近年來，隨著室內導航自動化的領域的應用漸漸普及，各類演算法篷勃發展，其中室內定位(Indoor Positioning)及室內導航(Indoor Navigation)系統利用藍牙(Bluetooth)或無線網路(Wi-Fi)收集訊號，透過最小平方估計(Least Square Approximation)或三邊測量法(Trilateration)，計算出定位座標，最後透過演算法抑制雜訊與誤差的影響並算出定位目標之速度、加速度等物理量以達到導航之目的。
本研究旨在開發基於機率性(Probabilistic)的室內定位方法，考量現實中數據帶有隨機誤差，並在原本定位導航功能上，加入考量隨機誤差的失效率(failure probability)概念。並透過電腦模擬環境，利用最小平方估計(Least Square Approximation)計算三點或三點以上定位座標，再透過蒙地卡羅模擬(Monte Carlo Simulations)得出定位座標之平均值達到定位效果，核密度估計(Kernel Density Estimation)得出機率密度函數，最後透過高斯可靠度分析集合法(EoGRA)算法得出定位之失敗概率邊界，已修正導航的結果，達成在可靠性設計最佳化（Reliability-based Design Optimization，RBDO）的方法下，可計算失效率(failure probability)的避障定位與導航。

In recent years, with the increasing application of indoor navigation automation, various algorithms have been developed. Indoor positioning and indoor navigation systems utilize signals collected through Bluetooth or Wi-Fi to calculate the positioning coordinates using techniques such as least square approximation or trilateration. The algorithms are designed to suppress the effects of noise and errors and determine physical quantities such as velocity and acceleration to achieve navigation objectives.
The aim of this study is to develop a probabilistic-based indoor positioning method that considers the presence of random errors in real-world data. In addition to the basic positioning and navigation functionality, this method incorporates the concept of failure probability, taking into account the random errors. Computer simulations are used to calculate the positioning coordinates based on three or more points using the least square approximation. Monte Carlo simulations are then employed to obtain the average values of the positioning coordinates, achieving the desired positioning effect. Kernel density estimation is used to derive the probability density function. Finally, the Gaussian reliability analysis ensemble (EoGRA) algorithm is utilized to determine the failure probability bounds of the positioning. This approach improves the navigation results by accounting for the failure probability, allowing for obstacle avoidance and navigation in the context of reliability-based design optimization.

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