grzegorzek, M., C. Theobalt, R. Koch, and A. Kolb, 2013. Time-of-Flight and Depth Imaging, Sensors, Algorithms and Applications: Dagstuhl Seminar 2012 and GCPR Workshop on Imaging New Modalities, 319 p.