Showing papers in "IEEE Transactions on Aerospace and Electronic Systems in 1992"

A CFAR adaptive matched filter detector

Abstract: An adaptive algorithm for radar target detection using an antenna array is proposed. The detector is derived in a manner similar to that of the generalized likelihood-ratio test (GLRT) but contains a simplified test statistic that is a limiting case of the GLRT detector. This simplified detector is analyzed for performance to signals on boresight, as well as when the signal direction is misaligned with the look direction. >

Radiometric detection of spread-spectrum signals in noise of uncertain power

Abstract: The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval. >

Performance analysis of bearing-only target location algorithms

Abstract: The performance of two well-known bearing-only location techniques, the maximum likelihood (ML) and the Stansfield estimators, is examined. Analytical expressions are obtained for the bias and the covariance matrix of the estimation error, which permit performance comparison for any case of interest. It is shown that the Stansfield algorithm provides biased estimates even for large numbers of measurements, in contrast with the ML method. The RMS error of the Stansfield technique is not necessarily larger than the RMS of the ML technique. However, it is shown that the ML technique is superior to the Stansfield method when the number of measurements is large enough. Simulation results verify the predicted theoretical performance. >

Observability analysis of piece-wise constant systems. I. Theory

Abstract: For pt.II see ibid., vol.28, no.4, p.1068-75, Oct. 1992. A method for analyzing the observability of time-varying linear systems which can be modeled as piece-wise constant systems (PWCS) is presented. An observability matrix for such systems is developed for continuous and discrete time representations. A stripped observability matrix (SOM) is introduced which simplifies the analysis in cases where the use of this matrix is legitimate. The observability analysis is presented as a step-by-step procedure. >

Direction finding using spatial smoothing with interpolated arrays

Abstract: The problem of estimating the directions of arrival (DOAs) of signals, some of which may be perfectly correlated, is considered. A computationally efficient estimation algorithm which combines the ideas of spatial smoothing and array interpolation is derived. In one of its forms the proposed algorithm uses the root-MUSIC (root multiple signal classification) technique to compute the DOA estimates, thus avoiding the search procedure associated with the conventional MUSIC algorithm. The proposed technique can be applied to arbitrary array geometries and a general signal covariance matrix. The performance of the algorithm was evaluated by extensive simulations, and compared with the Cramer-Rao lower bound for the DOA estimates. >

Current distribution control for parallel connected converters. II

Abstract: For pt.I, see ibid., vol.28, no.3, p.829-840 (1992). In the central-limit control (CLC), the multiloop controls are employed to regulate the output voltage and track the central weighted current, thus equalizing the output current of each converter module (CM). The current distribution error (CDE) between the output current of each CM is used as a criterion in judging system performance. The prediction and simulation results of this control scheme are illustrated. When incorporated with the maximum current limit, the proposed control method can determine the number of required converters in the active state for each load condition. As a result, the efficiency of a system can be increased significantly. A comparison between the performances of the system under master-slave control (MSC) and CLC is given. >

Optimal data fusion of correlated local decisions in multiple sensor detection systems

Abstract: Z. Chair and P.R. Varshney (1986) solved the data fusion problem for fixed binary local detectors with statistically independent decisions. Their solution is generalized by using the Bahadur-Lazarsfeld expansion of probability density functions. The optimal data fusion rule is developed for correlation local binary decisions, in terms of the conditional correlation coefficients of all orders. It is shown that when all these coefficients are zero, the rule coincides with the original Chair-Varshney design. >

Observability analysis of piece-wise constant systems. II. Application to inertial navigation in-flight alignment (military applications)

Abstract: For pt.I see ibid., vol.28, no.4, p.1056-67, Oct. 1992. The method of analyzing the observability of time-varying linear systems as piecewise constant systems (PWCS) is applied to the analysis of in-flight alignment (IFA) of inertial navigation systems (INS) whose estimability is known to be enhanced by maneuvers. The validity of this approach to the analysis of IFA is proven. The analysis lays the theoretical background to, and clearly demonstrates the observability enhancement of, IFA. The analytic conclusions are confirmed by covariance simulations. Although INS IFA was handled to various degrees in the past, a comprehensive control theoretic approach to the problem is introduced. The analysis yields practical conclusions and a procedure previously unknown. >

Error estimation of INS ground alignment through observability analysis

Abstract: A systematic analysis of the observability of an inertial navigation system (INS) in ground alignment with Bar-Itzhack and Berman's error model is presented. It is shown that the unobservable states are separately contained in two decoupled subspaces. The constraints on the selection of unobservable states are discussed. An estimation algorithm which is derived fully from the horizontal velocity outputs for computing the misalignment angles is provided. It reveals that the azimuth error can be entirely estimated from the estimates of leveling error and leveling error rate, without using gyro output signals explicitly. >

