Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L₀ known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.     

Instrumental variable adaptive array processing

An instrumental variable (IV) approach is presented for estimating the weights of an adaptive antenna array. Theoretical analysis of the IV method shows that the antenna gain weights are independent of finitely correlated noise, so that unbiased estimation of signal arrival angles is possible. Only matrix inversions are required to compute the weight estimates. In this sense, the IV method provides performance comparable with eigenvector techniques but with lower computational burden. Both minimal and overdetermined IV estimators are derived. The overdetermined estimators give the same theoretical array weights as minimal estimators, but yield more accurate weight estimates in real data situations. Simulation results are presented to compare these IV methods with one another and with conventional matrix inversion weight estimators. In these examples it is seen that IV methods are able to resolve closely spaced interference sources when conventional matrix inversion techniques cannot. It is also shown that overdetermined methods are capable of providing weight estimates with lower variances than those of minimal methods     

On Attitude Estimation Schemes for Fine-Pointing Control

This paper studies single-axis equations of motion that are applicable to a spacecraft or to a space experiment pointing assembly whose motion has been perfectly isolated from the carrier vehicle. It considers four state estimators for implementation in the control loop for a stellar observation experiment. The first three estimators are very general and do not make use of input torque in their prediction models, while the proposed fourth estimator utilizes this information, It is shown via closed-loop covariance analysis that the best achievable pointing performance with the best of the first three estimators is limited to about 0.125 are-sec (rms) with the given rate-gyro and star-tracker inaccuracies. It is also shown that the fourth estimator has the capability of achieving a pointing performance far superior to the performance achievable using the first three estimators. The fourth estimator relies on the ability to accurately generate the desired control torque (i.e., low input noise).     

Statistical description of monopulse parameters for trackingRayleigh targets

The conditional probability density function (pdf) is developed for each monopulse measurement of a Rayleigh target by conditioning the pdf of the complex monopulse ratio on the measured amplitude of the sum signal. The conditional pdf is used to develop the conditional Cramer-Rao Lower Bound (CRLB) for any unbiased estimator of the direction-of-arrival (DOA). Conditional maximum likelihood (CML) and conditional method of moments (CMM) estimators of the DOA are developed along with estimates of the variances associated with the monopulse ratio and DOA estimate. Using simulation results, the performances of the CML and CMM estimators of the DOA are compared with the performance of standard monopulse ratio and the performances of the variance estimators are also studied     

New maximum entropy spectrum using uncertain eigenstructureconstraints

A number of modern spectral estimators are shown to have a common generic formulation. These include minimum variance, MUSIC, and maximum entropy. A new maximum entropy spectral estimator is derived using constraints on the modal powers or the expected-square projections of the data onto the eigenvectors of the data covariance matrix. The formulation incorporates uncertainty in the modal power constraints and the signal-versus-noise subspace separation. The resulting estimators have forms which incorporate all other modern estimators, including maximum entropy and minimum norm. The new estimators allow further development when a priori information is used in the constraints. Comparison of one version of the estimator with the minimum norm verifies the greater probability of resolution of the minimum norm but indicates in some instances the value of the incorporated uncertainties. Another version uses complex constraints and reduces to conventional maximum entropy or minimum norm under certain conditions     

Multipath interferometry technique for airborne array calibration

A new technique is developed to compensate multiple-wavelength distortion in airborne antenna arrays. This approach exploits the phase information in microwave reflections from arbitrary terrain. To handle reflections incident over a broad angle, a range-Doppler preprocessor is used in each element channel to resolve wavefronts incident simultaneously from different directions. The phase information for each direction of arrival is compared between elements and processed by optimal estimators to determine the phase corrections needed to compensate the distortion. To develop the estimators, a statistical model of the complex baseband terrain reflections is developed. This is in turn used to generate conditional probability densities involving the range Doppler observations and the parameters to be estimated. These densities are subsequently used to develop minimum variance and maximum likelihood estimators. The new estimators use additional information that has not been exploited by previous techniques and therefore provide enhanced performance     

Estimation of Velocity Moments of Radar Targets

The Doppler-velocity spectrum of a coherent burst of radar pulses after reflection from the wake of a reentry body is considered. Time-domain estimators of the mean-wake velocity and velocity spread in a particular range cell are given in terms of the echo of a coherent N-pulse burst. These formulas yield values equivalent to common frequency-domain estimators, but, for short bursts (N < 50), are computationally faster than their frequency-domain counterparts.     

A Weighted Inner Product Estimator in the Geometric Algebra of Euclidean 3-Space for Source Localization Using an EM Vector-sensor

In this paper, the source localization by utilizing the measurements of a single electromagnetic (EM) vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space. In order to describe the orthogonality among the electric and magnetic measurements, two multivectors of the geometric algebra of Euclidean 3-space (G3) are used to model the outputs of a spatially collocated EM vector-sensor. Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3. Since the information used by the two estimators is different, a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error (MMSE). Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart. The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.     

