The main premise of this article is to develop a maximum entropy estimation of an unknown distribution using order statistics. The exact solution using constraints on the order statistic means is derived. The result is an integral of a rational parametric function whose parameters depend on the order statistic constraints. This integral equation can be solved directly for a small number of order statistic means, e.g., 1, 2, or at most 3, via a multidimensional search in the parameter space. As the number of constraints increases, the search for the optimum parameters becomes formidable. To resolve this problem we have proposed an approximate solution to the resultant integral equation based on Bernstein polynomials and estimates of a desired number of quantiles from available samples. The proposed approximation approach does not require any search in the parameter space and is formulated for any number of samples from an unknown distribution. Performance of this approach is evaluated under various practical conditions by using Kullback-Leibler divergence function.

An analytical expression for a probability density is usually required in detection and estimation problems, yet it is usually only assumed or selected from contenders by parameter estimation, or the histogram is smoothed with an arbitrary window function. In contrast, given a histogram containing R sample points, we derive a nonlinear differential equation (NDEQ) whose solution is a maximum entropy density given constraints that arise from assumptions that the samples are means of the order statistics of the parent distribution. We solve the NDEQ for R=1 and approximate the solution for general R using the fact that order means partition the density into equal probability regions, which we require to independently be maximum entropy. Finally we show with a Rayleigh density example what errors may result.

In this paper we propose a novel approach termed as dynamic copula time-frequency distribution (DCTFD) for the construction of positive time-frequency distributions (PTFDs). DCTFD models the dependency, i.e., correlation between time and frequency by a time-varying dependence parameter in copula function, and captures time-frequency dependency/correlation more accurately compared to static copula TFD (CTFD). In addition to presenting the under lying theory of the approach, a set of simulations are proved to demonstrate the advantages over CTFD and other classical methods, namely bivariate distributions.

There has been great interest in particle filtering as a sequential Bayesian estimation method for dynamic systems. The problem of detection in flat fading channels in the presence of autoregressive conditional heteroscedasticity (ARCH) noise is addressed. An auxiliary particle filtering (APF) algorithm is presented for the estimation of the transmitted sequence and ARCH noise variance. We introduce the ARCH process for the purpose of noise modelling. The applicability of the model is based on a variance change over time compatible to a large extent with non-stationarity and non-Gaussianity of wireless fading channels. We show, through simulation, the superiority of the proposed algorithm over the bootstrap particle filter (PF) even in the presence of the new noise model; i.e., the ARCH process.

We propose a new method for modeling practical non-Gaussian and non-stationary noise in array signal processing. GARCH (generalized autoregressive conditional heteroscedasticity) models are introduced as the feasible model for the heavy tailed probability density functions (PDFs) and time varying variances of stochastic processes. We use the GARCH noise model in the maximum likelihood approach for the estimation of directions-of-arrival (DOAs). Our analysis exploits time varying variance and spatially non-uniform noise in sensor array signal processing. We show through simulations that this GARCH modeling is suitable for high-resolution source separation and noise suppression in a non-Gaussian environment.

In this paper we present an effective scheme to excise impulsive noise pixels from a range-Doppler image or map. The temporal impulses in high frequency ocean surveillance radar (HFOSR) Doppler spectrum image arise due to local lightning discharges or man-made sources. Previous work focused on locating the noise position (detection) and applying a simple blanking technique, thereby burying targets in the noise spectrum. Built on these prior approaches, our current work develops an additional key step that uses weighted or block prediction method to estimate the possible true values of the destroyed ones. A range-Doppler image with much higher signal to clutter and noise ratio (SCNR) results. Another direct advantage over the former scheme is the improved robustness. Experimental images verify both the effectiveness and advantage of our method.

