Norm Minimization Criterion Research Articles

An Iteratively Reweighted Instrumental-Variable Estimator for Robust 3-D AOA Localization in Impulsive Noise

This paper considers the problem of robust three-dimensional (3-D) angle-of-arrival (AOA) source localization in the presence of impulsive α-stable noise based on the I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm minimization criterion. The iteratively reweighted least-squares algorithm (IRLS) is a well-known technique for solving I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm minimization with the desirable global convergence property. Adopting the IRLS for 3-D AOA localization requires nonlinear-to-pseudolinear transformation of azimuth and elevation angle measurement equations, thus resulting in a new variant of the IRLS, called the iteratively reweighted pseudolinear least-squares estimator (IRPLE). Unfortunately, there exists correlation between the measurement matrix and noise vector in the pseudolinear measurement equations, which consequently makes the IRPLE biased. To counter the bias problem of the IRPLE, a new iteratively reweighted instrumental-variable estimator (IRIVE) is proposed based on the exploitation of instrumental variables. The IRIVE is analytically shown to achieve the theoretical covariance of the general least I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm estimation. Extensive simulation studies are presented to demonstrate the performance advantages of the IRIVE over the IRPLE as well as other existing least-squares and least I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm estimators. The IRIVE is observed to produce nearly unbiased estimates with mean squared error performance very close to the Cramér-Rao lower bound.

Bayesian maximum entropy and data fusion for processing qualitative data: theory and application for crowdsourced cropland occurrences in Ethiopia

Categorical data play an important role in a wide variety of spatial applications, while modeling and predicting this type of statistical variable has proved to be complex in many cases. Among other possible approaches, the Bayesian maximum entropy methodology has been developed and advocated for this goal and has been successfully applied in various spatial prediction problems. This approach aims at building a multivariate probability table from bivariate probability functions used as constraints that need to be fulfilled, in order to compute a posterior conditional distribution that accounts for hard or soft information sources. In this paper, our goal is to generalize further the theoretical results in order to account for a much wider type of information source, such as probability inequalities. We first show how the maximum entropy principle can be implemented efficiently using a linear iterative approximation based on a minimum norm criterion, where the minimum norm solution is obtained at each step from simple matrix operations that converges to the requested maximum entropy solution. Based on this result, we show then how the maximum entropy problem can be related to the more general minimum divergence problem, which might involve equality and inequality constraints and which can be solved based on iterated minimum norm solutions. This allows us to account for a much larger panel of information types, where more qualitative information, such as probability inequalities can be used. When combined with a Bayesian data fusion approach, this approach deals with the case of potentially conflicting information that is available. Although the theoretical results presented in this paper can be applied to any study (spatial or non-spatial) involving categorical data in general, the results are illustrated in a spatial context where the goal is to predict at best the occurrence of cultivated land in Ethiopia based on crowdsourced information. The results emphasize the benefit of the methodology, which integrates conflicting information and provides a spatially exhaustive map of these occurrence classes over the whole country.

Nonlinear Gaussian mixture phd filter with an H∞ criterion

This paper is devoted to the problem of multitarget tracking with nonlinear models and uncertain noise statistics in the framework of random finite sets. Based on the linear approximation strategy, a robust closed-form solution to the probability hypothesis density recursion is proposed in terms of an H∞ norm minimization criterion. This idea is extended to develop another analytic implementation using the unscented transform technique. Simulations using the proposed approach are also presented.

Sun-Direction Estimation Using a Partially Underdetermined Set of Coarse Sun Sensors

A comparison of different methods to estimate the sun-direction vector using a partially underdetermined set of cosine-type coarse sun sensors (CSS), while simultaneously controlling the attitude towards a power-positive orientation, is presented. CSS are commonly used in performing power-positive sun-pointing and are attractive due to their relative inexpensiveness, small size, and reduced power consumption. For this study only CSS and rate gyro measurements are available, and the sensor configuration does not provide global triple coverage required for a unique sun-direction calculation. The methods investigated include a vector average method, a combination of least squares and minimum norm criteria, and an extended Kalman filter approach. All cases are formulated such that precise ground calibration of the CSS is not required. Despite significant biases in the state dynamics and measurement models, Monte Carlo simulations show that an extended Kalman filter approach, despite the underdetermined sensor coverage, can provide degree-level accuracy of the sun-direction vector both with and without a control algorithm running simultaneously. If no rate gyro measurements are available, and rates are partially estimated from CSS, the EKF performance degrades as expected, but is still able to achieve better than 10∘ accuracy using only CSS measurements.

