An extension of sigma-point Kalman filtering using nonlinear estimator bases

This paper investigates the problem of state estimation for nonlinear discrete-time dynamic systems. The estimator is parameterized as a linear combination of chosen basis functions. We seek the parameter that minimizes the mean squared estimation error (MSE); however, computing this objective is intractable. Hence, the MSE is approximated using the scaled unscented transform (SUT), which yields a discrete least-squares optimization problem. Tikhonov regularization is used to avoid overfitting the data supplied by the SUT. A double pendulum example is used to compare this estimation strategy to the unscented Kalman filter.