Showing papers in "IEEE Transactions on Aerospace and Electronic Systems in 1971"
TL;DR: In this paper, the effects of slowly moving targets as they appear in the output of an airborne coherent side-looking synthetic aperture imaging radar are considered, and two approaches to airborne moving target indication (AMTI) are summarized.
Abstract: This paper considers the effects of slowly moving targets as they appear in the output of an airborne coherent side-looking synthetic aperture imaging radar. The image of a moving reflector is described, and two approaches to airborne moving target indication (AMTI) are summarized. It is shown that the effects of target movement are decreased as the radar scan rate is increased, and are increased as the (Doppler processed) compression ratio is increased.
585Â citations
TL;DR: In this article, a differential equation for the orientation vector relating the body frame to a chosen reference frame is developed, where the time derivative of this vector is the sum of the inertially measurable angular velocity vector and non-measurable non-commutativity rate vector.
Abstract: A differential equation is developed for the orientation vector relating the body frame to a chosen reference frame. The time derivative of this vector is the sum of the inertially measurable angular velocity vector and of the inertially nonmeasurable noncommutativity rate vector. It is precisely this noncommutativity rate vector that causes the computational problems when numerically integrating the direction cosine matrix. The orientation vector formulation allows the noncommutativity contribution to be isolated and, therefore, treated separately and advantageously. An orientation vector mechanization is presented for a strap down inertial system. Further, an example is given of the applica tion of this formulation to a typical rigid body rotation problem.
450Â citations
TL;DR: In this article, a summary of the causes and effects of the reentry plasma sheath is presented, together with a discussion of reentry plasminarity diagnostic techniques, proposed methods of alleviating the communications blackout, and a review of various reentry flight experiments.
Abstract: Considerable progress has been made in the past few years toward understanding and solving the spacecraft communications blackout problem caused by the reentry plasma sheath. A summary of the causes and effects of the reentry plasma sheath is presented, together with a discussion of reentry plasma diagnostic techniques, proposed methods of alleviating the communications blackout, and a review of the reentry flight experiments performed to better our understanding of the reentry plasma.
282Â citations
TL;DR: Both heuristic argumentation and rigorous analysis are presented, as are the results of a simple laboratory experiment on how stretch affects signal slowdown, speedup, or time reversal.
Abstract: Stretch is a passive, linear, time-variant technique for performing temporal operations on many classes of signals. The technique employs three dispersive networks and a mixer. Signal slowdown, speedup, or time reversal can be attained by choice of network slopes. These temporal operations are performed within a signal "window," and the duration of the window is determined by the network time-bandwidth products. Both heuristic argumentation and rigorous analysis are presented, as are the results of a simple laboratory experiment.
252Â citations
TL;DR: In this article, the trajectories of an ideal missile homing on a target according to the proportional navigation law were analyzed and conditions were determined which enable one to demonstrate that the missile always reaches the target regardless of the initial conditions at launch; the rotational rate of the line of sight is decreasing at the pursuit end.
Abstract: This paper represents a study of the trajectories of an ideal missile homing on a target according to the proportional navigation law. A qualitative study is performed and conditions are determined which enable one to demonstrate that: 1) the missile always reaches the target regardless of the initial conditions at launch; 2) the rotational rate of the line of sight is decreasing at the pursuit end.
240Â citations
TL;DR: In this article, five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications.
Abstract: Five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications. A rationale for selecting among these filters, which include a Kalman filter, a simplified Kalman filter, an ?-s filter, a Wiener filter, and a two-point extrapolator, is illustrated by two examples taken from the authors' recent experience.
137Â citations
TL;DR: In this article, it was shown that the off-axis angle indicated by a conventional monopulse radar is only the real part of a complex indicated angle, which can be easily measured by processing the normally unused quadrature-phase component of the difference signal, and under certain conditions the angles, amplitude ratio, and relative phase of two unresolved targets can theoretically be determined by measuring the measured angles on two pulses separated by a short interval.
Abstract: The off-axis angle indicated by a conventional monopulse radar is only the real part of a "complex indicated angle." The presence of unresolved targets or multipath distorts the real part (causing an erroneous angle indication) and also produces an imaginary part, which can easily be measured by processing the normally unused quadrature-phase component of the difference signal. Under certain conditions the angles, amplitude ratio, and relative phase of two unresolved targets can theoretically be determined by meas urements of the complex indicated angle on two pulses separated by a short interval. In the special case of multipath, known relationships between the unresolved target and image theoretically permit determination of target elevation with a single pulse.
122Â citations
TL;DR: In this article, the utility of phase reversal codes is extended by the use of sidelobe suppression techniques that can be easily implemented in digital form, where the tapped delay line used to reduce the sidelobes has only a few distinct tap weights.
Abstract: The utility of Barker-type phase-reversal codes is extended by the use of sidelobe suppression techniques that can be easily implemented in digital form. It is shown that sidelobe suppression techniques can be found where the tapped delay line used to reduce the sidelobes has only a few distinct tap weights, in which case the complexity of the digital processor is greatly reduced. An example is given where the technique is applied to Barker codes with positive sidelobes, specifically, the 13-element Barker code. If higher pulse compression factors are desired than are obtainable with Barker codes, multistage Barker codes may be used. The sidelobes then may be suppressed for any one or all of the different coding stages.
120Â citations
TL;DR: This paper considers optimum (MMSE) linear recursive estimation of stochastic signals in the presence of multiplicative noise in addition to measurement noise.
Abstract: This paper considers optimum (MMSE) linear recursive estimation of stochastic signals in the presence of multiplicative noise in addition to measurement noise. Often problems associated with phenomena such as fading or reflection of the transmitted signal at an ionospheric layer, and also situations involving sampling, gating, or amplitude modulation, can be cast into such formulation. The different kinds of estimation problems treated include one-stage prediction, filtering, and smoothing. Algorithms are presented for discrete time as well as for continuous time estimation.
106Â citations
TL;DR: This paper presents the concept, theory of operation, characteris tic equations, and error analysis of four wide-band monopulse techniques, which are particularly applicable to monopulse direction finding systems that require frequency coverage over several octaves and open-loop angle bearing of several degrees.
Abstract: This paper presents the concept, theory of operation, characteris tic equations, and error analysis of four wide-band monopulse techniques. The basic techniques described, which include pure amplitude monopulse, phase and amplitude monopulse (two-and three-channel configurations), and pure phase monopulse interferometer, are particularly applicable to monopulse direction finding systems that require frequency coverage over several octaves and open-loop angle bearing of several degrees. Sufficient detail and working formulas are included to permit a trade-off analysis to be made between the direction-finding techniques for selection in specific hardware applications.
68Â citations
TL;DR: In this paper, an analysis of the noise power generated by a saturating A/D converter when the input signal has an assumed Gaussian probability density function was carried out, and two noise powers were found to contribute to the output device noise.
Abstract: This correspondence carries out an analysis of the noise power generated by a saturating A/D converter when the input signal has an assumed Gaussian probability density function. Two noise powers are found to contribute to the output device noise, i e., one due to quantization effects and one due to saturation effects. The results of this analysis should have application to a broad class of radar and sonar problems.
TL;DR: In this article, two adaptive array implementations which maximize the signal-to-noise ratio are described, where the variance of the array element weights and the additional noise in the array output are determined by the eigenvalues of the noise covariance matrix.
Abstract: Adaptive array receiving antennas can be designed to sense the external noise field and to optimize the array illumination function. A substantial improvement in signal-to-noise ratio can be obtained with adaptive arrays when the external noise field is nonuniformly distributed in angle. The external noise process may be time varying and contain both discrete sources and continuously distributed sources. Two adaptive array implementations which maximize the signal-to-noise ratio are described in this paper. Expressions are derived for control-loop noise, i.e., the variance of the array element weights, and for the additional noise in the array output due to this element weight noise. It is shown that both the element weight noise and the array convergence rate are determined by the eigenvalues of the noise covariance matrix.
TL;DR: Recursive methods are drived for computing detection probabilities for general fluctuating targets in Gaussian noise and for the generalized chi-square family of fluctuate targets, very simple and convenient recursive algrithms result.
Abstract: Recursive methods are drived for computing detection probabilities for general fluctuating targets in Gaussian noise. For the generalized chi-square family of fluctuating targets, very simple and convenient recursive algrithms result. The methods are also extended to cell-averaging CFAR. Although the detection probability is expressed iw: terms of an infinite series, a convenient expression is derived for the resulting error when the series is truncated. Cell-averaging CFAR results are computed for nonfluctuating, Swering case I, and Swerling case II fluctuating targets.
TL;DR: The influence of increasing range resolution on the detectability of targets with dimensions greater than the resolution cell is studied and graphs are presented which show the probability of detection as a function of signal-to-noise ratio (SNR) for various values of N k, and false alarm probability.
Abstract: The influence of increasing range resolution on the detectability of targets with dimensions greater than the resolution cell is studied. An N-cell target model is assumed, which contains k reflecting cells, each reflecting independently according to the same Rayleigh amplitude distribution. It will be referred to as the (N,k) target. Detection based on one transmitted pulse is performed against a background of white normal noise. Detection in stationary clutter is also considered. The optimum detector is obtained but, in view of its complexity, the performance of a simpler detector, the square-law envelope detector with linear integrator (SLEDLI), is analyzed, and a formula for the probability of detection is obtained. Graphs are presented which show the probability of detection as a function of signal-to-noise ratio (SNR) for various values of N k, and false alarm probability. For N/k not too large it is shown that the SLEDLI is near optimum.
TL;DR: A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described and a comparison is made with a detector based on the Mann-Whitney test, which usually is considered to be one of the betterNonparametric procedures for the two-sample case.
Abstract: A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.
TL;DR: In this paper, a unique algorithm has been devised to compute a dynamically corrected altitude reference by numerically integrating the physical relation for a column of air as a function of pressure, gravity, and absolute temperature.
Abstract: Inertial navigators determine inertial altitude and vertical velocity by a closed feedback loop in which the vertical accelerometer output is mixed with a pressure altitude reference. Pressure altitude is determined as a function of presure based on the standard atmosphere models. Since the atmosphere is almost always nonstandard, large inertial altitude and vertical velocity errors may result. A unique algorithm has been devised to compute a dynamically corrected altitude reference by numerically integrating the physical relation for a column of air as a function of pressure, gravity, and absolute temperature. The new algorithm has been flight tested and has been shown to yield accurate results.
TL;DR: The theory presented here permits a systematic approach to waveform selection, with the important benefit that the designer knows exactly where and how much he may have deviated from the best design, and why this was done.
Abstract: Radar measurement and resolution performance, as well as target detection in clutter, depend largely on the transmitted waveform This explains the sizable effort that has gone into studies of radar waveforms, including attempts at the synthesis of optimum waveforms This paper shows that, despite the unlimited variety of radar signals, waveform selection is a straightforward process There are only four classes of waveforms, each with distinct resolution properties When the target environment is analyzed for a particular application, it is rather evident which of these classes will fit the situation best Choice of the specific waveform within the selected class then is merely a matter of practical implementation Although the facts used in developing the unified theory of this paper are not new, it is demonstrated that these facts can be combined into an extremely simple theory of waveform design Much of today's work is guided by past approaches to a particular problem, and when a design is completed there may be a question as to how close to the optimum it is The theory presented here permits a systematic approach to waveform selection, with the important benefit that the designer knows exactly where and how much he may have deviated from the best design, and why this was done
TL;DR: In this paper, the error equations for a space-stable inertial navigation system are derived by directly perturbing the mechanization equations in the inertial frame and then transforming in open-loop fashion to the local-level frame.
Abstract: The error equations for a space-stable inertial navigation system are derived. This is done by directly perturbing the mechanization equations in the inertial frame and then transforming in open-loop fashion to the local-level frame. A rotating inertial platform and velocity and altitude damping are considered. The relations between errors in space-stable and local-level systems are noted. Numerical results are presented for certain random error sources.
TL;DR: In this article, a detailed development of the equations of motion for the stable member of a three-axis platform is presented, including the effects of friction, inertia, and torque motors.
