Resolution of a 2π ambiguity problem in multiple frequencyspectral estimation

An algorithm is proposed to resolve a fundamental 2π ambiguity problem occurring in multiple frequency spectral estimation. Given M frequencies f_m, and I separate frequency estimators with unambiguous bandwidths F_i, the ambiguity problem can be stated as solving for the fm, given the estimator outputs, α_mi, (1⩽m⩽M;1⩽i⩽I) where f_m=α_mi+K_miF_i and K_mi is some integer. The proposed algorithm exhaustively resolves all possible α_mi groupings into single frequency values using a noise insensitive technique that exchanges system bandwidth for noise protection. The correct multiple frequencies are then defined as the single frequencies that repeat a specified number of times. A complete analysis is included     

Fast automatic leveling subject to abrupt deterministic input

This investigation applies a modified Kalman filter with a recursive generalized M estimator (GME) of input to a class of leveling problems, that are subject to abrupt environmental disturbances and high noise levels. A least-squares estimator (LSE) based hypothetical testing scheme is also devised to detect the onset and presence of the input. Simulation results demonstrate that the leveling speed of convergence and accuracy is markedly higher than the original unmodified one     

Ground target tracking with variable structure IMM estimator

In this paper we present the design of a Variable Structure Interacting Multiple Model (VS-IMM) estimator for tracking groups of ground targets on constrained paths using Moving Target Indicator (MTI) reports obtained from an airborne sensor. The targets are moving along a highway, with varying obscuration due to changing terrain conditions. In addition, the roads can branch, merge or cross-the scenario represents target convoys along a realistic road network with junctions, changing terrains, etc. Some of the targets may also move in an open field. This constrained motion estimation problem is handled using an IMM estimator with varying mode sets depending on the topography, The number of models in the IMM estimator, their types and their parameters are modified adaptively, in real-time, based on the estimated position of the target and the corresponding road/visibility conditions. This topography-based variable structure mechanism eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. Data association is handled using an assignment algorithm. The estimator is designed to handle a very large number of ground targets simultaneously. A simulated scenario consisting of over one hundred targets is used to illustrate the selection of design parameters and the operation of the tracker. Performance measures are presented to contrast the benefits of the VS-IMM estimator over the Kalman filter and the standard IMM estimator, The VS-IMM estimator is then combined with multidimensional assignment to gain “time-depth.” The additional benefit of using higher dimensional assignment algorithms for data association is also evaluated     

Angle of arrival estimation of coherent signals using an arraydoublet in motion

Shown here is how the estimation of signal parameters via relational invariance techniques (ESPRIT) algorithm may be used with a single pair of antennas in motion to estimate angles of arrival (AOA) for coherent signals. The approach exploits the Doppler frequency shifts caused by the doubler in motion. With this estimator, the number of signals that can be handled is not limited by the size of the array, as in the usual ESPRIT application, but by an adjustable parameter. A theoretical performance analysis of the estimator and typical examples showing the use of this estimator are given     

State Estimation for Discrete Systems with Switching Parameters

The problem of state estimation for discrete systems with parameters which may be switching within a finite set of values is considered. In the general case it is shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time. For the Markov parameter case, it is found that the optimal estimator requires only N2 elemental estimators where N is the number of possible parameter values.     

A Modified Discrete Karhunen-Loeve Random Field Estimator

Based upon the modified Karhunen-Loeve model of the gravity disturbance vector proposed by us recently, a corresponding Karhunen-Loeve random field estimator is developed in this paper for a two-dimensional grid of gravity data in a local finite region.The new eigenvectors obey the "required" orthogonality relations on the chosen grid provided the KL expansion is now separated into odd and even integers. The closed-form solution of the estimator isthen obtained under the "diagonal" assumption for the gain coefficients. It is shown that this assumption, without which nosolution is possible, enables the estimator to reproduce the data atgrid points when the noise in the data is absent and the number of terms in the Karhunen-Loeve expansion are equal to the number of grid points.     

Efficient recursive state estimator for dynamic systems withoutknowledge of noise covariances

An efficient recursive state estimator for dynamic systems without knowledge of noise covariances is suggested. The basic idea for this estimator is to incorporate the dynamic matrix and the forgetting factor into the least squares (LS) method to remedy the lack of knowledge of noises. We call it the extended forgetting factor recursive least squares (EFRLS) estimator. This estimator is shown to have similar asymptotic properties to a completely specified Kalman filter state estimator. More importantly, the performance of EFRLS greatly exceeds that of existing filtering techniques when the noise variance is misspecified. In addition, EFRLS also performs well when there is cross-correlation between the process and measurement noise streams or temporal dependencies within those streams. Some discussions and a number of simulations are made to provide practical guidance on the choice of an optimal forgetting factor and evaluate the performance of the EFRLS algorithms, which strongly dominates that of the standard forgetting factor recursive least squares (FRLS) and some misspecified Kalman filtering     

Application of Maximum Likelihood Estimation of Persymmetric Covariance Matrices to Adaptive Processing

The optimum weights for an adaptive processor are determined by solving a particular matrix equation. When, as is usually true in practice, the covariance matrix is unknown, a matrix estimator is required. Estimating the matrix can be computationally burden some. Methods of decreasing the computational burden by exploiting persymmetric symmetries are discussed. It is shown that the number of independent vector measurements required for the estimator can be decreased by up to a factor of two.     

