Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few. Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf) which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest. Motivated by the widespread and practical need to assess the performance of a mismatched estimator, the goal of this paper is to help to bring attention to the main theoretical findings on estimation theory, and in particular on lower bounds under model misspecification, that have been published in the statistical and econometrical literature in the last fifty years. Secondly, some applications are discussed to illustrate the broad range of areas and problems to which this framework extends, and consequently the numerous opportunities available for SP researchers.Comment: To appear in the IEEE Signal Processing Magazin

Through-the-Wall Imaging and Multipath Exploitation

We consider the problem of using electromagnetic sensing to estimate targets in complex environments, such as when they are hidden behind walls and other opaque objects. The often unknown electromagnetic interactions between the target and the surrounding area, make the problem challenging. To improve our results, we exploit information in the multipath of the objects surrounding both the target and the sensors. First, we estimate building layouts by using the jump-diffusion algorithm and employing prior knowledge about typical building layouts. We also take advantage of a detailed physical model that captures the scattering by the inner walls and efficiently utilizes the frequency bandwidth. We then localize targets hidden behind reinforced concrete walls. The sensing signals reflected from the targets are significantly distorted and attenuated by the embedded metal bars. Using the surface formulation of the method of moments, we model the response of the reinforced walls, and incorporate their transmission coefficients into the beamforming method to achieve better estimation accuracy. In a related effort, we utilize the sparsity constraint to improve electromagnetic imaging of hidden conducting targets, assuming that a set of equivalent sources can be substituted for the targets. We derive a linear measurement model and employ l1 regularization to identify the equivalent sources in the vicinity of the target surfaces. The proposed inverse method reconstructs the target shape in one or two steps, using single-frequency data. Our results are experimentally verified. Finally, we exploit the multipath from sensor-array platforms to facilitate direction finding. This in contrast to the usual approach, which utilizes the scattering close to the targets. We analyze the effect of the multipath in a statistical signal processing framework, and compute the Cramer-Rao bound to obtain the system resolution. We conduct experiments on a simple array platform to support our theoretical approach

An Approximate MSE Expression for Maximum Likelihood and Other Implicitly Defined Estimators of Non-Random Parameters (extended version)

An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected cost/reward function as the parameter estimate. The maximum likelihood (ML) and the least squares estimators are among the well known examples of this class. In this paper, an exact MSE expression for implicitly defined estimators with a symmetric and unimodal objective function is given. It is shown that the expression reduces to the Cramer-Rao lower bound (CRLB) and misspecified CRLB in the large sample size regime for ML and misspecified ML estimation, respectively. The expression is shown to yield the Ziv-Zakai bound (without the valley filling function) when it is used in a Bayesian setting, that is, when an a-priori distribution is assigned to the unknown parameter. In addition, extension of the suggested expression to the case of nuisance parameters is studied and some approximations are given to ease the computations for this case. Numerical results indicate that the suggested MSE expression not only predicts the estimator performance in the asymptotic region; but it is also applicable for the threshold region analysis, even for IDEs whose objective functions do not satisfy the symmetry and unimodality assumptions. Advantages of the suggested MSE expression are its conceptual simplicity and its relatively straightforward numerical calculation due to the reduction of the estimation problem to a binary hypothesis testing problem, similar to the usage of Ziv-Zakai bounds in random parameter estimation problems

Direction Finding Estimators of Cyclostationary Signals in Array Processing for Microwave Power Transmission

A solar power satellite is paid attention to as a clean, inexhaustible large- scale base-load power supply. The following technology related to beam control is used: A pilot signal is sent from the power receiving site and after direction of arrival estimation the beam is directed back to the earth by same direction. A novel direction-finding algorithm based on linear prediction technique for exploiting cyclostationary statistical information (spatial and temporal) is explored. Many modulated communication signals exhibit a cyclostationarity (or periodic correlation) property, corresponding to the underlying periodicity arising from carrier frequencies or baud rates. The problem was solved by using both cyclic second-order statistics and cyclic higher-order statistics. By evaluating the corresponding cyclic statistics of the received data at certain cycle frequencies, we can extract the cyclic correlations of only signals with the same cycle frequency and null out the cyclic correlations of stationary additive noise and all other co-channel interferences with different cycle frequencies. Thus, the signal detection capability can be significantly improved. The proposed algorithms employ cyclic higher-order statistics of the array output and suppress additive Gaussian noise of unknown spectral content, even when the noise shares common cycle frequencies with the non-Gaussian signals of interest. The proposed method completely exploits temporal information (multiple lag ), and also can correctly estimate direction of arrival of desired signals by suppressing undesired signals. Our approach was generalized over direction of arrival estimation of cyclostationary coherent signals. In this paper, we propose a new approach for exploiting cyclostationarity that seems to be more advanced in comparison with the other existing direction finding algorithms

