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In this paper, we present a new nonlinear filter for high-dimensional state estimation, which we have named the cubature Kalman filter (CKF). The heart of the CKF is a spherical-radial cubature rule, which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear Bayesian filter. Specifically, we derive a third-degree spherical-radial cubature rule that provides a set of cubature points scaling linearly with the state-vector dimension. The CKF may therefore provide a systematic solution for high-dimensional nonlinear filtering problems. The paper also includes the derivation of a square-root version of the CKF for improved numerical stability. The CKF is tested experimentally in two nonlinear state estimation problems. In the first problem, the proposed cubature rule is used to compute the second-order statistics of a nonlinearly transformed Gaussian random variable. The second problem addresses the use of the CKF for tracking a maneuvering aircraft. The results of both experiments demonstrate the improved performance of the CKF over conventional nonlinear filters. Index Terms--Bayesian filters, cubature rules, Gaussian quadrature rules, invariant theory, Kalman filter, nonlinear filtering.

A square-root extension of the quadrature Kalman filter using matrix triangularizations is discussed. Excellent numerical characteristics are observed in the square-root quadrature Kalman filter.

We present a novel wideband multiple-input, multiple-output (MIMO) channel model, which we refer to as the structured model. The structured model is based on the eigenvalue decomposition (EVD) of the wideband channel correlation matrix. It does not assume the scatterers at the receiver fade independently of those at the transmitter. It also models correlation between delay bins in the power delay profile (PDP). With preliminary data gathered using McMaster's wideband MIMO Software Defined Radio (the WMSDR) in fixed outdoor locations, and Brigham Young University's (BYU) wideband channel sounder in fixed indoor locations, we show good agreement between modeled and measured data. The two platforms used and the environments in which the data were collected were very different. The proposed model performed equally well with both data sets, demonstrating its robustness. Index Terms--Antenna arrays, channel capacity, channel modeling, measured channel data, multiple-input multiple-output (MIMO), wideband.

Modeling wireless channels is essential to wireless communication systems. An autoregressive (AR) process of order one for wireless channel has long been assumed, but without a rigorous mathematical/physical basis. In this paper, we derive a first-order stochastic AR model for a flat stationary wireless channel, which comes from stochastic differential equation (SDE) theory concerning the nature of multipath fading channels. The resulting AR model describes more of the origin of multipath fading channels than previous AR models, and it can efficiently model and generate Rayleigh-distributed stationary fading channels. The Markovian property of the AR model is inherited through the SDE approach. Index Terms--Autoregressive (AR) process, multipath channels, Rayleigh, stochastic differential equation (SDE).

Recurrent neural networks (RNNs) have been successfully applied to communications channel equalization because of their modeling capability for nonlinear dynamic systems. Major problems of gradient-descent learning techniques commonly employed to train RNNs are slow convergence rates and long training sequences required for satisfactory performance. This paper presents decision-feedback equalizers using an RNN trained with Kalman filtering algorithms. The main features of the proposed recurrent neural equalizers, using the extended Kalman filter (EKF) and unscented Kalman filter (UKF), are fast convergence and good performance using relatively short training symbols. Experimental results for various time-varying channels are presented to evaluate the performance of the proposed approaches over a conventional recurrent neural equalizer. Index Terms--Channel equalization, extended Kalman filter (EKF), recurrent neural network (RNN), time-varying channel, unscented Kalman filter (UKF).

Stochastic correlative learning, as the basis for a broadly defined class of statistical learning algorithms, collectively known as the algorithm of pattern extraction (ALOPEX) family is addressed. Three different experiments are presented in support of the ALOPEX algorithms using synthetic and real-life data on binocular fusion of stereo images, on-line prediction, and system identification.

