Better terrain aided navigation method based on sigma-point Kalman filters

At present the relatively widely used terrain aided navigation (TAN) method is based on extended Kalman filter (EKF). We now present a new and better TAN method based on Sigma-point Kalman filters (SPKFs). In the full paper, we explain our TAN method in some detail; in this abstract, we just add some pertinent remarks to listing the three topics of explanation. The first topic is: the principles of the TAN. In this topic, we derive the input of the TAN measurement equation as shown in eq. (4) in the full paper. The second topic is: EKF. In this topic, we point out that EKF cannot guarantee the optimal estimation because terrain height measurement is nonlinear. The third topic is: SPKFs. In this topic, we calculate the Sigma points and use the points to calculate the mean and covariance of a state vector of the TAN system, as summarized in eqs. (32) and (33). Thus, SPKFs solve the nonlinearity and their solution is furnished to the TAN system. Finally we simulate our TAN method using real digital elevation map. The simulation results, given in Figs.4 and 5, show preliminarily that our TAN method reduces average circular error probability (CEP) to 22.10 m while the EKF method has the average CEP of 24.39 m, thus providing better accuracy for the TAN system, especially when the terrain is flat.