Nonlinear Approximations
Mohinder S. Grewal, Angus P. Andrews · 2014
The introduction of nonlinearity in the dynamic or measurement model corrupts the standard (linear) propagation of the mean and covariance. This chapter proposes methods for coping with such nonlinearities. Beyond approaches to modifying the Kalman filter implementation to better cope with model nonlinearities, there has been a long history of nonlinear stochastic system modeling. Although it has perhaps not produced anything more “snappy” than the Kalman filter, it has had some notable successes in modeling the behavior of thermodynamic systems, economic systems, and market systems-among others. Nonlinear approximations to Kalman filtering generally depend on the initial uncertainties being sufficiently small that nonlinear approximation errors are not likely to be statistically significant. Any assessment of the relative efficacies of the various nonlinear approximations will be highly dependent on the particulars of the application(s) assumed. Such assessments are best used for picking which approximation to choose for our particular application.