In this paper we investigate the use of an alternative to the extended Kalman filter (EKF), the unscented Kalman filter (UKF). First we give a broad overview of different UKF algorithms, then present an extension to the ensemble of UKF algorithms, and finally address the issue of how to add constraints using the UKF approach. The performance of the constrained approach is compared with EKF and ...

This paper describes the passive emitter localization using Time Difference of Arrival (TDOA) measurements. It investigates various methods for estimating the solution of this nonlinear problem: the Maximum Likelihood Estimation (ML) as a batch algorithm, the Extended Kalman Filter (EKF) as an analytical approximation, the Unscented Kalman Filter (UKF) as a deterministic sampling approach and f...

Recurrent neural networks (RNNs) trained with gradient-based algorithms such as real-time recurrent learning or back-propagation through time have a drawback of slow convergence rate. These algorithms also need the derivative calculation through the error back-propagation process. In this paper, a derivative-free Kalman filter, so called the unscented Kalman filter (UKF), for training a fully c...

This paper is concerned with filtering nonlinear multivariate time series. A new approximate Bayesian algorithm is proposed which generates sample points and corresponding probability weights that match exactly the predicted values of average marginal skewness and average marginal kurtosis of the unobserved state variables, in addition to matching their mean and the covariance matrix. The perfo...

A nonlinear semi-analytic filtering method to sequentially estimate spacecraft states and their associated uncertainties is presented. We first discuss the state transition tensors that characterize the localized nonlinear behavior of the spacecraft trajectory and illustrate the importance of higher order effects on orbit uncertainty propagation. We then present the semi-analytic filtering meth...

In this paper, an unscented Kalman filter (UKF) for curvilinear motions in an interacting multiple model (IMM) algorithm to track a maneuvering vehicle on a road is investigated. Driving patterns of vehicles on a road are modeled as stochastic hybrid systems. In order to track the maneuvering vehicles, two kinematic models are derived: A constant velocity model for linear motions and a constant...

A new filter named the maximum likelihood-based iterated divided difference filter (MLIDDF) is developed to improve the low state estimation accuracy of nonlinear state estimation due to large initial estimation errors and nonlinearity of measurement equations. The MLIDDF algorithm is derivative-free and implemented only by calculating the functional evaluations. The MLIDDF algorithm involves t...

In this note, we illustrate the effect of nonlinear state propagation in the unscented Kalman filter (UKF). We consider a simple nonlinear system, consisting of a two-axis inertial measurement unit. Our intent is to show that the propagation of a set of sigma points through a nonlinear process model in the UKF can produce a counterintuitive (but correct) updated state estimate. We compare the r...

The paper deals with implicit and explicit approaches for fractional nonlinear model order estimation using a benchmark model relating applied angular rate and neuron’s firing intensity within the vestibular system. The implicit approach is based on an interacting multiple models scheme, where several extended Kalman filters with fixed fractional order nonlinear models are running in parallel. ...

It has been demonstrated recently than use of chaotic spreading codes can significantly increase transmission privacy for direct-sequence spread spectrum systems. In this note, we consider the problem of receiver synchronization as a dual estimation of the clean state and the underlying model parameters from the observed noisy chaotic signal. An efficient implementation of the demodulator is in...