In this paper the problem of the speed estimation of an Unmanned Aerial Vehicle is addressed, when only the standard outputs (acceleration, angles and angular speeds) are available for measurement. We focus our analysis on a prototype drone a 4 rotors helicopter robotwhich is not equipped with GPS related devices and relies on the Inertial Measurement Unit (IMU) only. Two different approaches h...

The Kalman filter is a technique for estimating a time-varying state given a dynamical model for, and indirect measurements of, the state. It is used, for example, on the control problems associated with a variety of navigation systems. Even in the case of nonlinear state and/or measurement models, standard implementations require only linear algebra. However, for sufficiently large-scale probl...

This paper considers a sensor network where single or multiple sensors amplify and forward their measurements of a common linear dynamical system (analog uncoded transmission) to a remote fusion center via noisy fading wireless channels. We show that the expected error covariance (with respect to the fading process) of the time-varying Kalman filter is bounded and converges to a steady state va...

A number of algorithms to solve large-scale Kalman filtering problems have been introduced recently. The ensemble Kalman filter represents the probability density of the state estimate by a finite number of randomly generated system states. Another algorithm uses a singular value decomposition to select the leading eigenvectors of the covariance matrix of the state estimate and to approximate t...

In this paper the use of tools from optimal control theory, namely the Kalman filter, is introduced for chaotic Lur’e systems to replace the widely used error feedback synchronization. This allows to take into account observation noise on the strange attractor to be filtered. We show that the filtering performance is superior to that of synchronization, in particular if the noise level is non-n...

We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an extended Kalman filter that is driven by a noisy drive signal from the transmitter. Extensive computer simulations show that the filter is indeed suitable for synchronization of (noisy) chaotic t...

1 Equations To restate the contents of the notes in a way that more closely reflects my own implementation: Consider the case of modeling a single dimensional first order PDE: x(t+∆t) = x(t) + ẋ∆t ẋ(t+∆t) = ẋ(t) We assume that there will be some noise in the actual process, as well as some noise in our ability to measure the state process. More exactly, we introduce wi and vi for each time step...

For the sake of concreteness, let’s think about the problem of estimating visual depth. A commonly assumed framework for how an observer might go about judging the depth of a visual object defined by multiple visual cues is the following two-stage process. First, depth estimates based on individual cues are derived. Next, a weighted combination of these estimates is calculated and used as the o...

There is a growing interest in using Kalman-filter models for brain modelling. In turn, it is of considerable importance to represent Kalman-filter in connectionist forms with local Hebbian learning rules. To our best knowledge, Kalman-filter has not been given such local representation. It seems that the main obstacle is the dynamic adaptation of the Kalman-gain. Here, a connectionist represen...

The unscented Kalman filter (UKF) is formulated for the continuous-discrete state space model. The exact moment equations are solved approximately by using the unscented transform (UT) and the measurement update is obtained by computing the normal correlation, again using the UT. In contrast to the usual treatment, the system and measurement noise sequences are included from the start and are n...