Least squares pattern synthesis for conformal arrays

The problem of synthesising low sidelobe beams from conformal arrays consisting of few elements and large radius of curvature is addressed. Experimental results are presented for a 12 element array of linearly polarised elements forming a faceted array with radius of curvature 1.5 m. It is shown that by calculation of an aperture correcting matrix, sidelobe levels of 40 dB can be obtained from the array by application of conventional linear array Taylor weights. Beam steering is achieved by aperture phase tapering while low sidelobe levels are maintained     

Least squares order-recursive lattice smoothers

Conventional least squares order-recursive lattice (LSORL) filters use present and past data values to estimate the present value of a signal. This paper introduces LSORL smoothers which use past, present and future data for that purpose. Except for an overall delay needed for physical realization, LSORL smoothers can substantially outperform LSORL filters while retaining all the advantages of an order-recursive structure     

Least squares restoration of multichannel images

Multichannel restoration using both within- and between-channel deterministic information is considered. A multichannel image is a set of image planes that exhibit cross-plane similarity. Existing optimal restoration filters for single-plane images yield suboptimal results when applied to multichannel images, since between-channel information is not utilized. Multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches. A geometric interpretation of the estimates of both filters is given. Color images (three-channel imagery with red, green, and blue components) are considered. Constraints that capture the within- and between-channel properties of color images are developed. Issues associated with the computation of the two estimates are addressed. A spatially adaptive, multichannel least squares filter that utilizes local within- and between-channel image properties is proposed. Experiments using color images are described     

Least squares algorithm for region-of-interest evaluation in emission tomography

An accurate model of the nonstationary geometrical response of a camera-collimator system is discussed. The algorithm is compared to three other algorithms that are specialized for region-of-interest evaluation, as well as to the conventional method for summing the reconstructed quantity over the regions of interest. For noise-free data and for regions of accurate shape, least-squares estimates were unbiased within roundoff errors. For noisy data, estimates were still unbiased but precision worsened for regions smaller than resolution: simulating typical statistics of brain perfusion studies performed with a collimated camera, the estimated standard deviation for a 1-cm-square region was 10% with an ultra-high-resolution collimator and 7% with a low-energy all-purpose collimator. Conventional region-of-interest estimates show comparable precision but are heavily biased if filtered backprojection is used for image reconstruction. Using the conjugate-gradient iterative algorithm and the model of nonstationary geometrical response, bias of estimates decreased on increasing the number of iterations, but precision worsened, thus achieving an estimated standard deviation of more than 25% for the same 1-cm region.     

Least mean squares algorithm for fractionally spaced blind channelestimation

The authors consider the problem of blind estimation and equalisation of digital communication finite impulse response (FIR) channels using fractionally spaced samples. The system input is assumed to be a deterministic but unknown data sequence. Exploiting the periodicity of the transmitted data sequence in the frequency domain in the noise free case, it is shown that it is possible to form a linear system in terms of the unknown channel impulse response. In the presence of noise, a least mean squares (LMS) criterion is used to resolve the channel. The resulting algorithm has an appealing interpretation and can be considered as a single channel counterpart of the multi-channel cross-relation (CR) method. Finally, it is shown that the latter can be derived from the proposed algorithm     

Least squares adaptive antenna for angle of arrival estimation

The least squares formulation of an adaptive antenna is presented, which (with the aid of a calibration curve) may be used to estimate the angle of arrival in the presence of multipath as encountered in a low-angle tracking radar environment. A procedure (based on the Eckart-Young theorem) is proposed for improving the noise performance of the estimator.     

最小二乘与加权最小二乘空域矩阵滤波器设计

空域矩阵滤波器是一种新的信号处理技术,通过一个滤波矩阵与接收到的阵列数据相乘,可实现保留通带目标信号,抑制阻带干扰的目的.本文主要研究了最小二乘和加权最小二乘两类的空域矩阵滤波器.给出了空域滤波器设计基本原理,通过最优化问题得出了最优解.最小二乘空域矩阵滤波器是加权系数为1的加权加权最小二乘空域矩阵滤波器的特列.由加权最小二乘迭代仿真结果可以看出,迭代次数的增加使滤波器阻带响应极大值逐渐变小,可实现恒定阻带抑制效果,设计效率较高.     

