Henry Leung

Prediction of noisy chaotic time series using an optimal radial basis function neural network

This paper considers the problem of optimum prediction of noisy chaotic time series using a basis function neural network, in particular, the radial basis function (RBF) network. In the noiseless environment, predicting a chaotic time series is equivalent to approximating a nonlinear function. The optimal generalization is achieved when the number of hidden units of a RBF predictor approaches infinity. When noise exists, it is shown that an optimal RBF predictor should use a finite number of hidden units. To determine the structure of an optimal RBF predictor, we propose a new technique called the cross-validated subspace method to estimate the optimum number of hidden units. While the subspace technique is used to identify a suitable number of hidden units by detecting the dimension of the subspace spanned by the signal eigenvectors, the cross validation method is applied to prevent the problem of overfitting. The effectiveness of this new method is evaluated using simulated noisy chaotic time series as well as real-life oceanic radar signals. Results show that the proposed method can find the correct number of hidden units of an RBF network for an optimal prediction.

The use of fractals for modeling EM waves scattering from rough sea surface

A rough surface model based on fractal geometry is presented for the study of surface scattering. In particular, the Pierson-Moskowitz spectrum is incorporated into this model to represent a fully developed sea surface. The Kirchoff approximation is used to evaluate the scattered field from this rough surface. Some interconnection are found between the surface model developed and the statistical characteristics of the scattered field. These include: 1) the relationship between the surface correlation length and the surface fractal dimension; 2) the relationship between the shape parameter of the K-distribution and the surface fractal dimension; 3) the mean value of the scattered amplitude as a function of the surface fractal dimension; and 4) the effect of the incident angle on the scattered field.

Blind equalization using a predictive radial basis function neural network

In this paper, we propose a novel blind equalization approach based on radial basis function (RBF) neural networks. By exploiting the short-term predictability of the system input, a RBF neural net is used to predict the inverse filter output. It is shown here that when the prediction error of the RBF neural net is minimized, the coefficients of the inverse system are identical to those of the unknown system. To enhance the identification performance in noisy environments, the improved least square (ILS) method based on the concept of orthogonal distance to red the estimation bias caused by additive measurement noise is proposed here to perform the training. The convergence rate of the ILS learning is analyzed, and the asymptotic mean square error (MSE) of the proposed predictive RBF identification method is derived theoretically. Monte Carlo simulations show that the proposed method is effective for blind system identification. The new blind technique is then applied to two practical applications: equalization of real-life radar sea clutter collected at the east coast of Canada and deconvolution of real speech signals. In both cases, the proposed blind equalization technique is found to perform satisfactory even when the channel effects and measurement noise are strong.

Signal detection using the radial basis function coupled map lattice

Conventional detection methods used in current marine radar systems do not perform efficiently in detecting small targets embedded in a clutter environment. Based on a recent observation that sea clutter, radar echoes from a sea surface, is chaotic rather than random, we propose using a spatial temporal predictor to reconstruct the chaotic dynamic of sea clutter because electromagnetic wave scattering is a spatial temporal phenomenon which is physically modeled by partial differential equations. The spatial temporal predictor used here is called radial basis function coupled map lattice (RBF-CML) which uses a linear combiner to fuse either measurements in different spatial domains for an RBF prediction or predictions from several RBF nets operated on different spatial regions. Using real-life radar data, it is shown that the RBF-CML is an effective method to reconstruct the sea clutter dynamic. The RBF-CML predictor is then applied to detect small targets in sea clutter using the constant false alarm rate (CFAR) principle. The spatial temporal approach is shown, both theoretically and experimentally, to be superior to a conventional CFAR detector.

A new approach for estimating indoor radio propagation characteristics

Presents a new approach for estimating the propagation characteristics of indoor radio channels. The technique is based on the use of principal component analysis and the information theoretic criterion. It is shown, based on the simulation results, that the new technique can be used to overcome difficulties experienced by conventional methods and, as a result, is able to produce greater accuracy in its estimates of the channel parameters. The authors demonstrate the use of this technique by carrying out data analysis using measured indoor radio channel data. >

Radial basis function neural network for direction-of-arrivals estimation

The authors propose the use of a radial basis function (RBF) network for direction-of-arrival (DOA) estimation. The RBF network is used to approximate the functional relationship between sensor outputs and the direction of arrivals. Simulation results show that the new technique has a better performance in terms of estimation errors than the standard MUSIC algorithm.<<ETX>>

A spatial temporal dynamical model for multipath scattering from the sea

new method for modeling sea scattered signals is proposed in this paper. Instead of using a probabilistic model, a spatial temporal dynamical model is employed to model the sea scatter phenomenon. Our approach is empirical in the sense that a model is constructed based on experimental data. We extend the approach of using a temporal predictor for temporal dynamical system reconstruction to a spatial temporal predictor for reconstructing a spatial temporal one. The basic spatial temporal dynamical model used in this study is a couple map lattice (CML) rather than the conventional partial differential equation. The Radial Basis Function (RBF) neural network is incorporated into the CML to enhance the function approximation ability, and the autocorrelation function is used to determine the spatial effect across individual channel. An array antenna was used to collect real spatial temporal sea scattered data for this study. Preliminary results shows that the new model provides an accurate description of the sea scattered signals, and has the potential for signal processing applications.

An efficient decentralized multiradar multitarget tracker for air surveillance

We present an efficient multiradar multitarget tracking (MTT) algorithm for air surveillance. This tracker uses a multisensor track-to-track correlation method called the sequential minimum normalized distance nearest neighbor (SMNDNN) correlation with the majority decision making MDM/OR logic to solve the multisensor assignment problem. A sequential fuser based on the mean square error criterion is then used to fuse the tracks generated by the trackers. Real-life multiradar data collected from an air surveillance radar network located along the coastline of Canada is used to evaluate the effectiveness of this distributed tracker. Analysis shows that this tracker provides a reliable air surveillance picture.

Genetic algorithm for multiple target tracking data association

The heart of any tracking system is its data association algorithm where measurements, received as sensor returns, are assigned to a track, or rejected as clutter. In this paper, we investigate the use of genetic algorithms (GA) for the multiple target tracking data association problem. GA are search methods based on the mechanics of natural selection and genetics. They have been proven theoretically and empirically robust in complex space searches by the founder J. H. Holland. Contrary to most optimization techniques, which seek to improve performance toward the optimum, GA find near-optimal solutions through parallel searches in the solution space. We propose to optimize a simplified version of the neural energy function proposed by Sengupta and Iltis in their network implementation of the joint probability data association. We follow an identical approach by first implementing a GA for the travelling salesperson problem based on Hopfield and Tanks neural network research.

Separation of a mixture of chaotic signals

A new technique is specifically devised to separate chaotic signals. In this approach, the authors reconstruct the trajectory of the mixture in an embedding space. The correlation characteristics of the trajectory in each dimension of the embedding space are then determined and used to reduce the separation problem into an eigen-problem that can be solved using linear algebra.