三分量磁传感器定位模型建立及可观测性分析

Three-component Magnetic Sensor Positioning Model Establishment and System Observability Analysis

摘要:

针对单个三分量磁传感器的定位理论问题进行了研究，建立了单个三分量磁传感器的定位理论模型，并对系统可观测性进行了详细的理论分析。基于磁性目标的点源磁偶极子等效性，将定位过程中的目标视为匀速运动，推导得到了单个三分量磁传感器的定位理论模型。基于该定位模型，利用批量的观测数据对目标运动状态参数进行估计。对于系统可观测性问题，通过考察 Fisher 信息矩阵的奇异性，严格证明了单矢量磁传感器的定位系统的不可观测性。根据现实应用情景，推导了在部分先验条件已知下的可观测性，得到以下结论：1)单个三分量传感器定位模型是不可观测的；2)在部分先验已知的条件下，系统是可观测的。 最后，通过仿真试验验证了本文结论的正确性，为接下来采用单个三分量传感器对汽车、水面舰艇等一些低动态运动目标的跟踪提供了重要的理论依据。

Abstract:

In this paper，the positioning theory of single three-component magnetic sensor is studied. The positioning theory model of single three-component magnetic sensor is established，and the theoretical observability of the system is analyzed in detail. Based on the equivalence of the point source magnetic dipole of the magnetic target，the target in the positioning process is regarded as a uniform motion，and the positioning theory model of the single three-component magnetic sensor is derived. Based on the model，the target motion state parameters can be estimated using batch observation data. For the system observability problem，by examining the singularity of the Fisher information matrix，the un-observability of the positioning system of the single vector magnetic sensor is strictly proved. According to the actual application scenario，the observability under partial prior known conditions is derived. The following conclusions are drawn：(1)the single three-component sensor positioning model is unobservable；(2)under partial prior known conditions，the system is observable. Finally，the correctness of the conclusion is verified by simulation experiments，which can provide an important theoretical basis for the tracking of some low dynamic moving targets such as cars and surface ships by single three-component sensors.