Bias compensation for the bearings-only pseudolinear target track estimator

The bearings-only pseudolinear target track estimator is known to suffer from severe bias problems. This paper presents a bias analysis for the pseudolinear estimator and develops a method of bias compensation, resulting in a closed-form reduced-bias pseudolinear estimator. The reduced-bias estimator is then incorporated into an instrumental variable estimator to produce asymptotically unbiased target motion parameter estimates. Unlike batch iterative estimators, the proposed instrumental variable estimator has a closed-from solution and therefore avoids the convergence problems associated with iterative estimators. The performance of the proposed instrumental variable estimator is illustrated by way of simulation examples and is shown to be almost identical to that of the computationally more demanding iterative maximum likelihood estimator.     

An asymptotically unbiased estimator for bearings-only and Doppler-bearing target motion analysis

Bearings-only (BO) and Doppler-bearing (DB) target motion analysis (TMA) attempt to obtain a target trajectory based on bearings and on Doppler and bearing measurements, respectively, from an observer to the target. The BO-TMA and DB-TMA problems are nontrivial because the measurement equations are nonlinearly related to the target location parameters. The pseudolinear formulation provides a linear estimator solution, but the resulting location estimate is biased. The instrumental variable method and the numerical maximum likelihood approach can eliminate the bias. Their convergence behavior, however, is not easy to control. This paper proposes an asymptotically unbiased estimator of the tracking problem. The proposed method applies least squares minimization on the pseudolinear equations with a quadratic constraint on the unknown parameters. The resulting estimator is shown to be solving the generalized eigenvalue problem. The proposed solution does not require initial guesses and does not have convergence problems. Sequential forms of the proposed algorithms for both BO-TMA and DB-TMA are derived. The sequential algorithms improve the estimation accuracy as a new measurement arrives and do not require generalized eigenvalue decomposition for solution update. The proposed estimator achieves the Cramer-Rao Lower Bound (CRLB) asymptotically for Gaussian noise before the thresholding effect occurs.     

伪线性主动段弹道估计方法

该文主要分析了星载被动传感器对目标的运动参数估计问题,它也是空间预警系统的关键技术之一。文中提出的伪线性测量-卡尔曼滤波(PM-KF)的弹道估计方法减小了测量方程非线性所带来的估计误差,较之EKF滤波有更好的估计精度。     

Some quick and efficient methods for bearing-only target motionanalysis

Batch processing estimation methods for a target's trajectory, assumed to be linear and uniform, based only on the observation of its bearings, are presented. First, the observer is assumed to have constant velocity, so that one can only estimate the target's motion, up to a multiplicative constant. This motion is parameterized by three bearings at three judiciously chosen times, and some simple, quick, yet highly efficient estimators for them are proposed. The case of an observer moving nonuniformly is then considered. A quadratic estimator that is similar to the pseudolinear estimator but does not have bias is introduced. For the case in which the observer's motion can be decomposed into a finite number of constant velocity segments, two sets of quasi-sufficient statistics that permit considerable saving in computation with no significant loss of efficiency are also introduced. Expressions for the covariance matrix of the estimators and for their Cramer-Rao bounds are provided     

Sensorless Control of Induction Machines by a New Neural Algorithm: The TLS EXIN Neuron

This paper proposes two speed observers for high-performance induction machine drives, both adopting an online adaptation law based on a new total least-squares (TLS) technique: the TLS EXIN neuron. The first is a model reference adaptive system (MRAS) observer with a neural adaptive integrator in the reference model and a neural adaptive model trained online by the TLS EXIN neuron. This observer, presented in a previous article of the authors, has been improved here in two aspects: first, the neural adaptive integrator has been modified to make its learning factor vary according to the reference speed of the drive, second, a neural adaptive model based on the modified Euler integration has been proposed to solve the discretization instability problem in field-weakening. The second observer is a new full-order adaptive one based on the state equations of the induction machine, where the speed is estimated by means of a TLS EXIN adaptation technique. Both these observers have been provided with an inverter nonlinearity compensation algorithm and with techniques for the online estimation of the stator resistance of the machine. Moreover, a thorough theoretical stability analysis has been developed for them both, with particular reference to the field-weakening region behavior for the TLS MRAS observer and to the regenerating mode at low speeds for the TLS adaptive observer. Both speed observers have been verified in numerical simulation and experimentally on a test setup, and have also been compared experimentally with the BPN MRAS observer, the classic adaptive observer and with an open-loop estimator. Results show that both proposed observers outperform all other three observers in every working condition, with the TLS adaptive observer resulting in a better performance than the TLS MRAS observer     

