Signal Estimation Problem Research Articles

A RELAX Based Method for Spotlight SAR Imaging

The imaging problem of spotlight SAR is converted to a parameter estimation problem of several monochromatic signals in additive white Gaussian noisy condition in this paper. Moreover, a spotlight SAR imaging algorithm based on RELAX is presented in detail. Traditional polar format algorithm and the presented method are applied to spotlight SAR imaging respectively, and the imaging results are compared. Simulation results show that the polar format algorithm doesn’t give satisfactory imaging results, while the proposed method adapts the noisy environment better and obtains better results.

A RELAX Based Method for Spotlight SAR Imaging

The imaging problem of spotlight SAR is converted to a parameter estimation problem of several monochromatic signals in additive white Gaussian noisy condition in this paper. Moreover, a spotlight SAR imaging algorithm based on RELAX is presented in detail. Traditional polar format algorithm and the presented method are applied to spotlight SAR imaging respectively, and the imaging results are compared. Simulation results show that the polar format algorithm doesn’t give satisfactory imaging results, while the proposed method adapts the noisy environment better and obtains better results.

Beyond the Fisher-Matrix Formalism: Exact Sampling Distributions of the Maximum-Likelihood Estimator in Gravitational-Wave Parameter Estimation

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise realizations, as well as the leading-order width of the posterior probability, but it is limited to high signal strengths often not realized in practice. By contrast, Monte Carlo Bayesian inference provides the full posterior for any signal strength, but it is too expensive to repeat for a representative set of noises. Here I describe an efficient semianalytical technique to map the exact sampling distribution of the maximum-likelihood estimator across noise realizations, for any signal strength. This technique can be applied to any estimation problem for signals in additive Gaussian noise.

Quadratic Filtering Algorithm Based on Covariances Using Correlated Uncertain Observations Coming from Different Sensors

The least-squares quadratic estimation problem of signals from observations coming from multiple sensors is addressed when there is a nonzero probability that each observation does not contain the signal to be estimated. We assume that, at each sensor, the uncertainty about the signal being present or missing in the observation is modelled by correlated Bernoulli random variables, whose probabilities are not necessarily the same for all the sensors. A recursive algorithm is derived without requiring the knowledge of the signal state-space model but only the moments (up to the fourth-order ones) of the signal and observation noise, the uncertainty probabilities, and the correlation between the variables modelling the uncertainty. The estimators require the autocovariance and cross-covariance functions of the signal and their second-order powers in a semidegenerate kernel form. The recursive quadratic filtering algorithm is derived from a linear estimation algorithm for a suitably defined augmented system.

Optimal Estimation and Detection in Homogeneous Spaces

This paper presents estimation and detection techniques in homogeneous spaces that are optimal under the squared error loss function. The data is collected on a manifold which forms a homogeneous space under the transitive action of a compact Lie group. Signal estimation problems are addressed by formulating Wiener-Hopf equations for homogeneous spaces. The coefficient functions of these equations are the signal correlations which are assumed to be known. The resulting coupled integral equations on the manifold are converted to Wiener-Hopf convolutional integral equations on the group. These are solved using the Peter-Weyl theory of Fourier transform on compact Lie groups. The computational complexity of this algorithm is reduced using the bi-invariance of the correlations with respect to a stabilizer subgroup. The theory of matched filtering for isotropic signal fields is developed for signal classification where given a set of template signals on the manifold and a noisy test signal, the objective is to optimally detect the template buried in the test signal. This is accomplished by designing a filter on the manifold that maximizes the signal-to-noise-ratio (SNR) of the filtered output. An expression for the SNR is obtained as a ratio of quadratic forms expressed as Haar integrals over the transformation group. These integrals are expressed in the Fourier domain as infinite sums over the irreducible representations. Simplification of these sums is achieved by invariance properties of the signal function and the noise correlation function. The Wiener filter and matched filter are developed for an abstract homogeneous space and then specialized to the case of spherical signals under the action of the rotation group. Applications of these algorithms to denoising of 3D surface data, visual navigation with omnidirectional camera and detection of compact embedded objects in the stochastic background are discussed with experimental results.

