Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

Fluctuating Target Detection in Clutter Using Sidelobe Blanking Logic

In an earlier paper, Maisel [6] considered two-channel detection systems using a sidelobe blanking logic when a nonfluctuating target was present. This paper is an extension of the earlier work to include fluctuating targets. The Swerling I, II, III, and IV models are considered when single-pulse detection is of interest. An adaptive threshold procedure is also briefly discussed whereby the probability of false alarm at any given resolution cell is maintained constant, even though the input clutter level may vary from cell to cell or from beam position to beam position. Useful data are presented for detection probabilities in the range 0.5 to 0.9, for false alarm probabilities in the range 104 to 10-8, and for a false detection probability of 0.1 for a sidelobe target yielding an apparent signal to total noise power density ratio of 13.0 dB in the main beam receiver.     

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.     

Analysis of Some Modified Cell-Averaging CFAR Processors in Multiple-Target Situations

A serious degradation of detection probability (Pd) in a cellaverging constant false alarm rate (CA-CFAR) detector is known to be caused by the presence of an interfering target in the set of reference cells. A technique which is often used to prevent excessive false alarms at clutter ?edges? is a ?greatest of? (GO) selection between the leading and lagging sets of cells (GO-CFAR). However, it is demonstrated for a Rayleigh target that the abovementioned suppression effect is more acute in the GO-CFAR. Practically, detection of closely separated targets is almost inhibited. Selection of the ?smallest of? (SO) the means for the adaptive threshold has been proposed to alleviate this problem. An analytic expression for Pd of this detector is also derived, and it is shown that though it does prevent the suppression effect, a large sensitivity loss is introduced unless the number of reference cells is sufficiently large. A modified CO-CFAR detector, combining a ?censoring? circuit, is proposed for automatic detection in a complex nonhomogeneous environment.     

Moving target detection via airborne HRR phased array radar

We study moving target detection in the presence of temporally and spatially correlated ground clutter for airborne high range resolution (HRR) phased array radar. We divide the HRR range profiles into large range segments to avoid the range migration problems that occur in the HRR radar data. Since each range segment contains a sequence of HRR range bins, no information is lost due to the division and hence no loss of resolution occurs. We show how to use a vector autoregressive (VAR) filtering technique to suppress the ground clutter. Then a moving target detector based on a generalized likelihood ratio test (GLRT) detection strategy is derived. The detection threshold is determined according to the desired false alarm rate, which is made possible via an asymptotic statistical analysis. After the target Doppler frequency and spatial signature vectors are estimated from the VAR-filtered data as if a target were present, a simple detection variable is computed and compared with the detection threshold to render a decision on the presence of a target. Numerical results are provided to demonstrate the performance of the proposed moving target detection algorithm     

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     

Probability of Detecting a Swerling I Targetet on Two Correlated Observations

Modern radars characterized by electronically steered beams, frequency agility, and range-ambiguous waveforms can use a processing technique whereby each new detection is followed by a second dwell to verify the initial detection. The second dwell is used to minimize false alarms and to resolve range and/or Doppler ambiguities. Under the assumption of a Swerling I target model, the target cross section remains constant when both dwells occur on the same scan and the same transmission frequency is used. Analytic expressions have been developed for the probability of detecting a Swerling I target on both of the correlated dwells (same target cross section). These expressions are used to calculate the probability of a second dwell detection given a first dwell detection and the probability of at least one detection on two dwells. These probabilities are compared with those of independent dwells (independent target cross sections) which result when two transmission frequencies of sufficient separation are utilized.     

Optimization of waveform and detection threshold for range and range-rate tracking in clutter

We address an optimization problem to obtain the combined sequence of waveform parameters (pulse amplitudes and lengths, and FM sweep rates) and detection thresholds for optimal range and range-rate tracking in clutter. The optimal combined sequence minimizes a tracking performance index under a set of parameter constraints. The performance index includes the probability of track loss and a function of estimation error covariances. The track loss probability and the error covariances are predicted using a hybrid conditional average algorithm. The effect of the false alarms and clutter interference is taken into account in the prediction. A measurement model in explicit form is also presented which is developed based on the resolution cell in the delay-Doppler plane for a single Gaussian pulse. Numerical experiments were performed to solve the optimization problem for several examples.     

Measurements of L-band inland-water surface-clutter Doppler spectra

Although radar surface-clutter reflectivities from terrain are generally much greater than those from water, strong Bragg resonances at low but non-zero Doppler frequencies in backscatter from small inland bodies of water might potentially cause false alarms for moving target indicator (MTI) or other Doppler signal-processing techniques designed for target detection in ground clutter. To provide data for investigating this concern, measurements of L-band radar backscatter were recorded from the surface of a small inland freshwater reservoir in central Massachusetts. These measurements were of unusually high system stability and spectral purity so as to provide up to 80 dB of available spectral dynamic range. Strong Bragg spikes occurred in the clutter Doppler spectra from the reservoir at low (3 to 4 Hz) but non-zero Doppler frequencies. This strong Bragg resonance was persistent in time and space throughout the measurements. Spectral results are presented for all four combinations of linear polarization. Comparison with tree clutter spectral results indicates that, when an occasional water body comes under surveillance at vertical polarization in otherwise generally forested terrain, water clutter spectral density is expected to exceed surrounding-terrain tree clutter spectral densities in the Bragg-offset Doppler vicinity by large amounts     

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     

Optimal polarimetric detection of radar target in a slowlyfluctuating environment of clutter