Abstract: This paper presents a detailed development of the equations of motion for the stable member of a three-axis platform. Kinematic relations are presented for an x, z, y Euler sequence. This development includes the effects of friction, inertia, and torque motors. A set of six first-order differential equations of state are presented representing the equations of motion of the system members. These equations may be integrated and the resulting Euler angles and rates used to describe the stable member motions. When combined with the servo loops, the motion of the stable member represents the angular motion environment of the stable member mounted instruments.
TL;DR: In this paper, envelope hard limiting in the control loops is proposed to reduce the dependence of the external noise field on the performance of an adaptive array antenna, including transient response rate and control loop noise.
Abstract: The properties of an adaptive array antenna, including transient response rate and control loop noise, depend on the intensity of the external noise field. This dependence can be reduced by envelope hard limiting in the control loops, without degrading the performance of the adaptive array.
TL;DR: In this paper, the radio-emission characteristics of the strong discrete (celestial) radio sources, of the sun, and of the moon are presented, and problems encountered when the sensitivity is insufficient for complete radiation pattern determination, when the width of the radio source is comparable to the beamwidth of the antenna, when the illumination of antenna aperture varies with pointing direction, or when the techniques are extended (after determining the gain of the ground-based antenna) to the measurement of the effective radiated power from a satellite are discussed.
Abstract: Extraterrestrial radio sources, whose emission characteristics (flux density, spectrum, angular size) and coordinates have been firmly established by careful observations, have application in the measurement of the effective area (aperture efficiency and gain) of an antenna and its radiation pattern. The radio-emission characteristics of the strong discrete (celestial) radio sources, of the sun, and of the moon are presented. Problems encountered when the sensitivity is insufficient for complete radiation pattern determination , when the width of the radio source is comparable to the beamwidth of the antenna, when the illumination of the antenna aperture varies with pointing direction, or when the techniques are extended (after determining the gain of the ground-based antenna) to the measurement of the effective radiated power from a satellite are discussed.
TL;DR: The rotary transformer has the desireable characteristics of high reliability and low noise which qualify it as a potential replacement for slip rings as discussed by the authors, and is built in modular sections, each capable of transferring 500 watts across a gap at efficiencies greater than 88 percent, dc to dc.
Abstract: Many future satellite configurations will require the transfer of signals and power across rotating interfaces. Satellite systems are particularly cost effective for both commercial and military communications applications if their useful lifetime can be demonstrated to be greater than five years. The rotary transformer has the desireable characteristics of high reliability and low noise which qualify it as a potential replacement for slip rings. This paper describes the development of a rotary transformer for typical spacecraft applications. The transformer is built in modular sections, each capable of transferring 500 watts across a gap at efficiencies greater than 88 percent, dc to dc. The design effort included a study of pertinent electrical characteristics required for typical spacecraft configurations, electrical design and analyses of the overall dc-dc converter, mechanical design of the transformer cores and their assembly, and a study of transformer core and winding characteristics. Breadboard test results have demonstrated the desired level of efficiency, satisfactory operation over temperature, and satisfactory electrical characteristics.
TL;DR: In this paper, a statistical analysis of the number of repeaters is presented as the basis for a crime control system consisting of a transponder carried by each convicted person after he was released from confinement.
Abstract: A review of some of the underlying reasons for crime is presented, together with a perspective-setting view of the present status of crime in the United States. A statistical analysis of the number of repeaters is presented as the basis for a crime control system consisting of a transponder carried by each convicted person after he is released from confinement. Real-time tracking of these transponders is done by a computer-radio system; when a crime is committed a quick check shows at least who was not involved. Countermeasures and some social implications are also covered.
TL;DR: The M out of N detection algorithm is defined and detection performance is calculated for the special cases of the nonfluctuating target and Swerling cases I and 11 for false alarm probabilities of 106, 10-8 and 10-10.
Abstract: A problem f requently encountered by radar systems analysts is the evaluation of the "double-threshold" or M out of N detection process. Detection probabilities of this process are binomially distributed, making it difficult to obtain exact results for large values of the number of samples and for low probabilities of false alarm. In this paper, the M out of N detection algorithm is defined and detection performance is calculated for the special cases of the nonfluctuating target and Swerling cases I and 11 for false alarm probabilities of 106, 10-8 and 10-10.