Multiple-model estimation with variable structure. IV. Design andevaluation of model-group switching algorithm

For pt. III see ibid., vol. 35, pp. 225-41 (1999). A variable-structure multiple-model (VSMM) estimator, called model-group switching (MGS) algorithm, has been presented in Part III, which is the first VSMM estimator that is generally applicable to a large class of problem with hybrid (continuous and discrete) uncertainties. In this algorithm, the model-set is made adaptive by switching among a number of predetermined groups of models. It has the potential to be substantially more cost-effective than fixed-structure MM (FSMM) estimators, including the Interacting Multiple-Model (IMM) estimator. A number of issues of major importance in the application of this algorithm are investigated here, including the model-group adaptation logic and model-group design. The results of this study are implemented via a detailed design for a problem of tracking a maneuvering target using a time-varying set of models, each characterized by a representative value of the expected acceleration of the target. Simulation results are given to demonstrate the performance (based on more reasonable and complete measures than commonly used rms errors alone) and computational complexity of the MGS algorithm, relative to the fixed-structure IMM (FSIMM) estimator using all models, under carefully designed and fair random and deterministic scenarios     

Multiple-model estimation with variable structure. III. Model-groupswitching algorithm

A general multiple-model (MM) estimator with a variable structure (VSMM), railed model-group switching (MGS) algorithm, is presented. It assumes that the total set of models can be covered by a number of model groups, each representing a cluster of closely related system behavior patterns or structures, and a particular group is running at any given time determined by a hard decision. This algorithm is the first VSMM estimator that is generally applicable to a large class of problems with hybrid (continuous and discrete) uncertainties. It is also easily implementable. It is illustrated, via a simple fault detection and identification example, that the MGS algorithm provides a substantial reduction in computation while having identical performance with the fixed-structure Interacting Multiple-Model (FSIMM) estimator     

Stability of Parameter Estimates for a Gaussian Process

Maximum-likelihood estimates for the levels of the mean value function and the covariance function of a Gaussian random process are investigated. The stability of these estimates is examined as the actual covariance function of the process deviates from the form assumed in the estimators. It is found that the time-bandwidth product for stationary processes represents an upper bound on the number of estimator terms that can be safely used when estimating with uncertainty about the process covariance function. This result is consistent with other interpretations of the time-bandwidth product and tempers the conclusion that, in principle, an infinite number of estimator terms can be used to obtain a perfect estimate of the covariance level. In practice, the estimate of the level can never be perfect, and the accuracy of the estimate depends on the observation interval. Finally, conditions are established to ensure asymptotic stability of the estimates and physical interpretations are presented.     

Precision large scale air traffic surveillance using IMM/assignmentestimators

We present the development and implementation of a multisensor-multitarget tracking algorithm for large scale air traffic surveillance based on interacting multiple model (IMM) state estimation combined with a 2-dimensional assignment for data association. The algorithm can be used to track a large number of targets from measurements obtained with a large number of radars. The use of the algorithm is illustrated on measurements obtained from 5 FAA radars, which are asynchronous, heterogeneous, and geographically distributed over a large area. Both secondary radar data (beacon returns from cooperative targets) as well as primary radar data (skin returns from noncooperative targets) are used. The target IDs from the beacon returns are not used in the data association. The surveillance region includes about 800 targets that exhibit different types of motion. The performance of an IMM estimator with linear motion models is compared with that of the Kalman filter (KF). A number of performance measures that can be used on real data without knowledge of the ground truth are presented for this purpose. It is shown that the IMM estimator performs better than the KF. The advantage of fusing multisensor data is quantified. It is also shown that the computational requirements in the multisensor case are lower than in single sensor case, Finally, an IMM estimator with a nonlinear motion model (coordinated turn) is shown to further improve the performance during the maneuvering periods over the IMM with linear models     

Emitter number estimation from pulse trains using the GIC

An information theoretic criterion based approach for estimating the number of emitters from a set of interleaved pulse trains is proposed. In the approach, a new pulse signal model is formulated to handle large number of pulses. The approach is based on the application of the general information criteria (GIC) and has the advantage of not requiring any threshold setting procedures. When compared with classical information theoretic criterion based approaches, the GIC-based approach is more flexible, and it does not involve any computationally sophisticated maximum likelihood estimator. Computer simulations are used to demonstrate the effectiveness of the proposed approach.     

