Scaling Parameter in Unscented Transform: Analysis and Specification

The paper deals with an analysis of the scaling factor of the unscented transform as a method to provide approximate means and covariance matrices of random variables in nonlinear systems. It is a basis of the unscented Kalman filter, which provides a state estimate of nonlinear stochastic dynamic systems. The scaling factor represents a design parameter significantly affecting quality of the approximation. The analysis provides an important insight into the parameter role and its impact on the quality. It also justifies recently published techniques for adaptive setting of the scaling parameter within the unscented Kalman filter. Usage of such an adaptive setting of the scaling parameter is illustrated in a bearings-only tracking example.