Stochastic magnetic measurement model for relative position and orientation estimation

This study presents a stochastic magnetic measurement model that can be used to estimate relative position and orientation. The model predicts the magnetic field generated by a single source coil at the location of the sensor. The model was used in a fusion filter that predicts the change of position and orientation by integration of acceleration and angular velocity measured by inertial sensors. If the uncertainty associated with the position and orientation exceeds a predefined threshold, the filter decides to perform a magnetic update by actuating only that coil which results in the largest reduction of the uncertainty. The difference between the actual magnetic measurement and the prediction of the measurement was used to reduce the drift caused by integration of acceleration and angular velocity. The model is accurate as confirmed by the small rms differences between validation measurements and predictions of the magnetic field using the model. The use of a linearized version of the measurement model for the fusion filter and the appearance of a ferromagnetic object in the vicinity of the source or sensor were defined as two sources of error that may lead to divergence of the fusion filter. Both sources of error were analyzed and it appeared that the linearized model introduces errors which generally increase for sensor locations near the source. Moreover, it appeared that a ferromagnetic object influences the measurements only if it is located near or between the source and the sensor.