Recursive nonlinear target state estimation: Error compensation and robustness to clutter

Many real-world estimation problems require the use of recursive methods which process measurements as they are obtained to provide a real-time solution. For most of these problems either the target dynamic model is nonlinear or the measurements are related nonlinearly to the target state. The most commonly used solution is the Extended Kalman filter (EKF), which relies on Taylor series expansion and the optimum linear minimum mean square error framework. The major issue with linearization methods is that errors induced by nonlinearities can introduce biases that are not reflected by the Kalman filter error covariance. The first major contribution is the development of a method called the debiased conversion where the mean and covariance of the errors due to a nonlinear conversion of measurements is derived and utilized explicitly in the covariance structure of the estimator. This approach is applied to an active sonar/radar target tracking problem where superior estimation accuracy is demonstrated when compared with existing estimators using the standard measurement conversion based upon linearization and the commonly used mixed coordinate Extended Kalman Filter.;Another major problem encountered in practical target tracking applications, that often leads to a nonlinear solution (even if the state plant and measurement equations are linear), is performing reliable state estimation in the presence of false alarms or clutter. When tracking a maneuvering target in the presence of clutter the occurrence of a maneuver is difficult to discern due to the conflict between data association and maneuver detection. The second major contribution provides a solution for tracking weak targets through maneuvers by combining the use of the target amplitude feature, which reflects the strength or intensity of a measurement, with the multiple model approach. This work provides an interesting connection between state estimation and multiple observation detection theory. The new estimator which depends on the amplitude feature for robust performance in clutter is shown to be the only reliable method for tracking weak targets that undergo maneuvers. Important applications to passive bearings-only tracking and active sonar or radar tracking are presented.