Exploring estimator bias-variance tradeoffs using the uniform CRbound

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that defines an “unachievable region” of the delta-sigma plane for a specified statistical model. In order to place an estimator on this plane for comparison with the delta-sigma tradeoff curve, the estimator variance, bias gradient, and bias gradient norm must be evaluated. We present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log-likelihood. We demonstrate the methods developed in this paper for linear Gaussian and nonlinear Poisson inverse problems     

频点自跟踪自适应频率估计器性能研究

基于二阶自适应陷波滤波器的频率估计器是工程上常用的单频信号频率估计器,其前提是参考信号相对输入信号频偏较小.随着频偏的增大,自适应频率估计的偏差和方差也随之增大.本文分析了自适应频率估计器的性能及频偏的影响,得出了自适应频率估计方差下限的公式及达到此下限的条件.提出了频点自跟踪自适应频率估计器.仿真与理论结果均表明相同条件下该估计器较自适应频率估计器明显减小了估计偏差和方差,在中等信噪比下估计方差可减小到自适应频率估计方差的百分之一.只要信噪比不甚低,频点自跟踪频率估计是无偏的且估计方差接近理论下限.     

Deconvolution estimation of motor unit conduction velocity distribution

A conduction velocity distribution (CVD) estimator that incorporates volume conductor modeling of the muscle voluntary response is introduced in this paper. The CVD estimates are obtained from two correlation functions, an autocorrelation and a cross, computed from myoelectric signal recorded at the skin surface. The performance of the proposed estimator is evaluated for simulated and experimental data. The study includes assessment of the estimator bias and standard deviation, as well as its sensitivity to errors in the model parameters. Simulations show its good performance in terms of estimator bias. A filtering technique also helps reduce its variance. However, the inaccuracy introduced in the estimation of model parameters considerably deteriorates the estimator performance.     

Pseudolinear estimation of fractionally integrated ARMA (ARFIMA)models with automotive application

A novel pseudolinear method for the estimation of fractionally integrated ARMA (ARFIMA) models that are capable of representing combined long- and short-term dependency, is introduced. The method is based on the relationship of the AR/MA parameters and the coefficients of the fractional power operator binomial series expansion with the model's inverse function. These lead to the formulation of a special-form regression problem that can be decomposed into a univariate nonlinear and a multivariate linear regression and may be thus tackled via a special pseudolinear procedure. This decomposition in turn leads to the elimination of the need for initial guess parameter values, drastic simplification in the detection and handling of potential local extrema problems, as well as computational simplicity. The method's strong consistency is established, whereas its performance characteristics are assessed via Monte Carlo experiments and comparisons with the maximum likelihood method. The pseudolinear method is also used for the ARFIMA modeling and prediction of power consumption in an experimental automobile fully active suspension system, the consumption of which is shown to exhibit long-term dependency. A comparison with ARMA/ARIMA type modeling is also made, and the obtained ARFIMA models are shown to achieve improved predictive performance at a drastically reduced parametric complexity     

The interior-point method for an optimal treatment of bias in trilateration location

