Canonical transform for tracking with kinematic models

This paper presents a canonical transform that converts kinematic model for target tracking into a decoupled dimensionless canonical form. The coupling is due to the nonzero off-diagonal terms in the covariance matrices of the process noise and/or the measurement noise, which can be used to model the coupling of motion and/or measurement between coordinates. An effective and efficient technique is presented to decouple the kinematic model by simultaneously diagonalizing the noise covariance matrices, followed by a space-time normalization procedure, so that the system is transformed into a decoupled dimensionless canonical form. This canonical form is independent of the physical specifications of an actual system. Each subsystem corresponding to a canonical coordinate is characterized by a parameter called the canonical kinematic index, which is a generalization of the tracking index. A number of applications of this canonical form are discussed. The usefulness of the canonical transform is illustrated via an example of the performance analysis of maneuvering target tracking in an air traffic control system.