Statistical Physics of Signal Estimation in Gaussian Noise: Theory and Examples of Phase Transitions

We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal and its noisy version. The paper consists of essentially two parts. In the first, we derive several statistical-mechanical relationships between a few important quantities in this problem area, such as the MMSE, the differential entropy, the Fisher information, the free energy, and a generalized notion of temperature. We also draw analogies and differences between certain relations pertaining to the estimation problem and the parallel relations in thermodynamics and statistical physics. In the second part of the paper, we provide several application examples, where we demonstrate how certain analysis tools that are customary in statistical physics, prove useful in the analysis of the MMSE. In most of these examples, the corresponding statistical-mechanical systems turn out to consist of strong interactions that cause phase transitions, which in turn are reflected as irregularities and discontinuities (similar to threshold effects) in the behavior of the MMSE.

Denoising signals corrupted by chaotic noise

We consider the problem of signal estimation where the observed time series is modeled as y i = x i + s i with { x i } being an orbit of a chaotic self-map on a compact subset of R d and { s i } a sequence in R d converging to zero. This model is motivated by experimental results in the literature where the ocean ambient noise and the ocean clutter are found to be chaotic. Making use of observations up to time n, we propose an estimate of s i for i < n and show that it approaches s i as n → ∞ for typical asymptotic behaviors of orbits.

A new sample-profile estimation signal in dynamic-mode atomic force microscopy

In this paper, a design scheme is proposed that separates the issues of sample-profile estimation and amplitude regulation in dynamic-mode atomic force microscopy. In current AFM, the control signal for amplitude regulation is also used as the estimate for the sample-profile. Therefore, the sample profile estimation signal is accurate as long as the sample-profile signal perceived by the cantilever is well within the bandwidth of the control transfer function. In the proposed design scheme, maintaining a constant amplitude while scanning at high bandwidth does not impose limitations on the reconstruction of the sample topography. In fact, we analytically prove that the sample-profile signal estimation problem can be solved independently of the control design scheme for amplitude regulation. Therefore, accurate sample-profile estimations can be obtained even at frequencies near and beyond the closed-loop control bandwidths. However, we show that the robustness of estimation does depend on the control design for regulation and in fact, the robustness of estimation is described by the closed-loop sensitivity transfer function. The independence of the profile-estimation problem from the control design is another salient distinguishing characteristic of this work. The estimation bandwidths by this new scheme are improved significantly over commonly used signals. Comparison with the existing methods of using the control signal as the image is provided. The experimental results corroborate the theoretical development.

Signal estimation with nonlinear uncertain observations using covariance information

This paper addresses the signal estimation problem in situations where the observations are nonlinear functions of the signal and the measure mechanism is prone to failure or some observations are accidentally lost (uncertain observations). A recursive filtering and fixed-point smoothing algorithm is proposed assuming that the Bernoulli random variables describing the uncertainty in the observations are independent and the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are available. A numerical simulation example concerning the phase modulation problem shows the effectiveness of the proposed algorithm.

Fast Iterative Maximum-Likelihood Algorithm (FIMLA) for Multipath Mitigation in the Next Generation of GNSS Receivers

In this paper, we efficiently solve the maximum likelihood (ML) time-delay estimation problem for GNSS signals in a multipath environment. Exploiting the GNSS signal model structure and the spreading code periodicity, we develop an efficient implementation of the Newton iterative likelihood maximization method by finding simple analytical expressions for the first and second derivatives of the likelihood function. The proposed fast iterative ML algorithm (FIMLA) for timedelay estimation, which uses the correlation function of the received signal with its local replica, is shown to be an attractive technique for mitigation of closely-spaced multipath arrivals. For the future modernized GPS and the European Galileo signals based on binary offset carrier (BOC) waveforms, the correlation function has multiple positive and negative peaks leading to potential tracking ambiguities. Instead of the standard crosscorrelation, we propose an implementation characterized by a different choice of the local replica so as to cancel the sub-carrier phase, thus eliminating ambiguities. The asymptotic performance of FIMLA is analyzed by deriving the corresponding Cramer-Rao bound (CRB). Representative simulation examples are included to illustrate the FIMLA is performance for delay estimations in the presence of multipath for both C/A code and BOC signals.