This paper presents a new position-determination estimator for trilateration location. The proposed estimator takes the measurement bias into consideration and improves the location accuracy of a mobile location system. In case that a mobile station (MS) utilizes signals from a set of base stations for its location, the computed location is largely affected by nonline-of-sight (NLOS) error in signal propagation. A constrained optimization method in a three-stage estimation structure is proposed to estimate and eliminate the measurement bias contained in each pseudorange and mainly caused by the NLOS error. A linear observation model of the bias is formulated, and the interior-point optimization technique optimally estimates the bias by introducing a feasible range of the measurement bias. It is demonstrated that the new three-stage estimator successfully computes an accurate location of an MS in a realistic environment setting. The location accuracy of the proposed estimator is analyzed and compared with the existing methods through mathematical formulations and simulations. The proposed estimator efficiently mitigates the effect of a measurement bias and shows that the iterated least square (ILS) accuracy of 118 m [67% distance root-mean-square (DRMS)] can be improved to about 17 m in a typical urban environment.     

A new subspace identification algorithm for high-resolution DOA estimation

In this paper, we propose a new direction of arrival (DOA) estimator for sensor-array processing. The estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal-plus-interference model, which we develop in this paper. The estimator we propose is a signal subspace scaled MUSIC algorithm, which we call SSMUSIC. It is not a subspace weighted MUSIC, because the scaling depends on the eigenstructure of the estimated signal subspace. SSMUSIC has the advantage of simultaneously estimating the DOA and the power of each source. We employ a second-order perturbation analysis of the estimator and derive stochastic representations for its bias and squared-error. We compare the new DOA estimator with the MUSIC estimator, based on these representations. Numerical results demonstrate the superior performance of SSMUSIC relative to MUSIC and the validity of the perturbation results.     

Total least squares phased averaging and 3-D ESPRIT for jointazimuth-elevation-carrier estimation

The method of total least squares (TLS) phased averaging for high-performance subspace fitting in the three-dimensional (3-D) case of spectral estimation with 3-D ESPRIT is introduced and applied to the joint azimuth elevation-carrier estimation problem with two-dimensional (2-D) uniform rectangular arrays. The method is highly efficient computationally and is suitable for large arrays. Detailed computer experiments and comparisons are provided. For a 16×16 array of sensors and heavy noise, TLS phased-averaging 3-D ESPRIT exceeds the 3-D TLS unitary ESPRIT estimator by 300% in RMSE performance     

Whitening prefiltered TLS linear predictor for frequency estimation

A new total least squares (TLS) technique for linear prediction based on a whitening procedure is presented. This technique can solve the problems due to the bias inherent in the prefiltered TLS solution so as to give a good performance over a wide range of SNRs, thereby outperforming common TLS solutions     

Timing estimation for a filtered Poisson process in Gaussian noise

The problem of estimation of time shift of an inhomogeneous casually filtered Poisson process in the presence of additive Gaussian noise is discussed. Approximate expressions for the likelihood function, the MAP estimator, and the MMSE estimator that becomes increasingly accurate as the per-unit-time density of superimposed filter responses becomes small are obtained. The optimal MAP estimator takes the form of a cascade of linear and memoryless nonlinear components. For smooth point process intensities, the performance of the MAP estimator is studied via local bias and local variance. A rate distortion type lower bound on the MSE of any estimator of time delay is then derived by identification of a communications channel that accounts for the mapping from time delay to observation process. Results of numerical studies of estimator performance are presented. Based on the examples considered it is concluded: (1) the small-error MSE of the nonlinear MAP estimator can be significantly better than the small-error MSE of the optimal linear estimator: (2) the rate distortion lower bound can be significantly tighter than the Poisson limited bounds determined in previous studies     

Joint RSSD/AOA Source Localization: Bias Analysis and Asymptotically Efficient Estimator

In this paper we study blind source localization problem based on the joint received signal strength difference (RSSD) and angle of arrival (AOA) measurements with unknown transmit power of source. Since RSSD and AOA measurements are uncorrelated, combining two methods leads to a better performance for source localization. This paper focus on the pseudo linear estimator (PLE) with a closed-form and low complexity solution. One of the main limitations in this estimator is the bias created from the correlation between system matrix and error vector, which is not vanished by increasing the number of measurements. To overcome this problem first, we present a bias compensated PLE using the closed instrumental variable (IV). Then, for improving the localization performance a weighting IV estimator (WIV) is presented. Finally, for achieving the Cramer–Rao lower bound (CRLB) an improved WIV (IWIV) estimator is used based on the known relation between the estimated parameters of WIV estimator. The proposed IWIV estimator is proved to be asymptotically efficient (i.e., obtaining zero bias and the Cramer–Rao lower bound). Numerical simulations also verify the theoretical development and show source localization using hybrid information RSSD/AOA has a superior performance than RSSD and AOA solely.

