因子图(Factor Graph，FG)理论的产生与发展，为位置服务开辟了新的研究方向。与传统的定位技术相比，FG方法充分考虑了信号参数测量误差的随机性，更能反映出定位场景的真实情况，提高定位精度。采用局部线性化技术，对信号测量参数与位置坐标之间的非线性关系进行线性近似化处理，以满足因子图中软信息的传递机制，有效地处理了因子图模型各节点之间交换的软信息，降低计算复杂度。 对于重大会议场所、考场、非法基站检测及办公室复杂环境，存在的未知频率、未知功率复杂情况的非法信号源定位，一直是备受关注的问题，改进的FG理论与定位方法提供了有效的手段。 已有的研究大多针对信号接收器(Access Point，AP)的定位，而对于发射频率和功率未知的信号源定位研究相对较少。本课题围绕FG方法的基本理论，采用适用于信号源定位的信号接收强度差(Received Signal Strength Difference，RSSD)和到达角(Angle of Arrival，AOA)测量参数，完善了因子图定位理论与模型，并深入研究了在室内二维(Two-dimensional，2-D)和三维(Three-dimensional，3-D)复杂环境中对单个静态信号源的定位问题，为信号源在室内复杂环境的定位提供了新的方法，拓宽了FG方法在信号源室内定位检测的应用领域。 首先，针对基于RSS的FG定位技术不能实现信号源的定位，以及指纹数据库中具有较大信号参数测量方差的参考点影响FG模型精度的问题，引入RSSD参数并结合加权最小二乘法(Weighted Least Square，WLS)，建立了RSSD-WLSFG数学模型。采用所选参考点测量值与估计值之间的随机RSSD误差权重矩阵，提高了FG模型准确度。应用和积法则，推导了RSSD-WLSFG算法的定位过程。研究了在室内2-D环境中，不同AP数量和栅格距离对算法定位精度的影响。实验结果表明，与传统的定位算法相比，本文所提出算法在室内2-D环境中具有更好的定位性能。 其次，针对采用基于单一RSSD或AOA信号参数的FG定位技术定位精度不够高的问题，提出了基于RSSD与AOA联合参数的FG定位算法。将RSSD与AOA相融合，建立了基于联合参数的RSSD-AOAFG模型。应用泰勒级数展开法和独立随机变量乘积法则，对模型中有关AOA与位置坐标之间的非线性关系进行线性近似处理，更好地保证了模型中软信息的高斯分布特性与传递机制。此外，研究了在室内2-D环境中，不同AP数量和样本数量对定位精度的影响。结果表明，与采用单一参数的RSSD-FG和AOA-FG技术相比，所提出的RSSD-AOA FG算法能够获得更好的定位性能。 最后，针对3-D空间信号源定位存在信号参数多且复杂、信号与位置坐标耦合性高的问题，并考虑不同定位场合的适用性因素，分别提出了适用于室内3-D环境的基于RSSD参数的3-D FG定位算法和基于AOA参数的3-D FG定位算法。第一，通过分析空间中AOA的方位角和仰角分别与目标和AP位置坐标之间的几何关系，建立了基于AOA的3-D FG模型。利用泰勒级数展开法和独立随机变量乘积法则线性近似了AOA与位置坐标的非线性函数关系。此外，在室内3-D复杂环境中讨论了不同AP数量和目标测试样本数量对定位精度的影响。结果表明，与传统AOA-LS定位算法相比，所提出的定位算法具有更好的定位性能。第二，利用线性化技术并结合最小二乘法(Least Square，LS)建立了RSSD与位置坐标之间的3-D FG模型。采用和积法则将测量参数以高斯分布形式在FG模型中进行迭代传递，最终获取精确的目标空间估计位置。此外，在室内3-D环境中研究了不同栅格距离和AP数量对算法定位精度的影响。实验结果表明，所提出的3-D RSSD-FG算法在不同栅格距离和AP数量的情况下，比K近邻算法(K-Nearest Neighbor，KNN)和LS算法具有更好的定位性能。所提出的两种方法为室内3-D复杂环境信号源的位置检测提供了较好的解决方案，具有很好的应用前景。 关键词：因子图；室内定位；信号源；和积法则；泰勒级数展开；加权最小二乘法

 The generation and development of Factor Graph (FG) theory have opened up a new research direction for location service. Compared with the conventional positioning technique based on the deterministic model, the FG method fully considers the randomness of signal parameter measurement error, which can reflect the real positioning scenario and improve the positioning accuracy. In addition, the local linearization technique is used to approximate the nonlinear relationship between the signal measurement parameters and the location coordinates, so as to coincide with the transfer mechanism of the soft-information in FG model, effectively deal with the soft-information exchanged between the nodes of the FG model and reduce the computational complexity. For major meeting occasion, examination rooms, illegal base station detection and office complicated environment, the localization of the illegal radio transmitter with unknown frequency and power in the complicated scenario has been received more and more attention, so the improved FG theory and positioning method provides an effective approach. Most of the existing researches focus on the localization of signal receiver (AP),while there are few relative researches related to the localization of radio transmitter with unknown transmitting frequency and power. On the basis of FG theory, this dissertation used the measurement parameters of received signal strength difference (RSSD) and angle of arrival (AOA) suitable for radio transmitter positioning to consummate the positioning FG theory and model. Moreover, the localization of a single static radio transmitter in the indoor complicated environment of two-dimensional (2-D) and three-dimensional (3-D) is deeply studied. Our work not only develops new methods for the indoor localization of radio transmitter but also exploits the application field of FG method for the detection of the unknown radio transmitter. First, since the FG-based positioning technique using the received signal strength (RSS) information cannot realize the localization of the unknown radio transmitter and the reference points with larger measurement variance in the fingerprint database affects the precision of the FG model, this dissertation combines the RSSD parameter and the weighted least square (WLS) method to establish an RSSD-WLSFG mathematical model. By using the error weighted matrix of the selected reference point between measured value and the estimated value, the accuracy of FG model is improved. The positioning process of the proposed RSSD-WLSFG algorithm is deduced by using the sum-product rule. The effects of different AP numbers and grid distances on the positioning accuracy of the algorithm are explored in indoor 2-D environment. Experimental results show that the proposed algorithm has better positioning performance in indoor 2-D environments than the conventional algorithm. Second, to solve the problem that FG positioning technique based on single RSSD or AOA signal parameter is not accurate enough, an FG positioning algorithm combining RSSD and AOA parameters is proposed. A new RSSD-AOA FG model based on joint parameters is established. The Taylor series expansion method and the product rule of independent random variables are used to approximate the nonlinear relation between AOA and position coordinates in the proposed FG model, which ensures the Gaussian distribution characteristic and the transmitting mechanism of the soft-information. Besides, the effects of different AP numbers and sample numbers on positioning accuracy are studied in indoor 2-D environment. The results show that the proposed RSSD-AOA FG algorithm can achieve better positioning performance compared with RSSD-FG and AOA-FG techniques using a single parameter. Finally,considering the problems of multiple and complex signal parameters, high coupling between the signal and the location coordinates in the 3-D scenario, and the applicability of various positioning occasions, this dissertation also develops two kinds of 3-D FG positioning algorithms using the RSSD or AOA parameter. Firstly, the 3-D FG model using AOA parameter is constructed by analyzing the geometric relationship between the azimuth angle and elevation angle of spatial AOA parameter with the location coordinates, as well as the distance between the target and the AP. The nonlinear function relationship between AOA and location coordinates is approximated linearly by Taylor series expansion approach and the product rule of independent random variables. Moreover, the effects of different numbers of AP and target test samples on positioning accuracy are discussed. The results demonstrated that compared with the conventional AOA-LS positioning algorithm, the proposed algorithm has better positioning performance. Secondly, the 3-D FG model between RSSD and location coordinates is established by utilizing linearization manner and least square (LS) approach. By using the sum-product rule, the measured parameters are iteratively transported in the form of Gaussian distribution in the FG model, and the accurate estimated location of the target space is finally obtained. In addition, the effects of different grid distances and the AP numbers on the positioning accuracy are studied. The experimental results show that the proposed 3-D RSSD-FG algorithm has better positioning performance than K-Nearest Neighbor (KNN) and LS algorithm in the case of different grid distances and AP numbers. Our proposed two algorithms provide a good solution for detection of the unknown radio emitter in indoor 3-D space and has a good application prospect. Key words: factor graph; indoor positioning; radio transmitter; sum-product rule; Taylor series expansion; weighted least square method