An Orthogonal Local Coordinate System on the Earth's Ellipsoid

We propose a locally defined orthogonal curvilinear coordinate system based on arc-length parameterization of meridians and parallels on the Earth’s ellipsoid. The coordinate lines correspond to meridians and parallels, which are orthogonal on a rotational ellipsoid. Measurements from multiple sources are first transformed into geodetic coordinates on the ellipsoid and subsequently mapped to a local two-dimensional Cartesian frame. The proposed coordinate system based on Ellipsoidal Equirectangular Projection (EEP), preserves orthogonality of coordinate directions and provides locally consistent distance scaling, thereby reducing geometric nonlinearity and mitigating distortions inherent in standard latitude–longitude–based representations. Unlike commonly used local Cartesian coordinate systems such as ENU, whose accuracy degrades as the spatial extent increases, the proposed coordinate system remains well conditioned over large geographic areas by construction on the Earth’s ellipsoid. This leads to improved numerical behavior in Kalman filter implementations. We further derive the corresponding transformations of measurement covariances required for Kalman filter updates. The approach is applicable to a wide range of tracking problems, including air traffic control, satellite tracking, maritime surveillance, and ground vehicle monitoring.