Subspace-Based Algorithm for Parameter Estimation of Polynomial Phase Signals

In this correspondence, parameter estimation of a polynomial phase signal (PPS) in additive white Gaussian noise is addressed. Assuming that the order of the PPS is at least 3, the basic idea is first to separate its phase parameters into two sets by a novel signal transformation procedure, and then the multiple signal classification (MUSIC) method is utilized for joint estimating the phase parameters with second-order and above. In doing so, the parameter search dimension is reduced by a half as compared to the maximum likelihood and nonlinear least squares approaches. In particular, the problem of cubic phase signal estimation is studied in detail and its simplification for a chirp signal is given. The effectiveness of the proposed approach is also demonstrated by comparing with several conventional techniques via computer simulations.

Signal estimation based on covariance information from observations featuring correlated uncertainty and coming from multiple sensors

The linear least-squares estimation problem of signals from observations coming from multiple sensors is addressed when there is a non-zero probability that each observation does not contain the signal to be estimated ( uncertain observations). At each sensor, this uncertainty in the observations is modeled by a sequence of Bernoulli random variables correlated at consecutive sampling times. To estimate the signal, recursive filtering and (fixed-point and fixed-interval) smoothing algorithms are derived without requiring the knowledge of the signal state-space model but only the means and covariance functions of the processes involved in the observation equations, the uncertainty probabilities and the correlation between the variables modeling the uncertainty. To measure the estimation accuracy, recursive expressions for the estimation error covariance matrices are also proposed. The theoretical results are illustrated by a numerical simulation example where a signal is estimated from observations featuring correlated uncertainty and coming from two sensors with different uncertainty characteristics.

Linear least-squares estimation based on covariances from multiple correlated uncertain observations

In this paper, the linear least-squares estimation problem of signals from correlated uncertain observations coming from multiple sensors is addressed. It is assumed that, at each sensor, the signal is measured in the presence of additive white noise and that the uncertainty in the observations is characterized by a set of Bernoulli random variables which are only correlated at consecutive time instants. Assuming that the probability and correlation of such variables are not necessarily the same for all the sensors, a recursive filtering and fixed-point smoothing algorithm is proposed. The derivation of such algorithm does not require the knowledge of the signal state-space model, but only the covariance functions of the processes involved in the observation equation of each sensor, as well as the probability and correlation of the Bernoulli variables modeling the uncertainty. Recursive expressions for the estimation error covariance matrices are also provided, and the performance of the estimators is illustrated by a numerical simulation example wherein a signal is estimated from correlated uncertain observations coming from two sensors with different uncertainty characteristics.

Guaranteed estimation of signals with bounded variances of derivatives

Consideration is given to the problem of signal estimation against the background of the white noise when the information about the signal is represented in the form of numerical characteristics such as constraints on the variance of the signal itself and variances of some its derivatives. We proposed a method to solve this problem using the technique of filtering in the time domain by minimizing the functional that is a combination of the H 2-norm of the transfer function from the measurement noise to the error of estimation and the H ?-norm of the transfer function from the generating noise to the error of estimation.

Robust estimation of signal and interference power in rayleigh fading channels

This paper deals with the problem of signal and interference power estimation in communication over wireless fading channels. In this work, a new class of estimators for joint estimation of signal and Gaussian interference variance is proposed. Our study includes developing a unified framework that covers the design and performance analysis of the estimators. The estimators addressed in this paper, namely maximum likelihood, minimum variance unbiased, best linear unbiased and sub-space estimators, require knowledge of eigenvectors and eigenvalues of the channel autocorrelation matrix. To relax this requirement, a tracking mechanism for least-squares estimation of the channel eigen-space is devised. Several aspects of the statistical characteristics of the resulting estimators are presented. As a salient feature, the proposed methods are suitably applicable to estimation of signal and interference power in wideband code division multiple access (WCDMA) used in third generation (3G) mobile wireless communication systems

Blind signal estimation in conjugate signal models with application to I/Q imbalance compensation

This letter addresses the blind signal estimation problem in the so-called conjugate signal model, where the observed signal is a linear combination of the desired signal and its complex conjugate. It will be shown that blind signal recovery in this kind of signal model is feasible using only the second-order statistics of the observed signal, under the assumption of circular or proper complex signals. Furthermore, one practical example application in the field of communications receiver signal processing will be given, where the image signal interference caused by amplitude and phase mismatches of the receiver analog branches is digitally attenuated. In addition to the analytical results and practical implementation algorithms, the efficiency of the proposed estimation concepts in the digital image rejection application is evaluated using computer simulations, showing impressive performance results.

Distributed computation of averages over ad hoc networks

In this paper, we develop algorithms for distributed computation of averages of the node data over networks with arbitrary but fixed connectivity. The algorithms we develop are linear dynamical systems that generate sequences of improving approximations to the desired computation at each node, via iterative processing and broadcasting. The algorithms are locally constructed at each node by exploiting only locally available and macroscopic information about the network topology. We present methods for optimizing the convergence rates of these algorithms to the desired computation, and evaluate their performance characteristics in the context of a problem of signal estimation from multinode noisy observations. By conducting simulations based on simple power-loss propagation models, we perform a preliminary comparison of the algorithms we develop against other types of distributed algorithms for computing averages, and identify transmit-power optimized algorithmic implementations as a function of the size and density of the sensor network.

Periodic signal analysis by maximum likelihood modeling of orbits of nonlinear ODEs

This paper treats a new approach to the problem of periodic signal estimation. The idea is to model the periodic signal as a function of the state of a second-order nonlinear ordinary differential equation (ODE). This is motivated by Poincare theory, which is useful for proving the existence of periodic orbits for second-order ODEs. The functions of the right-hand side of the nonlinear ODE are then parameterized by a multivariate polynomial in the states, where each term is multiplied by an unknown parameter. A maximum likelihood algorithm is developed for estimation of the unknown parameters, from the measured periodic signal. The approach is analyzed by derivation and solution of a system of ODEs that describes the evolution of the Cramer–Rao bound over time. This allows the theoretically achievable accuracy of the proposed method to be assessed in the ideal case where the signals can be exactly described by the imposed model. The proposed methodology reduces the number of estimated unknowns, at least in cases where the actual signal generation resembles that of the imposed model. This in turn is expected to result in an improved accuracy of the estimated parameters.

GRADIENT BASED METHODS: FUNCTIONAL VS PARAMETRIC FORMS

Reproducing kernel Hilbert spaces (RKHS) provide a unified framework for the solution of a number of function approximation and signal estimation problems. A significant problem with RKHS methods for real applications is the poor scaling properties of the algorithms with the number of data. It is therefore often necessary to use iterative algorithms. Steepest descent and conjugate gradient solutions for approximation in RKHS are presented in this paper. Four different approaches are described and compared on a benchmark system identification problem.

Linear estimation for discrete systems with uncertain observations: an application to the correction of declared incomes in inquiry

A new algorithm is derived for estimating the state of discrete systems with uncertain observations in which the state and measurement noises are correlated on a finite time interval. At the moment, the estimation problem of signals in systems with uncertain observations is seen as important research topic in the area of the detection and estimation of problems for communication systems. In this paper we propose an application in the economic field, specifically, we assume that declared incomes obtained through inquiry can be corrected using the new estimation algorithm presented in this paper.