An adaptive level of detail approach to nonlinear estimation

In this work, we present a general method for approximating non-linear transformations of Gaussian mixture random variables. It is based on transforming the individual Gaussians with the unscented transform. The level of detail is adapted by iteratively splitting those components of the initial mixture that exhibited a high degree of nonlinearity during transformation. After each splitting operation, the affected components are re-transformed. This procedure gives more accurate results in cases where a Gaussian fit does not well represent the true distribution. Hence, it is of interest in a number of signal processing fields, ranging from nonlinear adaptive filtering to speech feature enhancement. In simulations, the proposed approach achieved a 48-fold reduction of the approximation error, compared to a single unscented transform.