Bearings-only and Doppler-bearing tracking using instrumental variables

Abstract: In bearings-only tracking (BOT) or Doppler and bearing tracking (DBT), both common passive sonar problems, the measurement equations are nonlinear. To apply the Kalman filter, it is necessary either to linearize the equations or to embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence, while the latter produces biased estimates. A formulation of BOT and DBT which has a constant state vector and simplifies the tracking problem to one of constant parameter estimation is given. The solution is by the instrumental variable method. The instrumental variables are obtained from predictions based on past measurements and are therefore independent of the present noisy measurements. The result is a recursive unbiased estimator. The theoretical developments are verified by simulation, which also shows that the formulation leads to near optimal estimators whose errors are close to the Cramer-Rao lower bound (CRLB). >

Automatic censored CFAR detection for nonhomogeneous environments

Abstract: In constant false alarm rate (CFAR) detection, the clutter background in the cell under test is estimated by combining the outputs of the nearby resolution cells. In a nonhomogeneous background environment, the false alarm regulation capabilities and the detection performance of a CFAR detector depend on the robustness of the noise level estimator. The authors propose and study automatic censoring algorithms for nonhomogeneous clutter background environments. A cell-by-cell criterion for accepting or rejecting reference samples is introduced. The detection schemes that are considered do not require any a priori knowledge about the background environment. The case where a clutter edge is present in the reference window is considered, and the case of multiple target situations is studied. The case when both interfering targets and a clutter edge appear in the reference window of the cell under test is considered. The performances of the proposed schemes are compared with that of the trimmed-mean (TM) CFAR detector, in which the censoring points are preassigned. >

A persymmetric multiband GLR algorithm

Abstract: By exploring the covariance structure information to reduce the uncertainty in adaptive processing, a persymmetric generalized likelihood ratio algorithm (PGLR) is developed together with the closed-form expressions of probabilities of detection and false alarm. This multiband algorithm, which requires less computation, can significantly outperform the corresponding unstructured multiband GLR algorithm, especially in a severely nonstationary and/or nonhomogeneous interference environment. Simulation shows that the constant false alarm rate (CFAR) performance of the new algorithm is as insensitive as that of the unstructured multiband GLR to the departure of interference distribution from Gaussian. >

Efficient gating in data association with multivariate Gaussian distributed states

Abstract: An efficient algorithm for evaluating the (weighted bipartite graph of) associations between two sets of data with Gaussian error, e.g., between a set of measured state vectors and a set of estimated state vectors, is described. A general method is developed for determining, from the covariance matrix, minimal d-dimensional error ellipsoids for the state vectors which always overlap when a gating criterion is satisfied. Circumscribing boxes, or d-ranges, for the data ellipsoids are then found and whenever they overlap the association probability is computed. For efficiently determining the intersections of the d-ranges, a multidimensional search tree method is used to reduce the overall scaling of the evaluation of associations. Very few associations that lie outside the predetermined error threshold or gate are evaluated. The search method developed is a fixed Mahalanobis distance search. Empirical tests for variously distributed data in both three and eight dimensions indicate that the scaling is significantly reduced. Computational loads for many large-scale data association tasks can therefore be significantly reduced by this or related methods. >

A maximum likelihood approach to data association

Abstract: An approach is presented to data association (DA) problems for which measurements are independent from scan to scan. It is demonstrated that maximum likelihood (ML) estimation of target parameters may be efficiently implemented by an EM iterative scheme. The algorithm is applied to multitarget trajectory estimation of constant-velocity targets from passive (bearing-only) sensors. >

Distributed detection by a large team of sensors in tandem

Abstract: The problem of decentralized binary hypothesis testing by a team consisting of N decision makers (DMs) in tandem is considered. Each DM receives an observation and transmits a binary message to its successor; the last DM has to decide which hypothesis is true. The necessary and sufficient condition for the probability of error to go asymptotically to zero as N to infinity is that the log-likelihood ratio of the observation of each DM be unbounded. The result is generalized for multiple hypotheses and multiple messages. An easily implementable suboptimal decision scheme is also considered; in this case, the necessary and sufficient condition for the probability of error to asymptotically go to zero is that the log-likelihood ratio of the observation of each DM be unbounded from both above and below. The tradeoff between the complexity of the decision rules and their performance is examined, and numerical results are presented, in order to demonstrate that the performance of both decision schemes is comparable. >