It is shown that in a situation where a radar target is distant enough from the radar and is included in a natural or artificial clutter environment in such a manner that the conventional detection methods fail, it is possible to improve the radar detection performance by using appropriate signal processing on two orthogonal polarization states. A CFAR (constant false alarm rate) polarimetric detection system based on the study of the polarization difference between clutter and target is proposed. Since the polarization state of the clutter echoes fluctuates slowly from cell to cell, an autoregressive model can be applied to the components of the polarization vector to predict the detection thresholds needed to follow the polarization state variation. The detection thresholds are determined to maintain a false alarm probability equal to 10^-6. The presence of a target registers as a significant variation of the estimation error of the polarization vector. Results obtained from measurements of simple and canonical targets with artificial clutter are presented, and these results validate the principle of polarimetric detection     

Clutter Map CFAR Analysis

An analysis of the probability of target detection for a clutter map CFAR using digital exponential filtering has been performed. General performance equations are derived. The probability of detection versus signal-to-noise ratio is plotted for a false alarm probability of 1.E-06 for several weight values. The CFAR loss is plotted for a detection probability of 0.9 and false alarm probabilities of 1.E-06 and 1.E-08.     

An Alternative Method for Analyzing the Double Threshold Detector

An alternative method for analyzing the performance of a double threshold or M-out-of-N detector is discussed. Detection performance for the suggested method is based on the probability that a return crosses the threshold for the Mth time (a detection is declared) on the kth return or look. It is shown that this formulation has many advantages, as compared with the conventional method of analysis which employs the binomial probability distribution, since the upper limit N is not contained in the resulting probability expressions. It is shown that the probability of detection obtained by the alternate method is the same as that obtained if the detection method were analyzed as a Markov chain with M+1 states. Use of the method results in simple expressions for the mean and variance of the number of looks before detection, provides an alternative way of estimating the probability of a threshold crossing, and leads to computationally simple bounds for the probability of false alarm.     

A robust exponential mixture detector applied to radar

Exponential mixture probability density functions (pdfs) are shown to be useful models of radar sea clutter. The variability of certain parameters leads to estimation error and degradation in the performance of detection algorithms derived from this model. Robust implementations are introduced by assuming that parameters are known within certain intervals and selecting values to prevent an excessive number of false alarms. An empirical study demonstrates an average 6-9 dB gain in comparison with a constant false-alarm rate (CFAR) processor     

Adaptive False Alarmrm Regulation in Double Threshold Radar Detection

In practical situations the false alarm probability in double threshold radar detection, sometimes known as binary integration with sliding window detection, is dependent on the nonstationarity and azimuthal correlation of the clutter which is present. Control of the false alarm probability can be achieved, to a certain extent, by the adjustment of the second threshold in the detection process. In this study two adaptive control techniques which are based on the statistical characteristics of the data are compared. Comparing the results for a technique based on first-order statistics with one based on second-order statistics, it is shown that the second-order, or correlation sensitive, technique can give a reduction of 30 to 45 percent in the false alarm probability with no corresponding loss in the detection probability. An interesting aspect of the results is the fact that the effects of the size of the sample area and the bias in the correlation estimator are clearly evident.     

Modified Difference Change Detector for Small Targets in SAR Imagery

One of the most straightforward techniques for detecting changes in an image involves forming the difference between a test image and a reference image. Unfortunately, such a technique can give rise to a large number of false alarms due to the statistical variability of the underlying pixel values, as has been well established within the radar community over the years. One method for dealing with this large number of false alarms involves forming the ratio, rather than the difference, of two synthetic aperture radar (SAR) images. We introduce a modified version of the standard differencing technique to overcome problems associated with pixel value variability. The new (modified) differencing approach utilizes assumptions about the statistics of the image background and the object being sought (target) to reduce the number of false alarms due to highly variable background (clutter) regions, and it includes the standard ratio test as a special case. In fact, we find that the modified difference approach can also be viewed as a modified version of the ratio test with a threshold that varies as a function of the background clutter radar cross section (RCS). We also present an abridged, albeit suboptimal, version of this approach that eliminates assumptions regarding the target's probability distribution, and we analyze both of the approaches. We then compare these results with those obtained with a standard ratio test, and illustrate how the modified difference test reduces to the ratio test under certain operating conditions. The abridged version of the modified approach is applied to high resolution synthetic aperture radar imagery and compared with results obtained with the classical differencing technique, and following this, the modified difference technique is compared with the standard ratio test. Results suggest that under appropriate conditions the abridged, modified technique can successfully detect changes without the need for any image segmentation.     

Near-Field Analysis of Helicopter Rotating Blades Modulation Interference

A near-field analysis is carried out to obtain the level of modulation interference due to rotating blades in a helicopter-borne pulse Doppler radar system. The interference power spectra are calculated for different values of antenna depression angle and helicopter (radar) speed at a constant helicopter altitude of 300 m. Numerical results for the case of 1 kW radiated power show that blade interference level is about 5 to 8 dBW/Hz less than that of the direct ground clutter in the clutter region. It extends, however, into the clutter-free region which may cause false alarms and degradation of the radar performance.     

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.     

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     

Distributed CFAR detection in homogeneous and nonhomogeneousbackgrounds

The performance of distributed constant false alarm rate (CFAR) detection with data fusion both in homogeneous and nonhomogeneous Gaussian backgrounds is analyzed. The ordered statistics (OS) CFAR detectors are employed as local detectors. With a Swerling type I target model, in the homogeneous background, the global probability of detection for a given fixed global probability of false alarm is maximized by optimizing both the threshold multipliers and the order numbers of the local OS-CFAR detectors. In the nonhomogeneous background with multiple targets or clutter edges, the performance of the detection system is analyzed and its performance is compared with the performance of the distributed cell-averaging (CA) CFAR detection system