使用載波相位方法之室內物體位置姿態判定統

Abstract

本篇論文主要目的為發展一套利用Cricket硬體套件來建構室內物體定位與三軸姿態判定的系統。Cricket是一套超音波接收/發射系統，主要用於室內物體定位。本研究希望藉由不同接收端接收訊號相位的量測與處理，將其功能擴大至三軸姿態測量。類似的作法可見於室外GPS系統，其作法假設發射端與不同接收端之路徑近似平行，藉由不同接收端所接收訊號之相位差與上述路徑所構成的三角函數關係式來得到物體旋轉角度。此假設並不適用於室內定位系統，因為發射端與接收端距離太近，故無法符合平行訊號的假設，因此本篇論文將會修改上述之基本概念。 本篇論文重新推導發射端與接收端的向量方程式，使其適用於室內環境下的物體定位與三軸姿態判定。首先利用數個發射端的訊號與牛頓法來分別計算不同接收端的三維位置，接著利用發射端與接收端之座標位置計算基線向量(不同接收端所構成之向量)與視線向量(發射端與接收端所構成之向量)，再採用相關分析法來計算不同接收端接收同一發射端的訊號相位差，最後將上述之基線向量、視線向量與相位差組成最佳化問題，並利用Wahba所提出之最佳化方法來計算三軸物體旋轉角度。 本篇論文利用Matlab來模擬整個物體定位與姿態判定，由模擬結果得知最少需利用四個接收端與三個發射端，方可利用訊號相位差的方式來計算獲得物體三軸姿態。由初步的實驗結果得知：若利用本實驗器材(Cricket)與載波相位方法來獲得距離資訊，其距離量測精度（標準差）為0.3294mm（Cricket系統的距離量測精度原本為1cm）。若由此精度推算三軸姿態判定，其精度（標準差）為1.2031度。

This paper proposed an indoors location and attitude determination system using a commercial production system (Cricket). The Cricket system was originally designed for the 3D positioning for indoors applications. This research intends to enhance its functionality for the 3-axis attitude determination by using the carrier phase techniques. A similar approach can be found in the multi-antenna GPS system. In the GPS system, the signals from one satellite to different antennas are assumed to be parallel. This assumption is acceptable because the distance between antenna and satellite is quite long. However, this assumption cannot be applied to the indoor positioning system since the distance between transmitter and receivers is relatively short. Therefore, we derived new equations for the indoors positioning system so that it can do the attitude determination without the parallel-signal assumption. In this approach, we used the “baseline vectors,” “line of sight vectors,” and phase differences between received signal of different receivers to determine the attitude of the object. The baseline vector is the relative position vector between different receiver, which is obtained by design. The line-of-sight vector is the relative position vector between transmitter and receiver, This can be obtained by the original Cricket function. And, the phase difference between received signals can be obtained by the “correlation analysis” method. With these three information, the attitude determination was formulated into an optimization problem and solved by the “Wahba method.” The proposed method is verified using Matlab simulations and some preliminary experimental results. According to the simulations, the system needs, at least, three transmitters and four receivers to achieve 3D positioning and 3D attitude determination. When using the Cricket system combined with the carrier phase measurements, the distance measurement accuracy is 0.3294mm, which was 1 cm from the original Cricket system output. Using this distance accuracy to estimate the accuracy for the attitude determination, the accuracy of the rotation angle is 1.2031 degree.