     

Low bias frequency domain SNR estimator using DCT in mobile fading channels

The authors analyze the cause of bias in a fast Fourier transform (FFT)-based frequency domain signal-to-noise ratio (SNR) estimator by deriving the upper bound of the bias. The analysis is then used to propose a new frequency domain estimator using discrete cosine transform (DCT), which has lower bias. In addition, a criterion is proposed for use when maximum Doppler frequency information is available; it is based on the derived upper bound and can be used to improve the mean squared error (MSE) performance of the proposed DCT-based estimator. Simulation results show that the proposed estimator reduces the MSE remarkably by diminishing the bias.     

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting any approximation about the observation statistics or the a priori distribution of the parameters. The proposed solution is obtained minimizing the estimator variance subject to some constraints on the estimator bias. The resulting optimal estimator is found to depend on the observation fourth-order moments that can be calculated analytically from the known signal model. Unfortunately, in most cases, the performance of this estimator is severely limited by the residual bias inherent to nonlinear estimation problems. To overcome this limitation, the second-order minimum variance unbiased estimator is deduced from the general solution by assuming accurate prior information on the vector of parameters. This small-error approximation is adopted to design iterative estimators or trackers. It is shown that the associated variance constitutes the lower bound for the variance of any unbiased estimator based on the sample covariance matrix. The paper formulation is then applied to track the angle-of-arrival (AoA) of multiple digitally-modulated sources by means of a uniform linear array. The optimal second-order tracker is compared with the classical maximum likelihood (ML) blind methods that are shown to be quadratic in the observed data as well. Simulations have confirmed that the discrete nature of the transmitted symbols can be exploited to improve considerably the discrimination of near sources in medium-to-high SNR scenarios.     

基于Zernike-Facet模型和总体最小二乘的弱小目标检测

弱小目标一般是图像局部区域的极值点。针对这个特点,依据二元三次函数的极值理论,该文提出了一种新的弱小目标候选点的检测方法。发展了一种新的图像局部灰度拟合模型,即Zernike-facet模型,模型参数的求解采用比最小二乘(LS)抗噪能力更强的总体最小二乘(TLS)算法。新检测方法通过Zernike-facet模型和TLS对原始图像中每一个像素的局部区域进行曲面拟合,然后在拟合曲面上提取极值点作为目标候选点。仿真表明,新方法在抑制噪声上优于其他常用方法。可见光/红外图像小目标检测实验也证实了新方法的有效性。     

Improved estimation of low velocities in color Doppler imaging byadapting the mean frequency estimator to the clutter rejection filter

An adaptive mean frequency estimator is proposed for color flow imaging. It is based on a series expansion of the first derivative of the autocorrelation function of the Doppler signal at origin. Its bias can be reduced by shifting the integration bounds in the series expansion and its variance adjusted by adapting the coefficients of the serial-development. This estimator can be fitted to the specific characteristics of the clutter rejection filter using the signal-to-noise ratio (SNR) of the Doppler signal as an adaptive parameter. Its performance is compared to that of the usual correlation angle estimator, and its thresholded version, as well as that of the general mean frequency estimator, using a model of Doppler signal. The detection of low frequencies was significantly improved. The mean square error (MSE) was reduced an average 15 fold over a 25-dB range on the SNR, compared to the correlation angle estimator (CAE) or the general mean frequency estimator. A two-fold reduction in the MSE was obtained compared to the thresholded correlation angle estimator