The problem of controlling the power spectral density (PSD) of random modulation techniques has attracted considerable interest recently in power electronics field. In this paper we analyze the PSD of DC/DC converter that uses randomized switching frequency pulse width modulation with constant duty cycle. We give a novel understanding for the peaks visible in the PSD. Based on the analysis we derive a reasonable means to null at a point or suppress the PSD over a band of specified frequencies. We also present the analysis of the limitation imposed by practical constraints on the range and mean of the switching frequencies. Simulation results verify our approach.

The use of multiple element antennas-both transmitting and receiving-has great potential for increasing the capacity of wireless systems. The maximum capacity is computed for an "edge-excited" cell with 3 base sites and a subscriber terminal with a 3 element array, for line-of-sight channels. In an attempt to approach this capacity, we show that the use of innovative signal processing at the receiver (blind source separation technique) seems to allow the system to achieve a significant portion of this great capacity promised by information theory.

We derive a technique for estimating a small number of parameters of a spatially or temporally varying transfer function for which a parametric model is known. Such systems occur in transmission lines with faults or mismatches, ultrasonic imaging, semiconductor layering and tomography in various applications. We assume that it is important not only to know that a boundary exists but also to estimate the spatially parameters of the medium across the boundary. The method does not require that the input need be known, but it must be applied to the diverse paths simultaneously, such as with a plane wave hitting a plane surface. The output signals at the various points are time synchronous unless delay is the varying parameter. The transfer function model may be nonlinear in the parameters, and we may also have to estimate the nominal values around which the parameters are locally varying. The procedure is constructed in the context of estimating at any point in space the parameters of the system by using the eigenstructure of the covariance matrix of vectors whose elements are Fourier transform values of the responses. We require that the available responses in the spatial neighborhood are independent enough to yield a good estimate of the covariance matrix. As an example we examine the case of an unknown parameter in a thin layer between 2 semi-infinite layers.

A number of algorithms have a higher resolution than the common beamformer. These often require the calculation of a pseudoinverse of a matrix, which makes the algorithm very slow for repeated applications. We consider updating the pseudoinverse for window motions either in time or in space for two-dimensional (2-D) data taken from a linear array. Our results are shown to reduce the computational complexity of the multiple sidelobe canceller (MSC), for example, by more than 75% for a downward window movement (with time) and more than 55% for a sideways window movement (across traces).

Ocean bottom classification performed using an an installed technology base requires compensation for the existing technology's constraints, including the fact that the digitized signal is the envelope of the convolution of the bottom's impulse response and the source ping. We present a method by which the impulse response coefficients may be estimated given the source signal and the envelope of the received signal. This is accomplished by modelling the Hilbert transform definition of an envelope as a finite-length second-order Volterra kernel, and then performing a constrained optimization on the non-linear filter coefficients.

Discrete time state-space models for multiple source frequency modulated communications environments are developed and coupled digital phase-locked loop (CDPLL) estimator structures are derived based on the extended Kalman filter (EKF). Unlike related efforts found in the literature, the receiver presented includes both passband and baseband coupling between the DPLLs. Separability of two sources is investigated by examination of state observability and by simulations of the derived estimators. The relationship between the EKF and the CDPLL is presented and their linear and nonlinear behavior discussed. As the CDPLLs exhibit chaotic behavior during acquisition and cannot be linearized during tracking, acquisition and tracking characteristics are extracted from simulations. One simulation result is the effect of state observability on the coupling between the DPLLs; when the states are "strongly" observable, the states are not as tightly coupled. It is also shown that the loop bandwidths decrease during periods of "weak" observability.

1 GHz complex impulse response data in mountainous terrain is measured at closely spaced locations, and is processed as data from a synthetic aperture array. Experimental data from linear and crossed arrays with 50 or 100 elements is considered. The direction of arrival for each delayed component is identified, and contour plots of the receiver power at bearings and distances are produced. These contour plots closely match the topography of the region, and clearly indicate that the strongest mountain reflections come from the steepest slopes. These results are used to establish a relationship between the mountain reflection coefficients and the topography, thus making it possible to invert the problem and estimate the impulse response (multipath delay profile) in mountainous terrain directly from topographical map data. Such estimates can help to select cell site locations and antenna configurations to minimize the delay spread.>

A high-resolution estimator is derived from maximum likelihood (ML) principles, solving for values of bearing parameters for which the partial of the likelihood functions with respect to the bearing parameter (the score function) is zero. The estimator is shown to give optimal weights to the noise-space eigenvectors from the point of view of maximizing the slope of the score function at the solution point. Simulations show that this algorithm gives greater accuracy than minimum norm (MN) near-single sources. It is shown that MN and MUSIC can be interpreted as a particular windowing of ML.>

Two methods are proposed for designing transformation matrices in array processing and spectral analysis: the stochastic method and the p-norm based method. The authors had previously presented the stochastic method for spatial smoothing, but they did not explicitly formulate the problem using the concept of stochastic transformation. The stochastic method can also be used in other applications if the signal statistics are known or can be estimated. The stochastic method enjoys the advantage of being able to utilize a priori signal statistics. The p-norm based method chooses the vector p-norm as the objective function for optimization, and it provides options to satisfy different designing specifications.>

A method for the suppression of coherent noise in seismic data based on the eigendecomposition of a data covariance matrix is demonstrated. Based on the Karhunen-Loeve transform, the proposed procedure is useful against noise energy exhibiting both two-dimensional space and time coherencies or coherent two-dimensional patterns which are not necessarily linear and therefore cannot generally be velocity-filtered. This method trains on a region containing the undesired coherent noise; the dominant eigenvectors determined from the covariance matrix of that noise are used to reconstruct the noise in the region of interest. Subtracting the reconstruction from the original data leaves a residual in which the coherent noise has been suppressed. In the example considered, this method effectively suppresses the noise in a record of marine seismic data containing backscattered source energy.>

A method for tracking multiple narrowband sources by means of a passive sensor array is presented. The resulting system is composed of an array of coupled digital phase-locked loop pairs (CDPLLS), with each CDPLL pair tracking and canceling a unique source from the system's input signal composite. The performance of the CDPLL pair, including stability, convergence, equivalent bandwidth, and signal-to-noise ratio (SNR) threshold, is studied through either analysis or computer simulations. A simulated acquisition and resolution of two sources is presented.>

A method for the suppression of coherent noise in seismic data based on the eigendecomposition of a data covariance matrix is demonstrated. Coherent noise arising from the seismic energy source is frequently a problem in seismic exploration. The resulting noise manifests itself in seismic data in a variety of forms, depending on the type of energy source, geology, and numerous other factors. Based on the Karhunen-Loeve transform, this procedure is useful against noise energy exhibiting spatial and temporal coherency. Applied to a record of marine seismic data containing backscattered source energy, this method suppresses the noise. The results indicate that this technique could have application to many of the coherent noise problems found in seismic data.>

The Karhunen-Loeve transformation (KLT) is an optimal method for encoding images in the MSE sense. Only one spatially adaptive method is known to be reported in the literature. Many other suboptimal encoding methods have been developed to avoid the problems encountered in the application of the KLT. Such methods give performance which is inferior to the KLT in both MSE and visual quality, although some of them are quite efficient for first order Markov processes. A spatial domain adaptive algorithm, which, besides giving more compression than its nonadaptive counterpart, solves the problem of ill-conditioned eigenvectors is presented. It is also shown that for a large class of images the same code set may be used, thus avoiding the computational problem normally associated with the Karhunen-Loeve encoding scheme.

Directionally selective median filtering may be accomplished either by passing a data-selecting window over the two-dimensional (2D) data or by pre-aligning the data columns and passing a horizontally-directed median filter over the data. If the data has features which appear as constants along some directional path, these constants may be selectively passed or stopped (filter-subtracted) from the data. Directional selectivity and angular resolution may be designed through the concept of orthogonal 2D median filters. The filters in an orthogonal set have fixed-size sample patterns which are mutually median-exclusive (or have minority common count). Synthetic examples of seismic applications are given and show very positive results.

Target tracking with Kalman filters is hampered by target maneuvering and unknown process and measurement noises. We show that moving data windows may be used to analyze state and measurement error sequences, determining robust estimates of bias and covariance. For unknown large steps in the system forcing functions and non-Gaussian measurement errors the robust estimators yield improvements over linear bias and covariance estimators. Extensive simulations compare conventional, linear adaptive and robust adaptive average step responses of a first-order system filter.

The estimation of time-of-arrival differences for signals from a single source or target arriving at multiple sensors enables target location. Herein noises are taken to have equal spatial correlation for all sensor pairs. Resulting estimators are shown to be reasonable and reduce to previously derived estimators where noises are independent.

The layered subsurface geologic model leads to an approximate hyperbolic curve of delay vs sensor offset distance for seismic signals. Four "optimum" estimators for the rms seismic velocity are given and analyzed by simulation for rms error. Parameters varied include center-point depth (time), apriori velocity variance and mean, delay-estimate variance and inter-delay-estimate correlation. The maximum likelihood estimator is shown to be best when apriori information is relatively good, but a least mean square estimator is best otherwise.

Array processors are special purpose computers attached to mini or mainframe computing systems to perform repetitive calculations at rates often ten times faster than their host. Images with their large array dimensions are particularly appropriate for processing with array processors. The utility of the Floating Point Systems product AP-120B is demonstrated through a comparison of total processing time for the fast median filter algorithm recently published [1]. FORTRAN calls and data transfer times are included for completeness of the example. Typical calculation times and a means of performing large 2DFFT's are also presented.

Uniformly distributed noise is often added to the inputs of limiters, quantizers, and polarity correlators to decrease the effects of the nonlinearities. This paper derives the error autocorrelations of the outputs of those devices when the additive noise is not purely vhite, but is of sample-and-hold form as might easily be produced by a pseudorandom noise generator and a digital to analog converter. These error autocorrelations then permit analyses of the errors in the outputs of the analog filters which follow the limiters.

Automatic detection using correlation relies on a phaselocked loop for synchronization. If the loop contains an imperfect integrator, only a finite error frequency (pulse rate) can be tracked. This concise paper yields the transcendental equations (and some specific numerical results for a maximally flat loop response) that relate duty-cycle, loop-bandwidth, integrator imperfection, and pull-in frequency when the input is noiseless. Analysis is based on piecewise-linear methods which are exact, although solutions are found numerically. One exemplary result shows that for a duty cycle of 5 percent and an integrator pole(b)to loop zero(a)ratio of ofb/a = 0.005, the pull-in frequency is 1.05 times the undamped natural loop frequency.

A periodically pulsed sine wave in noise, typical in wildlife tracking systems, is often envelope demodulated in the signal detector. An automatic detector using correlation techniques might employ a binary (bang-bang) multiplier in the phase-lock loop to lock onto the demodulated pulse train. A threshold device in front of or incorporated into the multiplier to quantize the pulse envelope causes loop gain effects, which are analyzed in this paper. A trade off from high loop gain to low loop threshold is the result as the quantizer threshold is lowered to the point where noise envelope alone exceeds the threshold 37 percent of the time.

The detection problem arises due to the false-alarm vulnerability of remote unmanned, signal detectors, typical in current wildlife-tracking studies. Some rather old theory is modified to overcome the effects of transient noise sources such as automobile engines or lightning. The resulting equipment is a simple up-down counter, tending to advance in the presence of large signal-to-noise ratio (SNR) and down-count otherwise. Probability of error for various situations is derived, wherein it is shown that false-alarm probability will be upper bounded and then decrease as noise increases above its quiescent level. The cost of the noise protection in terms of probabilities of error versus SNR is indicated by an example.