A Lattice Structured Algorithm for Recursive Solution of the Extended Yule-Walker Equations

A method is proposed to improve the accuracy of the parameter estimates of highly damped sinusoidal signals in additive noise. The method first utilizes singular value decomposition (SVD) of the signal matrix to reduce the noise effect, then based on the noise-reduced signals the weighted sum of squared errors is minimized using an adaptive lattice filter algorithm to estimate the parameters in the backward linear prediction model. In the case of large damping factors, the experimental results show that the proposed method gives more accurate estimates than the eigenvector method. >

The paper considers the problem of signal parameter estimation using a collection of distributed sensors called a sensor pack. Each sensor quantizes its data to one-bit information and sends it to a fusion processor for the estimation of the parameter. Estimation of a constant signal in additive noise is considered. Estimators are formulated based on one-bit sensor data and their mean squared error (MSE) performances are evaluated through simulation studies. It is shown that selecting certain threshold values for quantizing the sensor outputs can lower the MSE. Genetic algorithms are used to find the optimal threshold values for the sensors. Results from this study show that robust estimation of parameter is possible by using a moderately large number of one-bit quantized sensor data. This work has significance in applications that demand high reliability in sensor networks in spite of sensor failures, limited sensor dynamic range, resolution, bandwidth for data transmission or even data storage.

Estimation of parameters of two-dimensional random amplitude chirp signal in additive noise

In this paper, we consider the superimposed exponential signals in zero-mean multiplicative and additive noise when all the noise are independently and identically distributed. We use a three-step iterative procedure to estimate the frequencies of the considered model. It is observed that the estimators are consistent and work quite well in terms of biases and mean square errors. Moreover, the convergence rate of the estimators attains O p (N −3/2), which is the best convergence rate in the case of only additive noise and constant amplitude.

We show that the concept of correlation detection of deterministic signals in additive Gaussian noise can be extended in a natural manner to the detection of signals that are transmitted through a "Gaussian" random channel besides being corrupted by additive Gaussian noise. Such situations are typical in communication over scatter-multipath channels (with or without a specular component). In the deterministic case, the receiver essentially crosscorrelates the received signal with the signal before the additive noise was introduced. When a random channel is present, however, this latter signal, i.e., the output of the random channel, is not known at the receiver, However, knowing the statistics of the channel and the noise, the receiver can make an estimate of it from the received signal on the hypothesis that a particular signal was transmitted. The optimum receiver then crosscorrelates this estimate with the received signal.

A new, efficient algorithm is developed for the sensitivity analysis of a class of continuous-time recurrent neural networks with additive noise signals. The algorithm is based on the stochastic sensitivity analysis method using the variational approach, and formal expressions are obtained for the functional derivative sensitivity coefficients. The present algorithm uses only the internal states and noise signals to compute the gradient information needed in the gradient descent method, where the evaluation of derivatives is not necessary. In particular, it does not require the solution of adjoint equations of the back-propagation type. Thus, the algorithm has the potential for efficiently learning the network weights with significantly fewer computations. The effectiveness of the algorithm in a statistical sense is shown, and the method is applied to the familiar layered network.

In this chapter we will begin our description of signal detection schemes for non-Gaussian noise by consideringn one of the simplest to formulate and most commonly encountered of all detection problems.This is the detection of real-valued deterministic signal which is completely know in a background of additive noise. We shall be concerned exclusively with discrete-time detection problems in this book. In many applications discrete-time observations are obtained by sampling at a uniform rate same underlying continuous-time observation process. In the next section we will give the example of detection of a pulse train in additive noise to illustrate how a discrete-time detection problem may arise in a different manner from an original problem formulation in the continuous-time domain.

The optimum detection of binary antipodal signals in additive white Gaussian noise (AWGN) channels with Gaussian channel estimation error has been studied in prior work. In this paper, we present the optimum detector based on the maximum- likelihood criterion for binary orthogonal signals in the presence of Gaussian distributed channel estimation error and AWGN. It is shown that the optimum detector is a linear combination of the optimum coherent and optimum noncoherent detectors. We derive the exact closed-form expression of the average bit error probability of the proposed optimum detector in Rayleigh fading channels with AWGN. It is found that if the variance of channel estimation error for a given average SNR is greater than a threshold, then orthogonal signalling outperforms antipodal modulation, and the analytical expression of this threshold is derived.

The structure and performance of locally optimum detectors for composite signals in additive and multiplicative noise are investigated. A generalised model representing the effects of multiplicative noise and additive noise is considered for signal detection problems. The signals considered here are composite signals which contain both deterministic and stochastic signal components. Locally optimum detectors consist of nonlinearities followed by an accumulator, whose output is then compared with a threshold. The detection nonlinearities for a probability density function are obtained to show the detection structures. Finite sample-size performance characteristics of the locally optimum detector are obtained and are compared with those of other detectors.

The use of information theory to design waveforms for the measurement of extended radar targets exhibiting resonance phenomena is investigated. The target impulse response is introduced to model target scattering behavior. Two radar waveform design problems with constraints on waveform energy and duration are then solved. In the first, a deterministic target impulse response is used to design waveform/receiver-filter pairs for the optimal detection of extended targets in additive noise. In the second, a random target impulse response is used to design waveforms that maximize the mutual information between a target ensemble and the received signal in additive Gaussian noise. The two solutions are contrasted to show the difference between the characteristics of waveforms for extended target detection and information extraction. The optimal target detection solution places as much energy as possible in the largest target scattering mode under the imposed constraints on waveform duration and energy. The optimal information extraction solution distributes the energy among the target scattering modes in order to maximize the mutual information between the target ensemble and the received radar waveform. >

The shifted inverse-gamma model for noise-floor estimation in archived audio recordings

A simple method is presented for detecting an unknown periodic signal in additive noise. The period is unknown, but the amplitudes of the fundamental and the first M - 1 harmonics are known to be nonzero. One application is the detection of a torpedo by a submarine sonar system from the observed acoustic line spectrum generated by the torpedo's blade motion.

The Adaptive Noise Canceller (ANC) is a commonly used adaptive filter for estimating signal in additive noise. An important factor that effects the performance of the ANC is the signal crosstalk between the primary and reference channels of the ANC. This results in reduced output Signal-to-Noise Ratios (SNR's) and undesirable signal distortion. A Crosstalk Resistant Adaptive Noise Canceller (CRANC), which is a cascade of two ANC's, can be designed to output a distortion free signal. This paper undertakes the performance analysis of the CRANC filter under the influence of various parameters. It is shown that the CRANC's performance is sensitive to the presence of uncorrelated noise sources. Equations are derived to show the effect of uncorrelated noise sources on the CRANC filter structure. The CRANC's performance in estimating the stimulus evoked nerve signal embedded in larger muscle interference is then evaluated through simulations. The results show that with no or little uncorrelated noise present, the CRANC gives a superior performance compared to the ANC. With higher levels of uncorrelated noise power, however, the CRANC's performance is shown to be comparable to that of the ANC. An alternate multichannel CRANC structure is then utilized to mitigate the effects of the uncorrelated noise sources, and its performance in estimating the nerve signal from the muscle interference is evaluated through simulations.

Two methods are considered for comparing the asymptotic efficiencies of robust detectors in the problem of detecting coherent signals in additive noise. The first of these methods considers the relative detector sample sizes for a fixed value of the detector power, while the second method considers the relative detector sample sizes for a fixed value of the local detector power, as measured by the local values of the slopes or curvatures of the detector power functions. These measures of efficiency are variations of the asymptotic relative efficiencies (AREs) of Pitman and Blomqvist, respectively, adapted to the robust detection problem. These two approaches are used to compare the performance of robust nonlinear correlators to that of robust M-detectors in both one-sided and two-sided detection problems, under an epsilon -contaminated mixture model for uncertainty in the noise statistics. Both measures of ARE, fixed-power and fixed-local-power, indicate that the robust nonlinear correlator outperforms the robust M-detector for this type of model. However, the fixed-local-power ARE is shown to be more useful in measuring the degree to which the robust nonlinear correlator is more efficient. >

Parametric and nonparametric detectors based on a sequential sample median test