The Volterra series have been successfully and widely applied as a nonlinear system modeling technique. Considered as a prototype, the second order Volterra filter (FV2) has an increased complexity in comparison with a linear filter. The filter based on the multi memory decomposition (MMD) structure represents a good approximation of the FV2 and significantly reduces the number of the filter op...

The gyroscope calibration problem is addressed for the Inertial Pseudo Star Reference Unit. A nonlinear scale factor error is described by two gyro error states (an amplitude and a decay constant) which enter the dynamics in a nonlinear fashion. A comparison is made between the extended Kalman filter (EKF) and the maximum likelihood system identification (MLSI) method for solving the resulting ...

We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective ...

The Kalman filter is known to be the optimal linear filter for linear nonGaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. ...

The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined....

Sigma-Point Kalman Filters (SPKFs) are popular estimation techniques for high nonlinear system applications. The benefits of using SPKFs include (but not limited to) the following: the easiness of linearizing the nonlinear matrices statistically without the need to use the Jacobian matrices, the ability to handle more uncertainties than the Extended Kalman Filter (EKF), the ability to handle di...

Kalman filters provide an important technique for estimating the states of engineering systems. With several variations of nonlinear Kalman filters, there is a lack of guidelines for filter selection with respect to a specific research or engineering application. This creates a need for an in-depth discussion of the intricacies of different nonlinear Kalman filters. Particularly of interest for...

In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions ...