Recursive Update Filtering for Nonlinear Estimation

Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. This work proposes a novel nonlinear estimator whose additional computational cost is comparable to (
N
-1) EKF updates, where
N
is the number of recursions, a tuning parameter. The higher
N
the less the filter relies on the linearization assumption. A second algorithm is proposed with a differential update, which is equivalent to the recursive update as
N
tends to infinity.