Non-Euclidean Kalman Filters for Nonlinear Measurements

Abstract

Target tracking in the presence of nonlinear measurements has long been recognized as a challenge. When measurements are in polar coordinates this sometimes manifests itself as the ‘contact lens’ distribution, especially in radar applications. The authors propose a new filtering paradigm - the Non-Euclidean Kalman Filter (NEUKF) - to efficiently represent these nonlinear distributions using isomorphic coordinate transforms, which requires only modest computation beyond the popular Unscented Kalman Filter. They propose a family of parabolic isomorphisms well suited for representing the contact lens distribution. The NEUKF using one of the parabolic transforms is compared to a number of other prominent filters in both single and multiple sensor scenarios. The NEUKF demonstrates either the best-in-class or competitive precision and accuracy across all four scenarios, and is the only filter to maintain near perfect covariance consistency at all times.