Passive localization of moving emitters using out-of-planemultipath

The purpose of this work is to establish how a moving emitter, such as a jammer, can be localized by a passive receiver through the use of out-of-plane multipath signals reflected by the terrain. This is a novel localization technique that assumes no a priori knowledge of the localization of the multipath sources. The emitter parameters of range, heading, velocity, and altitude are estimated by exploiting the correlation between the direct-path signal and the delayed and Doppler modulated signals. Two basis assumptions about the scattering properties of the terrain lead to different maximum likelihood estimators (MLEs). The Cramer-Rao lower bounds (CRLB) are used to study estimator performance versus emitter velocity for each case. The proposed estimators are successfully demonstrated using field data collected at White Sands Missile Range (WSMR) during the DARPA/Navy Mountaintop program     

含有正态相关变量的多设计点/多失效模式情况下的方向抽样可靠性灵敏度分析

针对含有正态相关变量的多设计点/多失效模式系统的可靠性问题,提出了两种有效的基于方向抽样的可靠性灵敏度分析方法。可靠性灵敏度分析方法的基本思路是首先将正态相关变量进行等价独立标准正态变换,利用改进的方向抽样可靠性灵敏度分析方法得到独立标准正态空间的可靠性及灵敏度结果;通过复合求导法则,将独立标准正态空间的可靠性及灵敏度结果转化到正态相关空间,得到失效概率对相关正态变量分布参数(均值、标准差和相关系数)的偏导数,并对所推导的可靠性及灵敏度估计值进行了方差分析。与经典的MonteCarlo数字模拟法相比较,文中所列的数值算例和简单工程算例的分析结果验证了所提方法的可行性与有效性。     

Simple Tracking Filters: Steady-State Filtering and Smoothing Performance

Computed data is presented, in normalized form, showing steady-state filtering and smoothing performance for optimum three-state estimators which assume exponentially correlated acceleration of the tracked object. The data are useful for preliminary design, gain selection, and performance prediction.     

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.     

广义Stokes问题的区域分裂解法及其事后误差估算

本文的主要目的在于将Ｌａｇｒａｎｇｅ乘子技术应用于广义Ｓｔｏｋｅｓ问题的非匹配网格上的区域分裂解法中;这种方法非常适用于有限元空间近似。Ｌａｇｒａｎｇｅ乘子是在分段常数函数的空间中近似的。同时,基于求解当地问题,我们还构造了离散近似的事后误差估算器,并基于此对网格进行了自适应处理。数值实验的结果验证了本文所发展的方法。     

Efficient implementation of Capon and APES for spectral estimation

Both the Capon and APES estimators can be shown to belong to the class of matched-filterbank spectral estimators and can be used to obtain complex spectral estimates that have more narrow spectral peaks and lower sidelobe levels than the fast Fourier transform (FFT) methods. It can also be shown that APES has better statistical performance than Capon. In this paper, we address the issue of how to efficiently implement Capon and APES for spectral estimation     

Performance of MAX family of order-statistic CFAR detectors

The MAX family of constant-false-alarm-rate (CFAR) detectors is introduced as a generalization of the greatest of CFAR (GO-CFAR) or MX mean-level detector (MX-MLD). Members of the MAX family use local estimators based on order statistics and generate both a near-range and a far-range noise-level estimate. Local estimates are always combined through a maximum operation; this insures false-alarm control at clutter edges. At the same time, order-statistic-based estimators result in a high-resolution detector. A complete detection analysis is provided for SWII targets and a reference channel contaminated by large outliers. Results are presented for the MX censored MLD (MX-CMLD) operating in clutter. The MX order statistic detector (MX-OSD) based on only a single-order statistic per window, is analyzed, and curves showing the required threshold, CFAR loss, optimum censoring point, and signal-to-noise ratio (SNR) loss in the presence of outliers are given. Simulations are used to compare the dynamic responses of various MX-OSD detectors in a clutter and a multiple-target environment     

Tracking targets with constant heading and variable speed

Two estimation procedures for tracking targets moving with variable speed in a fixed direction are presented and shown to be maximum likelihood estimators under differing sets of assumptions. Monte Carlo simulations are used to compare the accuracy of each method in a realistic tracking scenario. For miss-distance and heading estimation, it is often more accurate to make an approximate choice of speed profile than to make no choice at all     

Optimum and Suboptimum Synchronizer for Binary FSK Communication Systems

This paper considers a binary frequency-shift-keying (FSK) communication system with an adaptive receiver. Partially coherent detection is accomplished exploiting phase and bit synchronization directly extracted from the information-bearing waveform. The optimum (maximum a posteriori probability criterion) estimators of the relevant channel parameters are found along with some suboptimum realizations. It turns out that these schemes are decision-directed tracking systems that may be implemented using standard circuitry.     

The Open-Loop Transfer Matrix of an Estimator-Controller

Open-loop transfer matrices of continuous and sampled-data estimator-controllers (including those in predictor-corrector form) are derived. This paper complements an earlier paper in which open-and closed-loop transfer matrices of estimators and closed-loop transfer matrices of estimator-controllers were derived. Three different open-loop transfer matrices of each type of estimator-controller are derived by breaking the loop at different points. An example is included to illustrate the utility of such an open-loop transfer matrix.