Compressive Sensing and Time Reversal Beamforming Approaches for Ultrasound Imaging

The objective of this thesis is to develop a novel beamforming technique for ultrasound machines that enables field reconstruction at sampling rates much lower than the Nyquist rate. In our simulations, we use Field II, a MATLAB based program for simulating transducer fields and models of biological tissues for imaging applications. Field II is capable of generating the emitted and pulse-echo fields for a large number of transducers configurations, including linear, circular, and rectangular arrays. Once the ultrasound field is determined, the proposed imaging technique is applied to the received signals to reconstruct the image for reference biological tissues. Applying different adaptive beamforming techniques, including the delay and sum (DAS) and Capon algorithms, the received signals from Field II simulation program are used to render the ultrasound images. A second goal of the thesis is to apply compressive sensing (CS) on received signals to reconstruct full-length signals from a reduced number of samples. A third goal is to couple the principal of time reversal (TR) with compressive sensing to extend the CAPON beamformer for reconstructing images of biological tissues at low sampling frequencies in rich multipath environments. The outputs of compressive sensing and CAPON-based algorithms, alone or in conjunction with each other, are severely degraded in such environments. Through numerical simulations, I illustrate an enhancement in reconstructed quality of images depicting biological tissues with my time-reversal based compressive sensing, CAPON approach

Low-complexity three-dimensional AOA-cross geometric center localization methods via multi-UAV network

The angle of arrival (AOA) is widely used to locate a wireless signal emitter in unmanned aerial vehicle (UAV) localization. Compared with received signal strength (RSS) and time of arrival (TOA), AOA has higher accuracy and is not sensitive to the time synchronization of the distributed sensors. However, there are few works focusing on three-dimensional (3-D) scenarios. Furthermore, although the maximum likelihood estimator (MLE) has a relatively high performance, its computational complexity is ultra-high. Therefore, it is hard to employ it in practical applications. This paper proposed two center of inscribed sphere-based methods for 3-D AOA positioning via multiple UAVs. The first method could estimate the source position and angle measurement noise at the same time by seeking the center of an inscribed sphere, called the CIS. Firstly, every sensor measures two angles, the azimuth angle and the elevation angle. Based on that, two planes are constructed. Then, the estimated values of the source position and the angle noise are achieved by seeking the center and radius of the corresponding inscribed sphere. Deleting the estimation of the radius, the second algorithm, called MSD-LS, is born. It is not able to estimate angle noise but has lower computational complexity. Theoretical analysis and simulation results show that proposed methods could approach the Cramér–Rao lower bound (CRLB) and have lower complexity than the MLE

Performance evaluation and waveform design for MIMO radar

Multiple-input multiple-output (MIMO) radar has been receiving increasing attention in recent years due to the dramatic advantages offered by MIMO systems in communications. The amount of energy reflected from a common radar target varies considerably with the observation angle, and these scintillations may cause signal fading which severely degrades the performance of conventional radars. MIMO radar with widely spaced antennas is able to view several aspects of a target simultaneously, which realizes a spatial diversity gain to overcome the target scintillation problem, leading to significantly enhanced system performance. Building on the initial studies presented in the literature, MIMO radar is investigated in detail in this thesis. First of all, a finite scatterers model is proposed, based on which the target detection performance of a MIMO radar system with arbitrary array-target configurations is evaluated and analyzed. A MIMO radar involving a realistic target is also set up, whose simulation results corroborate the conclusions drawn based on theoretical target models, validating in a practical setting the improvements in detection performance brought in by the MIMO radar configuration. Next, a hybrid bistatic radar is introduced, which combines the phased-array and MIMO radar configurations to take advantage of both coherent processing gain and spatial diversity gain simultaneously. The target detection performance is first assessed, followed by the evaluation of the direction finding performance, i.e., performance of estimating angle of arrival as well as angel of departure. The presented theoretical expressions can be used to select the best architecture for a radar system, particularly when the total number of antennas is fixed. Finally, a novel two phase radar scheme involving signal retransmission is studied. It is based on the time-reversal (TR) detection and is investigated to improve the detection performance of a wideband MIMO radar or sonar system. Three detectors demanding various amounts of a priori information are developed, whose performance is evaluated and compared. Three schemes are proposed to design the retransmitted waveform with constraints on the transmitted signal power, further enhancing the detection performance with respect to the TR approach