Design of a CLOS guidance law via feedback linearization

Abstract: An application of the feedback linearization technique to the design of a new command to line-of-sight (CLOS) guidance law for short-range surface-to-air missiles is described. The key idea lies in converting the three-dimensional CLOS guidance problem to the tracking problem of a time-varying nonlinear system. The result may shed new light on the role of the feedforward acceleration terms used in the conventional CLOS guidance laws. Through computer simulation, the effect of the dynamics of the ground tracker and the autopilot on the guidance performance of the new CLOS guidance law is investigated. >

Improved strapdown coning algorithms

Abstract: Three improved algorithms for strapdown attitude computation utilizing accumulated gyro increments from the previous and current update are developed and evaluated analytically under classical coning motion. The error criterion of Miller is derived directly from the rotation vector concept. The accuracy of updating rotation vector estimation can be improved at least two orders of magnitude as compared with those of conventional algorithms. The proposed algorithm is equivalent to increasing the number of gyro samples used in the conventional method and it requires less computer loading. >

An adaptive array detector with mismatched signal rejection

Abstract: An adaptive detection algorithm with a sensibility parameter for rejecting unwanted signals is presented. This algorithm is a simple modification of the generalized likelihood ratio (GLR) detector (or test) for detecting a signal in zero mean Gaussian noise with unknown correlation matrix. Specifically, the adaptive detection algorithm is obtained by introducing an arbitrary positive scalar, which is called the sensitivity parameter, into the GLR detector as a multiplier of an already existing quadratic term. The GLR detector then becomes a special case of this detector for the unity sensitivity parameter. It is shown that the sensitivity parameter controls the degree to which unwanted signals are rejected. From numerical examples, it is demonstrated how the sensitivity parameter can be chosen such that unwanted signals, can be rejected while maintaining acceptable detection loss for slightly mismatched signals. Further insight into previous work on adaptive detection is also given. >

CFAR data fusion center with inhomogeneous receivers

Abstract: Detection systems with distributed sensors and data fusion are increasingly used by surveillance systems. A system formed by N inhomogeneous constant false alarm rate (CFAR) detectors (cell-averaging (CA) and ordered statistic (OS) CFAR detectors) is studied. A recursive formulation of an algorithm that permits a fixed level of false alarms in the data fusion center is presented, to set the optimum individual threshold levels in the CFAR receivers and the optimum 'K out of N' decision rule in order to maximize the total probability of detection. The algorithm also considers receivers of different quality or with different communication channel qualities connecting them with the fusion center. This procedure has been applied to several hypothetical networks with distributed CA-CFAR and OS-CFAR receivers and for Rayleigh targets and interference, and it was seen that in general the fusion decision OR rule is not always the best. >

Two-valued sequences with perfect periodic autocorrelation

Abstract: Periodic two-valued signals which exhibit two-level autocorrelation can, in many cases, be made to yield an out-of-phase autocorrelation value identically equal to zero. This can be achieved by replacing the two values of the sequence (normally +1 and -1) with the two values +1 and e/sup i phi /, or with +1 and beta ( beta real). Simple expression for phi and beta are given, based on the parameters of the difference set to which such signals correspond. Another strategy is to transmit a sequence of +1s and -1s, but of +1s and bs (b real and negative). An expression for b is also obtained. >

An efficient method of passive emitter location

Abstract: The problem of locating a stationary emitter from passive bearing and frequency measurements taken by a moving and autonomously operating sensor along its trajectory is considered. The estimation procedure based on bearings only is quite different from that based on frequency measurements. From the Cramer-Rao (CR) analysis of the single-measurement case, the characteristic features of each method become transparent and an intuitive understanding of both methods is provided. One of the major results is that the orientation of the error ellipses of the bearings method (BM) and frequency method (FM) differ significantly. From this a considerable integration gain in accuracy results, when processing the combined set of bearing and frequency measurements. The results of the theoretical CR analysis are verified in a numerical simulation based on the maximum-likelihood (ML) estimation. The simulations demonstrate that a combined method is definitely superior to BM and FM with respect to the bias and the size of the error ellipses. >

Bandwidth performance of linear adaptive arrays with tapped delay-line processing

Abstract: The nulling bandwidth of adaptive arrays with tapped delay-line processing is examined. Linear arrays with up to 10 elements are considered. It is shown how the number of taps in the delay lines and the amount of delay between taps affect the nulling bandwidth. For each size of array, the optimal number of delay-line taps and the optimal intertap delays are determined as functions of the required nulling bandwidth. >

Calculation of geometric dilution of precision

Abstract: A very simple closed-form formula for the calculation of the geometric dilution of precision (GDOP) in Global Positioning System (GPS) navigation and in Global Navigation Satellite System (GLONASS) navigation is presented, which requires less than 40 multiplications. >