Regularized fast recursive least squares algorithms for adaptivefiltering

Fast recursive least squares (FRLS) algorithms are developed by using factorization techniques which represent an alternative way to the geometrical projections approach or the matrix-partitioning-based derivations. The estimation problem is formulated within a regularization approach, and priors are used to achieve a regularized solution which presents better numerical stability properties than the conventional least squares one. The numerical complexity of the presented algorithms is explicitly related to the displacement rank of the a priori covariance matrix of the solution. It then varies between O(5m) and that of the slow RLS algorithms to update the Kalman gain vector, m being the order of the solution. An important advantage of the algorithms is that they admit a unified formulation such that the same equations may equally treat the prewindowed and the covariance cases independently from the used priors. The difference lies only in the involved numerical complexity, which is modified through a change of the dimensions of the intervening variables. Simulation results are given to illustrate the performances of these algorithms     

Efficient least squares adaptive algorithms for FIR transversalfiltering

A unified view of algorithms for adaptive transversal FIR filtering and system identification has been presented. Wiener filtering and stochastic approximation are the origins from which all the algorithms have been derived, via a suitable choice of iterative optimization schemes and appropriate design parameters. Following this philosophy, the LMS algorithm and its offspring have been presented and interpreted as stochastic approximations of iterative deterministic steepest descent optimization schemes. On the other hand, the RLS and the quasi-RLS algorithms, like the quasi-Newton, the FNTN, and the affine projection algorithm, have been derived as stochastic approximations of iterative deterministic Newton and quasi-Newton methods. Fast implementations of these methods have been discussed. Block-adaptive, and block-exact adaptive filtering have also been considered. The performance of the adaptive algorithms has been demonstrated by computer simulations     

A collaborative location model for cellular mobile position location

In cellular network, several Time Difference Of Arrival (TDOA) location algorithms can be applied to mobile position estimation. However, each algorithm has its own limitations and none of them is proved to be the most reliable one in different channel environments. In this paper Kleine-Ostmann‘s data fusion model is modified and a collaborative location model which incorporates position estimate of two TDOA location algorithms is proposed.Analysis and simulation show that more reliable and accurate mobile position estimation can be achieved based on this model.     

Least squares phase unwrapping in wavelet domain

Two-dimensional phase unwrapping is an important processing step in some coherent imaging applications. Least squares phase unwrapping is one of the robust techniques used to solve two-dimensional phase unwrapping problems. However, owing to its sparse structure, the convergence rate is very slow, and some practical methods have been applied to improve this condition. A new method for solving the least squares two-dimensional phase unwrapping problem is presented. This technique is based on the multiresolution representation of a linear system using the discrete wavelet transform. By applying the wavelet transform, the original system is decomposed into its coarse and fine resolution levels. Fast convergence in separate coarse resolution levels makes the overall system convergence very fast.     

Least squares approach to blind channel equalization

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm     

Least squares approach in measurement-dependent filtering for selective medical images

An image-processing method called measurement-dependent filtering has been introduced to improve the SNR (signal-to-noise ratio) of selective images produced by various medical imaging systems. The basic algorithm involves the combination of the low-frequency information of the selective image with the high-frequency information of a nonselective image. A spatially variant control function modulates the amount of high frequency to be added at each point. A least-mean-square (LMS) control function formed from two basis images, namely the high-passed versions of the nonselective image (M(b)) and the selective image (S(b)), is introduced. The original algorithm is now viewed as a two-stage filtering method, including the low-pass filtering noise reduction and least squares filtering for the edge restoration. An appropriate linear transformation is used to convert the original basis images M(b) and S(b) into a new pair with orthogonal noise. This allows the implementation of the LMS and control function with practically obtainable a priori knowledge.     

