Measures of Nonlinearity for Single Target Tracking Problems

The tracking of objects and phenomena exhibiting nonlinear motion is a topic that has application in many areas ranging from military surveillance to weather forecasting. Observed nonlinearities can come not only from the nonlinear dynamic motion of the object, but also from nonlinearities in the measurement model. Many techniques have been developed that attempt to deal with this issue, including the development of various types of filters, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), variants of the Kalman Filter (KF), as well as other filters such as the Particle Filter (PF). Determining the effectiveness of any of these techniques in nonlinear scenarios is not straightforward. Testing needs to be accomplished against scenarios whose degree of nonlinearity is known. This is necessary if reliable assessments of the effectiveness of nonlinear mitigation techniques are to be accomplished. In this effort, three techniques were investigated regarding their ability to provide useful measures of nonlinearity for representative scenarios. These techniques were the Parameter Effects Curvature (PEC), the Normalized Estimation Error Squared (NEES), and the Normalized Innovation Squared (NIS). Results indicated that the NEES was the most effective, although it does require truth values in its formulation.