Sensitivity analysis of DOA estimation algorithms to sensor errors

Abstract: A unified statistical performance analysis using subspace perturbation expansions is applied to subspace-based algorithms for direction-of-arrival (DOA) estimation in the presence of sensor errors. In particular, the multiple signal classification (MUSIC), min-norm, state-space realization (TAM and DDA) and estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithms are analyzed. This analysis assumes that only a finite amount of data is available. An analytical expression for the mean-squared error of the DOA estimates is developed for theoretical comparison in a simple and self-contained fashion. The tractable formulas provide insight into the algorithms. Simulation results verify the analysis. >

Calibration of complex polarimetric SAR imagery using backscatter correlations

Abstract: A technique for calibration of multipolarization synthetic-aperture radar (SAR) imagery is described. If scatterer reciprocity and lack of correlation between co- and cross-polarized radar echoes (for azimuthally symmetric distributed targets) are assumed, the effects of signal leakage between the radar data channels can be removed without the use of known ground targets. If known targets are available, all data channels can be calibrated relative to one another and radiometrically as well. The method is verified with simulation and application to airborne SAR data. >

Biparametric linear estimation for CFAR against Weibull clutter

Abstract: The authors deal with constant false alarm rate (CFAR) procedures against nonstationary clutter, modeled as a Weibull distributed process whose scale parameter alpha and shape parameter beta are both variable. It is shown that conventional CFAR procedures, which compensate only for alpha , degrade intolerably as beta deviates from beta =2, namely, as the Rayleigh distributional assumption is violated. A biparametric CFAR procedure is shown to be suited to such situations. The authors introduce a logarithmic transformation to reduce the Weibull probability density function (pdf) to a Gumbel pdf, i.e., to the location-scale type, and then exploit the best linear unbiased estimation (BLUE) of location-scale parameters to adjust the detection threshold. True CFAR is thus achieved when the clutter is locally homogeneous. Resilience against local inhomogeneities can also be conferred since BLUE lends itself to censoring. Through a performance analysis, the influence of various system and distributional parameters is elicited. >

Nonlinear observer and output feedback attitude control of spacecraft

Abstract: The problem of controlling a spacecraft by measuring only the angular position (roll, pitch, and yaw) is considered. A nonlinear observer is proposed which asymptotically reconstructs all the spacecraft state variables; if the spacecraft actuators are reaction wheels, the angular velocities of the wheels also must be measured. It is shown that if the observer is used in connection with asymptotically stable state feedback controllers, the extended system (spacecraft, controller, and observer) is still asymptotically stable. Simulation results are reported to illustrate the dynamic behavior of the observer. >

Narrowband interference suppression in impulsive channels

Abstract: Suppression algorithms are developed first for a channel containing only impulsive background noise and then for a channel containing a spread-spectrum signal as well. These algorithms are based on nonlinear filters that produce predictions of the interfering signals that are then subtracted from the received signal to suppress the interference. Several such filters, including both fixed and adaptive ones, are proposed and compared using extensive computer simulations. The independence of the filtering procedures from the noise distribution shape, given constant second-order statistics, is shown. >

Monopulse-radar angle tracking in noise or noise jamming

Abstract: In many monopulse radars, feedback in the angle-tracking servo system is taken to be directly proportional to the monopulse ratio. In those radars, monopulse measurements are conditioned on simultaneous occurrences of receiver sum-channel video exceeding a detection threshold: if a detection fails to occur, the measurement is ignored, and the angle-tracking servo is made to coast. Such conditioning is shown to be necessary in order that the noise power be finite in the servo feedback. The conditional mean value and conditional variance of the monopulse ratio are derived and quantified in terms of threshold level as well as signal-to-noise ratio. The formulation permits the noise covariance between receiver difference and sum channels to be complex rather than only real-valued, so that the sources of noise jamming are not required to be positioned in the receiving-antenna mainlobe and to be copolarized with the antenna response there. Nonfluctuating and Rayleigh-fluctuating target cases are considered and compared, and fluctuation loss is quantified. >

Periodic ambiguity function of CW signals with perfect periodic autocorrelation

Abstract: A periodic ambiguity function (PAF) is discussed which describes the response of a correlation receiver to a CW signal modulated by a periodic waveform, when the reference signal in the receiver is constructed from an integral number N, of periods T, of the transmitted signal. The PAF is a generalization of the periodic autocorrelation function, to the case of non-zero Doppler shift. It is shown that the PAF of N periods is obtained by multiplying the PAF of a single period by the universal function sin(N pi nu T)/N sin( pi nu T), where nu is the Doppler shift, to phase-modulated signals which exhibit perfect periodic autocorrelation when there is no Doppler shift. The PAF of these signals exhibits universal cuts along the delay and Doppler axes. These cuts are functions only of t, N and the number M, the modulation bits in one period. >