Over the last 20-30 years, the extended Kalman filter (EKF) has become the algorithm of choice in numerous nonlinear estimation and machine learning applications. These include estimating the state of a nonlinear dynamic system as well estimating parameters for nonlinear system identification (e.g., learning the weights of a neural network). The EKF applies the standard linear Kalman filter met...

-Target tracking is one of the major aspects often used in sonar applications, surveillance systems, communication systems, embedded applications etc. To obtain kinematic components of a moving target such as position, velocity, and acceleration, one of the most used approaches in target tracking is stochastic estimation approach. Movement of the target is described by state space dynamic syste...

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...

The unscented Kalman filter (UKF) is adopted in the interacting multiple model (IMM) framework to deal with the system nonlinearity in navigation applications. The adaptive tuning system (ATS) is employed for assisting the unscented Kalman filter in the IMM framework, resulting in an interacting multiple model adaptive unscented Kalman filter (IMM-AUKF). Two models, a standard UKF and an adapti...

Report [1] compares the Extended Kalman Filter [2, 3, 4], the Iterated Extended Kalman Filter, IEKF, [2, 3, 4] and the Linear Regression Kalman Filter [5] (e.g. the Unscented Kalman Filter, UKF, [6, 7, 8]) on (i) consistency and (ii) information content of their results (estimates and covariance matrices). The nonlinear filter proposed by Bellaire et al. in [9] is not discussed in report [1]. T...

In a series of recent studies a new approach for applying the Kalman filter to nonlinear system, referred to as Unscented Kalman filter (UKF), was proposed. In this contribution we apply the UKF to several speech processing problems, in which a model with unknown parameters is given to the measured signals. We show that the nonlinearity arises naturally in these problems. Preliminary simulation...

This article presents a new nonlinear joint (state and parameter) estimation algorithm based on fusion of Kalman filter and randomized unscented Kalman filter (UKF), called Kalman randomized joint UKF (KR-JUKF). It is assumed that the measurement equation is linear. The KRJUKF is suitable for time varying and severe nonlinear dynamics and does not have any systematic error. Finally, joint-EKF, ...

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...

Different approaches for the estimation of the states of linear dynamic systems are commonly used, the most common being the Kalman filter. For nonlinear systems, variants of the Kalman filter are used. Some of these variants include the LKF (linearized Kalman filter), the EKF (extended Kalman filter), and the UKF (unscented Kalman filter). With the LKF and EKF, performance varies depending on ...

This paper addresses the state-estimation problem for nonlinear systems in a context where prior knowledge, in addition to the model and the measurement data, is available in the form of a nonlinear equality constraint. Then three suboptimal algorithms based on the unscented Kalman filter (UKF) are developed, namely, the equality-constrained unscented Kalman filter (ECUKF), the projected unscen...