Regularized fast recursive least squares algorithms for finitememory filtering

Novel fast recursive least squares algorithms are developed for finite memory filtering, by using a sliding data window. These algorithms allow the use of statistical priors about the solution, and they maintain a balance between a priori and data information. They are well suited for computing a regularized solution, which has better numerical stability properties than the conventional least squares solution. The algorithms have a general matrix formulation, such that the same equations are suitable for the prewindowed as well as the covariance case, regardless of the a priori information used. Only the initialization step and the numerical complexity change through the dimensions of the intervening matrix variables. The lower bound of O (16m) is achieved in the prewindowed case when the estimated coefficients are assumed to be uncorrelated, m being the order of the estimated model. It is shown that a saving of 2m multiplications per recursion can always be obtained. The lower bound of the resulting numerical complexity becomes O(14m ), but then the general matrix formulation is lost     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Least squares subspace projection approach to mixed pixelclassification for hyperspectral images

An orthogonal subspace projection (OSP) method using linear mixture modeling was recently explored in hyperspectral image classification and has shown promise in signature detection, discrimination, and classification. In this paper, the OSP is revisited and extended by three unconstrained least squares subspace projection approaches, called signature space OSP, target signature space OSP, and oblique subspace projection, where the abundances of spectral signatures are not known a priori but need to be estimated, a situation to which the OSP cannot be directly applied. The proposed three subspace projection methods can be used not only to estimate signature abundance, but also to classify a target signature at subpixel scale so as to achieve subpixel detection. As a result, they can be viewed as a posteriori OSP as opposed to OSP, which can be thought of as a priori OSP. In order to evaluate these three approaches, their associated least squares estimation errors are cast as a signal detection problem ill the framework of the Neyman-Pearson detection theory so that the effectiveness of their generated classifiers can be measured by receiver operating characteristics (ROC) analysis. All results are demonstrated by computer simulations and Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data     

Least squares decoding in binomial frequency division multiplexing

This paper proposes a method that can reduce the complexity of a system matrix by analyzing the characteristics of a pseudoinverse matrix to receive a binomial frequency division multiplexing (BFDM) signal and decode it using the least squares (LS) method. The system matrix of BFDM can be expressed as a band matrix, and as this matrix contains many zeros, its amount of calculation when generating a transmission signal is quite small. The LS solution can be obtained by multiplying the received signal by the pseudoinverse matrix of the system matrix. The singular value decomposition of the system matrix indicates that the pseudoinverse matrix is a band matrix. The signal-to-interference ratio is obtained from their eigenvalues. Meanwhile, entries that do not contribute to signal generation are erased to enhance calculation efficiency. We decode the received signal using the pseudoinverse matrix and the removed pseudoinverse matrix to obtain the bit error rate performance and to analyze the difference.     

Least squares twin support vector machine withasymmetric squared loss

For classification problems, the traditional least squares twin support vector machine(LSTSVM) generates two nonparallel hyperplanes directly by solving two systems of linear equations instead of a pair of quadratic programming problems(QPPs), which makes LSTSVM much faster than the original TSVM. But the standard LSTSVM adopting quadratic loss measured by the minimal distance is sensitive to noise and unstable to re-sampling. To overcome this problem, the expectile distance is taken into consid...     

Least squares based and gradient based iterative identification for Wiener nonlinear systems

This paper derives a least squares-based and a gradient-based iterative identification algorithms for Wiener nonlinear systems. These methods separate one bilinear cost function into two linear cost functions, estimating directly the parameters of Wiener systems without re-parameterization to generate redundant estimates. The simulation results confirm that the proposed two algorithms are valid and the least squares-based iterative algorithm has faster convergence rates than the gradient-based iterative algorithm.     

Downlink adaptive array algorithms for cellular mobile communications

The capacity of wireless downlink communication to mobile receivers in a dense urban environment is limited primarily by co-channel interference. Downlink adaptive arrays can be used to mitigate this limitation by maximizing the power transmitted to desired in-cell mobiles in the reference cell while minimizing power to co-channel mobiles in neighboring cells. This is accomplished by using uplink measurements to estimate downlink covariance matrices and then solving a generalized eigenvalue problem. Several algorithms are proposed to adaptively estimate the optimal solution and are evaluated using a simplified signal model that allows efficient deterministic performance calculations.