Nonlinear filtering using the double exponential transformation

Abstract

Nonlinear Gaussian filters have traditionally used cubature rules and/or Gaussian quadrature to compute multidimensional expectation integrals recursively, which provide mean and covariance estimates of the state and state error, respectively. Minimal and near minimal-point filters attain moderate accuracy while avoiding the so-called "curse of dimensionality", but their accuracy can diverge over time. Recent trends in cubature-based filtering have opted for more evaluation points to increase accuracy at the cost of higher computational overhead, while still avoiding the dreaded curse. These methods use more complex and higher-degree cubature rules. The present work, contrary to recent trends, uses a quadrature method other than that of the Gaussian variety. Double exponential quadrature is used to achieve high levels of relative accuracy with a moderate number of evaluation points, rivalling that of current state-of-the-art Gaussian filters and the best-in-class Gauss-Hermite filter.