Optimum FFT-based frequency acquisition with application toCOSPAS-SARSAT

In the case of a single sinusoid or multiple well-separated sinusoids, a coarse estimator consisting of a windowed Fourier transform followed by a fine estimator which is an interpolator is a good approximation to an optimal frequency acquisition and measurement algorithm. The design tradeoffs are described. It is shown that for the fine-frequency estimator a good method is to fit a Gaussian function to the fast-Fourier-transform (FFT) peak and its two neighbors. This method achieves a frequency standard deviation and a bias in the order of only a few percent of a bin. In the case of short-time stationarity, for a moderate number of averages and for an adaptive threshold detector, only between 0.5 and 1 dB is lost when averaging is traded off for FFT length, in contrast to the asymptotic result of 1.5 dB. The COSPAS-SARSAT satellite system for emergency detection and localization is used to illustrate the concepts. The algorithm is analyzed theoretically, and good agreement is found with test results     

AHP中判断矩阵元素最优估计值的误差分析

在AHP模型中，请一组专家对某一属性进行评价，通过适当的数学处理方法，可得判断矩阵元素的最优估计值，并根据残差来确定所求估计值是否达到精度要求，若不符合精度要求则需返还给专家进行重新评估。这是AHP中构造判断矩阵的一种新方法。     

New Centroid Algorithm Based upon Amplitude-Angle Signature

A method of estimating the centroid location of a target utilizing radar scan return amplitude versus angle information is presented. The method is compared with three thresholding estimators and a first moment estimator in a computer-simulated automatic landing system. This new method is the most robust and accurate during periods of low signal-to-noise ratio. In periods of high signal-to-noise ratio the method has less error than the thresholding methods and is similar in accuracy to the first moment estimator. Furthermore, the number of pulse transmissions required to obtain a desired level of performance in noise is much less than that needed for the thresholding methods and the first moment estimator employed in this simulation.     

A novel multistage estimation of signal parameters

A multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of the Global Positioning Systems (GPS). In the proposed scheme, the first-stage estimator operates as a coarse estimator of the frequency and its derivatives, resulting in higher RMS estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second stage of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first-stage algorithm is a modified least-squares algorithm operating on the differential signal model and referred to as differential least squares (DLS). The second-stage algorithm is an extended Kalman filter, which yields the estimate of the phase as well as refining the frequency estimate. A major advantage of the proposed algorithm is a reduction in the threshold for the received carrier power-to-noise power spectral density ratio (CNR) as compared with the threshold achievable by either of the algorithms alone     

军用软件的可靠性统计分析

研究了军用软件的可靠性统计分析方法。对于失效数据极值分布函数的拟合检验,提出了一种解析法,克服了图解法的局限性;对于母体分布的参数估计,分别采用了最小二乘估计(LSE)和极大似然估计(MLE);最后通过一实例说明了统计过程,并用模拟的方法证明了最小二乘估计法较好。     

Analysis of a signal starting time estimator based on the Page test statistic

Many signal processing applications require the detection of an abrupt change with subsequent estimation of the actual time of occurrence of the change. The time of the most recent reset to zero of the Page test statistic is proposed for this purpose. The probability mass function of the estimator is determined analytically subject to a quantization of the Page test statistic update. Closed-form results for the first three uncorrected moments of the estimator are presented. The analytical results are verified by comparison to simulation results and the fineness of the quantization required for accurate representation is investigated by evaluation of the Kolmogorov-Smirnov statistic. The bias, standard deviation, and skewness of the estimator as a function of the signal strength and detector threshold are evaluated for Gaussian shift-in-mean and noncentral chi-squared changes in signal type.     

Estimating the Doppler centroid of SAR data

After reviewing frequency-domain techniques for estimating the Doppler centroid of synthetic-aperture radar (SAR) data, the author describes a time-domain method and highlights its advantages. In particular, a nonlinear time-domain algorithm called the sign-Doppler estimator (SDE) is shown to have attractive properties. An evaluation based on an existing SEASAT processor is reported. The time-domain algorithms are shown to be extremely efficient with respect to requirements on calculations and memory, and hence they are well suited to real-time systems where the Doppler estimation is based on raw SAR data. For offline processors where the Doppler estimation is performed on processed data, which removes the problem of partial coverage of bright targets, the ΔE estimator and the CDE (correlation Doppler estimator) algorithm give similar performance. However, for nonhomogeneous scenes it is found that the nonlinear SDE algorithm, which estimates the Doppler-shift on the basis of data signs alone, gives superior performance