The Accuracy of Navigation Using Magnetic Dipole Beacons

The position of an automobile within the lanes of a highway can be estimated from on-board measurements of the fields from magnets placed in the pavement at known positions and orientations. The accuracy of this navigation method is limited by background and sensor noise, and the magnitudes, orientations, and positions of the magnets relative to the path of the vehicle. The mean-squared position estimation error of this navigation system is determined by formulating the estimation problem as an extended Kalman filtering problem, linearized about an estimated vehicle trajectory. The estimation uncertainties are then characterized by a 3 × 3 covariance matrix, which is the solution of a matrix Riccati differential equation. This equation is solved in closed form for the nominal vehicle trajectory. The solution specifies the mean-squared position estimation error as a rational function of the mean-squared sensor noise, and the relative positions, orientations, and magnitudes of the magnets.