In earlier papers [1]-[5], we described a novel multitransmit, multireceive (MTMR) antenna system for wireless communications. This new system, turbo Bell-Labs layered space-time (T-BLAST) architecture, combines the benefits of layered space-time coding concepts and turbo principles in the multitransmit, multireceive antenna system design. In particular, the random layered space-time codes designed by using a set of block convolutional codes and random space-time interleavers and the space-time turbo-like decoding operation allow T-BLAST to realize the benefits of MTMR systems in a computationally feasible manner. The goal of this paper is to present experimental results of T-BLAST based on real-life data collected using the Bell-Labs experimental multiple antenna system with eight transmit and five and six receive antennas. The experimental results show the practical virtues of T-BLAST. Index Terms--Bell-Labs layered space-time (BLAST) architecture, interference cancellation, space-time codes, turbo processing.

A multitransmit multireceive (MTMR) antenna arrangement for high-throughput wireless telecommunications is discussed. It is shown that the combination of BLAST and turbo principles provideds an effective, reliable solution to high-data-rate transmission for wireless communications.

Multiple window (MW) time-frequency analysis (TFA) is a newly developed technique to estimate a time-varying spectrum for random nonstationary signals with low bias and variance. In this paper, we describe the application of MW-TFA techniques to electroencephalogram (EEG) and compare the results with those of the conventional spectrogram. We find that the MW-TFA provide us with not only low bias and variance time-frequency (TF) distribution for EEG but also TF coherence estimation between a single realization of EEG recorded from two sites. We also compare the performance of the MW-TFA using two sets of windows, Slepian sequences, and Hermite functions. If care is taken in matching the two windows, we find no noticeable difference in the resulting TF representations. Index Terms - Electroencephalogram (EEG), Hermite functions, multiple window (MW), Slepian sequences, spectrogram, time-frequency analysis (TFA).

An examination of two different approaches to the optimum nonlinear filtering problem found that a numerical solution to the stochastic partial differentiation equation approach produces the optimal performance available. This resulting performance can then be used to optimize a neural filter. A neural filter can be implemented through a recursive multilayer perceptron or a radial basis function network. Cascading this filter with a linear adaptive filter will facilitate a combination of learning and adaptation.

A unique modular learning method for the detection of a target signal of significance in a nonstationary environment is presented. The technique makes no assumptions on the environment and integrates the functional blocks of time-frequency analysis, feature extraction and pattern classification. Experimental findings based on actual radar data are presented to show the superior performance of the new detection method over a conventional detector utilizing constant false-alarm rate processing.

The one-to-correspondence between the recursive least-squares (RLS) and Kalman variables are used to develop extended forms of the RLS algorithm. Two forms of the extended RLS algorithm are examined, one concerning system identification assuming a first-order Markov model and another on tracking a chirped sinusoid in additive noise. Results show that the extended RLS algorithm performs better than the least-mean-square algorithm.

Novel detection schemes are developed using a coherent X-band radar for the detection of small pieces of icebergs. The methods use Wigner-Ville (WV) distribution to perform detection in a joint time-frequency space. Two separate methodologies are presented. The first method extracts classification features from the ambiguity function of the received signal and a neural network is used to perform detection based on these features. The second method uses the method of Principal Components Analysis (PCA) to extract essential information from the time-frequency space for classification. Using real radar data, results are presented and the developed methods are also compared to a conventional Doppler constant false-alarm rate (CFAR) processor.

The chirplet transform is a generalization of two transforms: the short-time Fourier transform (STFT) and the wavelet transform (WT). The STFT and WT are expressible as inner products of the signal to be analyzed under the action of specific operators. These operators form the time-frequency (TF) plane's two-dimensional affine coordinate transformations. A system of TF-affine coordinate transform operators with one wavelet forms the family of chirplets, with the chirplet transform as the signal representation.

The transform coding method presented here performs better than the optimal nonadaptive linear transformation. The system obtains perceptually significant characteristics from the test image in a self-organizing manner. The system contains a series of modules associated with distinct classes of input data. The compression ratio is same for same images. The performance of the method is discussed.