Sea Clutter Texture Estimation: Exploiting Decorrelation and Cyclostationarity

In recent work sea clutter has been modeled as the product of two components. The first one, referred to as speckle, is modeled as a stationary Gaussian process. It is characterized by a short correlation time. The second component, referred to as texture, is modeled as a stationary or cyclostationary process. It is characterized by a long correlation time. Two approaches for the estimation of the texture are introduced here. The first approach involves the correlation properties of texture and speckle. The texture spectrum is modeled as an autoregressive (AR) process, while the texture range profile within one pulse repetition interval (PRI) is identified by combining the AR estimation of the sea clutter sample auto-covariance with the empirical orthogonal functions (EOF) analysis. The second approach involves a mixed l2-l1 norm minimization criterion to account for the sparse harmonic structure of the texture, considered herein as a cyclostationary process within multiple coherent processing intervals (CPI).

Recursive estimation of three-dimensional unmanned aerial vehicle motion and structure based on the L∞-norm

This article presents a non-linear filtering framework to estimate three-dimensional motion and structure from a stream of images acquired by a monocular camera. Interest in this article is related more specifically to the case where the camera is onboard an unmanned aerial vehicle. Although there have been numerous attempts to solve the problem stated above, most formulations were based on the L2-norm, mainly represented by the extended Kalman filter (EKF). Instead, a new approach based on the L∞-norm minimization criterion is developed. Unlike former methods, framework described in this article allows better treatment of the linearization of the perspective projection function that is associated with inherent errors in the EKF solution and can lead to severely degraded performance. Moreover, the L∞ criterion does not assume Gaussianity or whiteness of the noises providing an elegant solution for the problem of biased measurements. Results on synthetic and real aerial imagery demonstrate the findings.

Facial Recognition and Destiny Foreseeing for Specified Persons Using Fuzzy Classification Technique

The purpose of this paper is to accomplish facial recognition and destiny foreseeing in real-time for a specified person using fuzzy classification technique. This system uses CCD camera to take a picture of a specified person in an appropriate distance, and then uses a skin color detection method to extract the facial area by separating skin color scope. After the human face is searched, we locate the facial contour by using the ellipse template method. Find out the locations of eye and lip on the human face, and then to get the complete shape of eye and lip separately by using image processing technique and morphology. In this research, we classify the sample template into some classes by using fuzzy classification technique in advance to accelerate real-time task of the facial recognition, 3D face modeling and destiny foreseeing. Afterward, we apply the-Norm/-Norm minimization criterion to calculate the certificate degree of the recognized face and estimated destiny.

An inverse model for the analysis of the Venice lagoon food web

A steady-state model of the Venice lagoon food web was constructed, based on a comprehensive set of data, which were collected in the years 2001–2005. Energy flows were estimated by means of an inverse methodology of constrained optimization based on the Minimum Norm criterion, i.e. on the minimization of both the sum of squares of the residuals and of the sum of squares of energy flows. The solution was constrained by a set inequalities, which were derived from general eco-physiological knowledge and site specific data on energy flows. The trophic network was represented by thirty-two nodes, including single-species compartments for the species of high economical or ecological relevance. Mass balance equations were weighted, in order to obtain meaningful results in presence of large differences, up to 5 orders of magnitude, among biomasses. A perturbation technique was applied, with the purpose of reducing the risk of finding solutions heavily affected by the set of constraints and of obtaining a more robust representation of the energy flows. The main patterns of energy flow are consistent with those obtained in previous attempts at modelling the Venice lagoon food web. Micro- and macro-phytobenthos account for the largest fraction of the primary production. Energy is then transferred towards higher trophic levels by means of two main pathways: the recycling of dead biomass through the detritus compartment and the direct consumption by grazers. The first pathway is the most important and accounts for approximately two/thirds of the energy transferred to the second trophic level.

A Penalty Interpretation for the Lagrange Multiplier Fields in Incompressible Multipolar Elasticity Theory

In a recent paper we considered the characterization of the incompressibility constraint for multipolar hyperelastic materials. An existence theorem was given for the associated two Lagrange multiplier fields, representative of the stress and “hyper-stress” constraint reactions, but a congenital non-uniqueness in the splitting of these constraint reactions was encountered. Based upon purely mathematical arguments (representation theorems for functionals defined on Sobolev spaces), a strategy was advanced in order to overcome such indeterminacy. This consisted in selecting, among all possible choices, the unique pair of fields that minimized the appropriately defined norm. Here, we provide a physical justification for the so-called “minimum norm criterion” by interpreting incompressibility through the limit of a sequence of auxiliary minimum problems where changes in volume are progressively penalized by a “penalty term” which is added to the potential energy. The idea is known as the penalty method in the area of numerical analysis. Through the notion of a “modified Lagrangian”, a one-to-one correspondence is established between the solution of each penalty problem in the sequence and an approximation to the two Lagrange multiplier fields for the original constrained problem. In fact, a major effect of the penalty term is that it brings into focus the underlying presence of the constraint manifold of incompressibility as an “attractor” and the “shape” of this manifold identifies a “direction” in which the sequence of approximations approaches its limit. Ultimately, the approximation converges to one and only one choice. We find that the unique limiting Lagrange multiplier fields must necessarily minimize the same norm that was introduced adscititiously in our aforementioned recent paper, but there only as a purely mathematical scheme. This provides justification for the “minimum norm criterion” as a suitable procedure for sorting out the constraint reaction contributions to stress and hyperstress in incompressible multipolar theory.

