PIR传感器网络中行为轨迹重构的几何代数方法

基于高密度、低成本的PIR（Passive Infrared Detector）被动式红外探测器传感器进行人群行为轨迹的定位与重建是人群行为分析的重要方向.PIR传感器通过0-1响应确定附近是否有行人通过，并通过不同传感器响应序列的时空序列关系实现对人群行为轨迹的识别与跟踪.已有PIR传感器网络分析方法多从群体行为视角揭示人群运动的统计特征，在行为估算精度、不确定性等方面仍存在诸多问题.本文针对PIR传感器网络中个人行为轨迹的重构问题，引入几何代数工具，实现PIR传感器网络拓扑、时空响应数据序列和行为轨迹的代数化统一表达，进而以传感器响应的时空关系为基础进行网络连通性的判定.基于几何代数算子构建轨迹路径的延拓与扩展规则，并集成传感器对轨迹的时空响应关系构建基于PIR传感器网络响应序列数据的行为轨迹重构算法.最后以MERL实验室连续观测数据为案例，论证了方法的合理性与有效性.

Geometric Algebraic Method for Behavior Trajectory Reconstruction in PIR Sensor Networks

Localization and reconstruction of the human motion trajectory based on high density and low cost PIR sensor is an important direction for the behavior analysis of people.The walking of persons can be detected through the 0-1 response of the PIR sensors.The identification and tracking of the behavior of the crowd can be achieved through the different sensor response sequence of spatio-temporal sequence relationship.Most of the existing analysis methods for PIR sensor network have revealed the statistical characteristics of crowd movement from the perspective of group behavior,but there still exists many problems in the estimation accuracy and uncertainty of behavior.Arming at the reconstruction of personal behavior trajectory in PIR sensor network,the geometric algebra is introduced to achieve the united expression of topological network of PIR sensor,spatial and temporal response of data sequence and the behavior of the person,thus judging the network connectivity according to the response of spatial and temporal relations of the sensors.Based on the geometric algebra operators,the extension and expansion rules of the trajectory are constructed,and behavioral trajectory reconstruction algorithm is constructed with the PIR sensor network response sequence data.Finally,the rationality and effectiveness of the method are demonstrated by using the continuous observation data of MERL laboratory.