TL;DR: In this article, it was analytically shown that this is the best normalization technique for analytic platforms and a geometrical interpretation of this result was also given, which is the case for the normalization in this paper.
Abstract: The normalization technique usually employed in "analytic platforms" in which quaternions are used to update the orientation of the vehicle is the one which divides the components of the quaternion by its magnitude. In this correspondence, it is analytically shown that this is the "best" normalization technique. A geometrical interpretation of this result is also given.
TL;DR: In this paper, a comparison of the error propagation in a local level reference frame is derived for two inertial navigation systems; one has a local-level configuration, and the other has a space-stable configuration.
Abstract: A comparison of the error propagation in a local-level reference frame is derived for two inertial navigation systems; one has a local-level configuration, and the other has a space-stable configuration. The error propagation is shown to be equivalent for the two cases considered. This equivalence is demonstrated by starting with the error propagation equations for the space-stable system and transforming them to a local-level reference frame. The transformed equations are then compared with the classical local-level error equations, and the equivalence is noted. The specific implementation used in each case considers velocity damping but not altitude damping.
TL;DR: In this article, it was shown that for detecting the presence of a sinusoid by means of Walsh analysis, the time scale should therefore be chosen so that the order of the Walsh function is a power of 2 and the Walsh functions is a Rademacher function.
Abstract: The Walsh spectrum of a sinusoid of frequency f = p/2q with p odd consists entirely of lines at orders s that are odd multiples of 2/2q, and the Fourier spectrum of a Walsh function of order 2p/2q consists entirely of lines at frequencies that are odd multiples of 1/2q. For all other frequencies or orders, the spectrum contains no lines, but the power spectral density takes all values in the range [0,oo] in every interval, however short, while being almost everywhere zero. For detecting the presence of a sinusoid by means of Walsh analysis, the time scale should therefore be chosen so that the order of the Walsh function is a power of 2 and the Walsh function is a Rademacher function, i.e., a hard-limited sinusoid of the frequency being sought.
TL;DR: In this article, the complex angle (CA) method for resolving a low angle target from its multipath signal is evaluated in the presence of system noise, and it is shown that standard deviation improvements of around 3-to-1 can be achieved at a 20dB signal-tonoise power ratio relative to a normal monopulse system without the CA.
Abstract: The complex angle (CA) method for resolving a low angle target from its multipath signal is evaluated in the presence of system noise. It is shown that standard deviation improvements of around 3-to-1 can be achieved at a 20-dB signal-to-noise power ratio relative to a normal monopulse system without the CA. It is also shown that the CA method is unbiased, giving bias improvements of as much as 100 times relative to normal monopulse. Evaluation of the assumptions in the technique shows very little sensitivity to knowledge of the reflecting surface's conductivity or dielectric constant. However, the method is somewhat sensitive to knowledge of surface roughness.
TL;DR: In this paper, the rotation of a spin-stabilized satellite employing a turnstile antenna for reception and retransmission affects two-way Doppler range-rate measurements.
Abstract: The rotation of a spin-stabilized satellite employing a turnstile antenna for reception and retransmission affects two-way Doppler range-rate measurements. Two different types of tracking systems are considered and, in both systems, the range-rate measurement is changed by the amount \begin{equation*} |\Delta \dot{r}| = \frac{|1 \pm 1/k|}{2} \lambda_{t}f_{s} \end{equation*} where k is the turn-around ratio of the satellite transponder, Xt is the wavelength of the ground-based transmitter, and fs is the spin rate of the satellite. The positive sign is used if the turnstile antenna elements are connected to give the same polarization for both reception and transmission. If the antenna connections result in different polarizations, the minus sign is used and the magnitude of the effect is reduced.
TL;DR: In this article, the angular coordinates of the midpoint of two unresolved targets and the slope of the line joining them were determined from measurements of pulse amplitudes and normalized error signals made with a conventional monopulse radar.
Abstract: From measurements of pulse amplitudes and normalized error signals made with a conventional monopulse radar it is possible in theory to determine the angular coordinates of the midpoint of two unresolved targets and the slope of the line joining them. Under special conditions it is also possible to determine the angular locations of the individual targets.