Quadratic Synthesis of Active Controls for a Quarter-Car Model

The design of active vehicle suspensions with integral constraints to control the response of a vehicle traversing a road is considered. The problem is initially formulated in the linear quadratic regulator (LQR) framework with full-state feedback. Alternate formulations based on optimal output feedback (OOFB) and the minimum norm criterion (MNC) approach in the absence of complete state information are then presented. A general expression for the required optimal value of the control force based on easily measurable feedback quantities is developed. To reduce the effect of the body jerk, the high rate of change of actuator control force is penalized by adding a roll-off prefilter to the control. Results based on LQR, OOFB, and MNC are compared, and it is shown that the OOFB and MNC give performances as effective as the full-state feedback without the need to measure the tire deflection. The effectiveness of the roll-off prefilter in reducing the body jerk is demonstrated in an example problem.

Robust extended Kalman filtering

Linearization errors inherent in the specification of an extended Kalman filter (EKF) can severely degrade its performance. This correspondence presents a new approach to the robust design of a discrete-time EKF by application of the robust linear design methods based on the H/sub /spl infin// norm minimization criterion. The results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications.

Interpolation of Convex Scattered Data in R3 Based upon an Edge Convex Minimum Norm Network

In this paper a characterization of the optimal (using the minimum norm criterion) interpolant, convex along the edges of a triangulation, usin data at the vertices is obtained. We thereby generalize results obtained by Nielson for the unconstrained case.

Properties of the FIR-ALE Structure

In this paper, results from the literature on sub-space methods are used to establish some properties of the FIR-ALE structure when the input consists of p real sinusoids in white noise. The low rank property of the covariance matrix of the sinusoids is used to show that the Wiener-Hopf solution is only dependent on the 2p dominant eigenvalues of the covariance matrix. This in turn results in the convergence of the LMS algorithm for the zero initial condition to depend on the dominant 2p eigenvalues, implying that the convergence is improved compared to the general case. Also it is shown that when a filter of length L much larger than 2p is used, the parameter sensitivity is fairly low. The low parameter sensitivity is traced to the minimum norm characterization of the solution in the noise free case. The minimum-norm criteria also turns out to be a useful in selecting an optimum value for the decorrelation delay Δ.

Analytic minimum-norm solution for rate coordination in redundant manipulators

In this article, we present a novel method that results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based upon a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that, for any spatial manipulator with 1, 2, or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. An example of the analytic formulation is given for a 3R planar case, substantiated with simulation results. The behavior of this algorithm in nonredundant and near singular situations is also discussed. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudoinverse arrived at in the course of the development is also presented. © 1992 John Wiley & Sons, Inc.

High-resolution multiple target angle tracking

An approach to high-resolution multiple-target-angle tracking that uses the output of an array of sensors is presented. The results of direction-of-arrival estimation by eigenstructure analysis are extended to derive a recursive procedure for tracking moving sources. This procedure involves recursive eigenvalue decomposition and a zero-tracking algorithm, using the coefficient derived from the minimum-norm criterion. The algorithm has superresolution capability in that a pair of closely spaced target angles can be resolved and tracked even though the angular separation between them is less than the reciprocal of the aperture size. Simulation results verify that the algorithm works well in tracking multiple-target sources.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A norm minimization criterion for the inversion of earthquake ground motion

SUMMARY A method is presented for obtaining a unique temporal and spatial slip distribution on a prescribed fault plane from inversion of earthquake ground motion. The inverse problem is formulated in the frcquency domain where the spatial distribution of slip is found for a set of frequency values. The time dependence of slip is then recovered by Fourier synthesis. A new norm minimization condition is presented, based upon the scalar wave equation, which produces the model having the most nearly constant rupture velocity and the most nearly constant slip amplitude distribution. Although a preferred rupture velocity is specified, no assumption on the geometrical shape of the rupture front is made. While time-domain inversion methods prescribe the hypocentre location, source time function, and rupture front geometry, the frequency-domain method actually solves for these important source properties. The wave equation minimization condition is tested using synthetic data from Haskell-type dislocation models in a homogeneous full-space. These solutions are compared with the traditional two-norm minimization solutions. The two-norm minimization models exhibit a strong dependence on the recording array geometry. The wave equation minimization models are smoother and devoid of many of the spurious features that are not actually required by the data but that, nevertheless, appear in the two-norm minimization models. The results of numerical experiments indicate that the solution need not conform to the specified rupture velocity value used in the construction of the wave equation norm if the data are sufficient to warrant otherwise.

On the functional optimization of a certain class of nonstationary spatial functions

Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail.