Statistical Analysis of Antenna Pattern Loss Effects

The generation of average probability-of-detection curves for threedimensional, or pencil-beam, radars, with compensation for random target position included statistically, is discussed. A fixed-array radar with step-scan operation is assumed and, with 3-dB beam crossover points, this is effectively the case of one pulse per beamwidth or one hit per scan. Numerical results are presented showing detection dependence on beam overlap, detection threshold, and amplitude scintillation. The fact that the average energy received from a target, assuming a uniform distribution of target position within a beam, does not lead to the correct average probability of detection at other than 0.5 P D is discussed and shown graphically.     

Low cost Doppler ratio detection radar with interclutter visibility

A low cost concept, called Doppler ratio detection (DRD), for suppressing the clutter residue of Doppler radars is described. The concept provides a simple way to establish a target detect-clutter reject threshold at each range cell, whether a MTI canceler only or a bank of Doppler filters is used. In its simplest form, the target detect/clutter reject threshold is based on the ratio of the magnitudes of Doppler-processed and non-Doppler processed signals. The experiment showed that clutter was rejected, but the amount of added degradation in detection sensitivity was not determined. This degradation will depend on a number of factors, including the number of pulses per beamwidth     

Target detection trials with a millimeter wave radar system

Unobstructed, large RCS targets, similar radar targets surrounded by moving foliage, and small targets in severe clutter have been used as test cases for two pre-processing algorithms and several threshold levels in an experimental millimeter wave radar system. The rather conventional "six-out-of-eight" pulse radar selection method with binary output has been compared to an algorithm that accepts a target if the pre-defined trigger level is crossed by the average of the eight consecutive pulses. In this case, however, the output is an analog value corresponding to the relative average video amplitude. In terms of plotted video, this process seems to give a slightly better combination of false alarm rate and detection probability. Large targets are easier to detect from foliage clutter with the conventional method.     

Effect of Monopulse Signal Thresholding on Tracking Multiple Targets

The monopulse angle of arrival measured from two targets may wander far beyond the angular separation of the targets. In order to remove large errors, angle of arrival measurements are passed through a threshold detector and the measurements which do not satisfy the threshold are rejected. Thresholding has the tendency to move the mean indicated angle of arrival away from the stronger target and toward the power centroid of the targets, which may be undesirable in some applications. Expressions for the probability density function, the mean, and the variance of the in-phase angle of arrival are developed in this paper as a function of the threshold setting. Background noise and interfering signals are neglected in the analysis.     

Reduction of Radar Tracking Errors with Frequency Agility

Frequency agility with random frequency in each pulse gives an improvement in radar angle tracking with a monopulse radar. With a conical-scan tracking radar, the glint error is reduced but fading error can be increased, and the net result must be studied in each case. A theory, usable for calculating angle tracking errors with a frequency agile radar, is given, and two examples showing the error reduction are presented. According to the theory, one part of the glint or fading spectra is ``smeared out' to half the pulse repetition frequency. Another part, the size of which depends on the degree of correlation between pulses, keeps the form of the original spectrum.     

Analysis of queuing behavior of automatic ESM systems

Radar electronic support measures (ESM) systems detect active emitters in a given area and determine their identities and bearings. The high arrival rate of radar pulses in dense emitter environments demands fast automatic processing of arriving pulses so that the ESM system can fulfill its functions properly in real time. Yet, the performance analysis of automatic ESM system in real life Is difficult since both pulse arrivals and widths can be specified only probabilistically. The success of queuing theory in many applications such as computer communication networks and flow-control has encouraged designers to utilize queuing theory in qualifying and judging the performance of automatic ESM systems in dense emitter environments. The queuing behavior of these systems is analytically evaluated under different service disciplines and elaborate computer simulations validate the results. The analysis involves statistical modeling of arrival and departure processes as well as distribution of service times. It permits estimating the blocking probability due to high arrival rates of intercepted radar pulses or due to limited speed of the deinterleaver processor. Queuing analysis is shown to be quite useful to quantitatively assess tradeoffs in ESM systems design     

