This paper presents a novel approach to deal with nonlinear filtering by augmenting an Unscented Kalman Filter (UKF) with an Optimal quantization algorithm, named OQ-UKF. The Unscented Kalman Filter uses a sigma-point based method to approximate the distribution of an unknown random variable onto which is applied a nonlinear transformation, providing a cloud of evolving points. However, the generation of these socalled sigma-points is done by a deterministic algorithm which needs tuning in order to accurately capture the distribution of the estimate. This tuning is often problem-dependent due to nonlinearities and sometimes not optimal. We propose to fuse an UKF with Optimal quantization whose objective is to find the best approximation of the density of a random variable. The designed OQ-UKF is described in this paper, and its performance is evaluated for some relevant practical problems, such as pose estimation of a two-dimensional mobile robot.

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.

The characterization of complex air traffic situations is an important issue in air traffic management (ATM). Within the current ground-based ATM system, complexity metrics have been introduced with the goal of evaluating the difficulty experienced by air traffic controllers in guaranteeing the appropriate aircraft separation in a sector. The rapid increase in air travel demand calls for new generation ATM systems that can safely and efficiently handle higher levels of traffic. To this purpose, part of the responsibility for separation maintenance will be delegated to the aircraft, and trajectory management functions will be further automated and distributed. The evolution toward an autonomous aircraft framework envisages new tasks where assessing complexity may be valuable and requires a whole new perspective in the definition of suitable complexity metrics. This paper presents a critical analysis of the existing approaches for modeling and predicting air traffic complexity, examining their portability to autonomous ATM systems. Possible applications and related requirements will be discussed.

Accurate wind magnitude and direction estimation is essential for aircraft trajectory prediction. For instance, based on these data, one may compute entry and exit times from a sector or detect potential conflict between aircraft. Since the flight path has to be computed and updated on real time for such applications, wind information has to be available in real time too.The wind data which are currently available through meteorological service broadcast suffer from small measurement rate with respect to location and time. In this paper, a new wind estimation method based on radar track measures is proposed. When on board true air speed measures are available, a linear model is developed for which a Kalman filter is used to produce high quality wind estimate. When only aircraft position measures are available, an observability analysis shows that wind may be estimated only if trajectories have one or two turns depending of the number of aircraft located in a given area. Based on this observability conditions, closed forms of the wind has been developed for the one and two aircraft cases. By this mean, each aircraft can be seen as a wind sensor when it is turning. After performing evaluations in realistic frameworks, our approach is able to estimate the wind vectors accurately.

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Many signal processing problems need to be solved in an adaptive way under some constraints. The paper introduces a constrained complex-valued neural network (CCNN) model. It is composed of two sub networks: a master which gives the main energy function (the error power between the master's output and a desired output), and a slave which gives a secondary energy function (related to the constraints imposed by the problem). The sum of these energy functions gives the cost function to be minimized by the CCNN. An extension of the classical back propagation algorithm to the complex plane, under some inequality constraints, is used for the training process. This model finds a natural application in the time-frequency analysis as it gives direct access to the time-frequency signature.>

Proposes a modified Fourier transform for the inversion of the visibility function acquired by an unidimensional interferometer observing the surface of the Earth from a low orbit. The inversion of the visibility function by the mean of the usual Fourier transform provides a profile of geometrically distorted brightness temperatures. A modified Fourier transform which takes into account the geometrical considerations of the problem and which avoids making geometrical corrections is described. The authors study the behaviour of this new transform when the input signal is corrupted with white noise. A convolution product associated with this modified Fourier transform is also defined.>