Explicit expressions for debiased statistics of 3D converted measurements

The method for tracking based on Kalman filter with debiased consistent converted 2D measurements was given and discussed by D. Lerro et al. (1993) and Y. Bar-Shalom et al. (1993). In this work explicit expressions for debiasing compensation terms and debiased covariance statistics related to the 3D case are presented. The proposed procedure can be employed in active sonar systems or long range radar systems especially when the cross-range errors are significantly large relative to the range errors.