基于统计置信度的湍流检测门限确定方法

机载气象雷达是检测飞行中湍流的重要设备,对于保障飞行的安全具有重大意义。它通过判断回波信号谱宽是否超过门限来检测湍流,关键在于检测门限的设定。将其看成一个统计问题进行解决,提出了利用统计学中置信度来设置门限的方法,根据湍流微粒的概率分布推导了置信度与检测门限的关系,并利用其进行检测门限设置。最后利用仿真的气象雷达回波信号进行了实验,实验结果表明提出的方法能够检测出实验中设置的湍流区域．验证了方法的有效性．     

Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal     

Detection Performance of Soft-Limited Phase-Coded Signals

General analytic expressions are developed for the soft-limited digital pulse compressor (matched filter). This theoretical development is then used for the hardware realization of a two-channel (I,Q), 3-bit-limited digital pulse compressor with a compression ratio of 255: 1. The realized hardware uses state of the art integrated circuit devices. An experimental laboratory setup is described. This setup is used to study hard-limited versus 3-bit-limited matched-filter performance characteristics with the data in the following areas: 1) constant false alarm rate (CFAR) characteristics as a function of threshold settings and noise levels; 2) single target detection characteristics as a function of input signal-to-noise ratio (SNR); and 3) two target performance characteristics: a) the amplitude of a weaker target as a function of target ratio and target overlap; and b) the detection characteristics of a weaker target as a function of weaker target SNR, strong target SNR, and target overlap.     

A Clutter Reduction Technique for Random Signal Radars

The performance of certain radars is degraded in environments with significant clutter returns, and since the clutter is signal-generated, increasing the transmitted power does not improve the situation. However, changing the pulse width and pulse period of the transmitted signal can increase the input signal-to-interference ratio. In this correspondence, the transmitted signal is made up of pulses of random waveforms and the receiver is a correlator where the reference signal extends over many pulses. An expression for input signal-to-interference ratio as a function of pulse width and period is obtained for the case of a distributed target. This expression could be maximized by any of several methods, but to further elucidate the clutter reduction technique, contour plots of the input signal-to-interference ratio are presented.     

Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance     

Sidelobe blanking with integration and target fluctuation

In radar systems, sidelobe blanking (SLB) is used to mitigate impulsive interference that enters the radar through sidelobes of the main antenna. SLB employs an auxiliary antenna channel with the output being compared with that of the main antenna channel and a decision is then made as to whether or not to blank the main channel output. SLB performance determination involves the evaluation of several probability functions. Based on the classical Maisel SLB architecture, this work extends previous performance results, in which detection was limited to the case of a single radar pulse with either Marcum or Swerling I target fluctuation. Probability expressions have been generalized to include both an arbitrary number of integrated pulses and target fluctuation models based on the gamma distribution. The Swerling fluctuation models are all special cases of the gamma distribution. Results are derived in terms of two generalized probability functions, one for detection and the other for blanking. With these generalized probability functions, the SLB design and performance results can be determined. Examples are presented and discussed.     

Low-altitude target detection by coastline operated marine radar

Relevant to a Richian family of fluctuating targets with a composite background of sea-plus-land clutter, the performance prediction of a radar operating in near-coastal regions is elucidated by assuming noncoherent integration of the pulses. Considering the dominance of land clutter, a modified K-distributed statistic is indicated for the overall clutter envelope; and the corresponding probability of false alarm and probability of detection are deduced for fixed threshold detection (s) based on N pulses integrated in the presence of the sea-plus-land clutter and the noise. Even when the target offers a dominant scattered echo, the worst situations of the land clutter affecting the detection performance are indicated     

Experiments in Adaptive Estimation of Unknown Binary Waveforms

A special-purpose adaptive machine is described which carries out estimation in real time of an unknown binary waveform which is perturbed with additive Gaussian noise. Unknown waveforms of over 103 samples in duration can be recovered. The unknown waveforms are of unknown epoch and can reappear at either random or periodic time intervals. The observed signal is received at moderate or low signal-to-noise ratios so that a single observation of the received data (even if one knew the precise signal arrival time) is not sufficient to provide a good estimate of the signal waveshape. Experimental results are described which show transient behavior waveform estimate. The transient behavior is expressed as the number of errors in the current estimate of the signal plotted vs. time. In a noisy environment, each ``learning' transient is a random time function. These learning transients are shown for several different signal-to-noise ratios and indicate the threshold noise levels for various types of initial states of the machine memory.     

Automatic detection and tracking of a small surface watercraft in shallow water using a high-frequency active sonar

A high-frequency (HF) active sonar can be used to detect and track a small fast surface watercraft in shallow water based on the evolution of the watercraft wake observed in the sonar image sequence. An automatic detection and tracking (ADT) algorithm is described for this novel application. For each ping, the measurement of the target's polar position consists of 2 steps. First, the target bearing is estimated by finding the direction of arrival of the cavitation noise emitted by the watercraft. Then range measurements are extracted from the range profile (constant-angle cut of the sonar image) at the estimated target bearing. Range normalization and clutter map processing are used to reduce the number of false measurements. Estimates of the target's Cartesian position and velocity are updated at the sonar pulse repetition rate using the Kalman filter with debiased consistent converted measurements and nearest neighbour data association. The proposed algorithm is demonstrated using real data.     

Threshold Control for Automatic Detection in Radar Systems

In automatic detection in radar systems an estimate of background clutter power is used to set the detection threshold. Usually detection cells surrounding the cell under test for the presence of a target are used to estimate the clutter power. In the research reported herein, the target location is taken to be uncertain and thus returns from a target could corrupt this clutter power estimate. It is shown how the threshold should be varied to compensate for the resulting degradation in detection performance. The threshold control procedure is based on a priori information about target location that could be supplied by the radar's tracking system. In addition, a simple procedure for calculating detection and false alarm probabilities for Swerling II target models is presented.     

Optimum Processing of Unequally Spaced Radar Pulse Trains for Clutter Rejection

A train of radar pulses from one resolution cell can be processed coherently to reject echoes from external clutter and detect targets moving radially with respect to the clutter. Optimum methods of signal processing are defined for systems in which the interpulse spacings are multiply staggered to avoid target blind speeds. Likelihood ratio tests are developed for systems in which the target Doppler frequency is known a priori and for systems employing a bank of filters to cover the target Doppler band. To implement such tests, the N pulses in the train are added with complex weights and the amplitude of the sum compared with a detection threshold. The set of weights which maximizes the average signal-to-clutter ratio is also computed for a single-filter system with unknown target Doppler frequency. When the clutter autocorrelation function is exponential, the clutter covariance matrix can be inverted analytically. This latter result is useful for comparing different interpulse-spacing codes for a particular system application.     

Conopulse Radar Angle Tracking Accuracy

An analysis is given of the tracking accuracy of a conopulse radar that angle-tracks on target echo pulses. The analysis includes effects of noises in both sum and difference channels, the effect of the tracking range gate's duration, and applies to any shape of radio frequency (RF) pulse envelope. For large single-pulse signalto-noise ratio and any shape of RF pulse envelope, accuracy approaches the theoretical accuracy of a conopulse system when a short-duration range gate is used. The inportant case of rectangular RF pulses is solved in detail.     

Probability Densities and Characteristic Functions for Fluctuating Targets

Probability density functions and characteristic functions for the projected area of a tumbling target object are derived together with the densities and characteristic functions for the corresponding signal-plus-noise voltage output of an infrared sensor. Several cases are considered in which the signal pulse arrival time is either known or unknown, a matched filter or a suboptimum filter is used; the signal pulse shape is either Gaussian or is unspecified; and the target orientation angles are either uniformly or nonuniformly distributed.     

Emitter Location Independent of Systematic Errors in Direction Finders

A scheme is suggested for the passive location of radio emitter position by using a mobile direction finder. The vehicle carrying the direction finder is made to maneuver such that the apparent direction of arrival is held constant. The resulting trajectory of the vehicle is a logarithmic spiral. The true direction of arrival can be obtained by monitoring the parameters of the spiral trajectory without using the value of the direction fimder reading. Two specific algorithms to eliminate direction finder bias are presented and their sensitivity to random errors in measurement assessed.