Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

图象序列中机动目标的形心跟踪

从边检测边跟踪的角度探讨了图象序列中机动目标的形心跟踪问题,深入分析了强高斯噪声背景下目标形心估计的统计性质及用于形心估计的图象预处理方法。指出经典的图象二值化变换分割后作形心估计的方法面临着估计偏差和方差的矛盾,提出了用自适应交互三模型(ATIMM)跟踪图象序列中机动目标的方法,同时发现在了解目标形状的条件下,空间匹配滤波,二值变换点集聚类和 ATIMM三者的结合对图象序列中的机动目标具有最好的跟踪性能。     

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     

Theory of partially adaptive radar

This work extends the recently introduced cross-spectral metric for subspace selection and dimensionality reduction to partially adaptive space-time sensor array processing. A general methodology is developed for the analysis of reduced-dimension detection tests with known and unknown covariance. It is demonstrated that the cross-spectral metric results in a low-dimensional detector which provides nearly optimal performance when the noise covariance is known. It is also shown that this metric allows the dimensionality of the detector to be reduced below the dimension of the noise subspace eigenstructure without significant loss. This attribute provides robustness in the subspace selection process to achieve reduced-dimensional target detection. Finally, it is demonstrated that the cross-spectral subspace reduced-dimension detector can outperform the full-dimension detector when the noise covariance is unknown, closely approximating the performance of the matched filter.     

Adaptive detection using low rank approximation to a data matrix

Using an accurate formula for the error in approximating a low rank component, we calculate the performance of adaptive detection based on reduced-rank nulling. In this principal component inverse (PCI) method, one temporarily regards the interference as a strong signal to be enhanced. The resulting estimate of the interference waveform is subtracted from the observed data, and matched filtering is used to detect signal components in the residual waveform. We also present a generalized likelihood-ratio test (GLRT) for adaptively detecting a low rank signal in the presence of low rank interference. This approach leads to a test which is closely related to the PCI method and extends the PCI method to the case where strong signal components are present in the data. A major accomplishment of the work is our calculation of the statistics of the output of the matched filter for the case in which interference cancellation and signal detection are carried out on the same observed data matrix. That is, no separate data is used for adaptation. Examples are presented using both simulated data and real, active-sonar reverberation data from the ARSRP, the Acoustic Reverberation Special Research Program of the Office of Naval Research     

Studies of target detection algorithms that use polarimetric radardata

Algorithms are described which make use of polarimetric radar information in the detection and discrimination of targets in a ground clutter background. The optimal polarimetric detector (OPD) is derived. This algorithm processes the complete polarization scattering matrix (PSM) and provides the best possible detection performance from polarimetric radar data. Also derived is the best linear polarimetric detector, the polarimetric matched filter (PMF), and the structure of this detector is related to simple polarimetric target types. New polarimetric target and clutter models are described and used to predict the performance of the OPD and the PME. The performance of these algorithms is compared with that of simpler detectors that use only amplitude information to detect targets. The ability to discriminate between target types by exploring differences in polarimetric properties is discussed     

Optimum Mismatched Filters for Sidelobe Suppression

This paper discusses the application of least-mean-squares approximate inverse filtering techniques to radar range sidelobe reduction. The method is illustrated by application to the 13-element Barker code. The performance of the least-mean-square inverse filter is compared with the matched filter and with the simplified sidelobereducing filters of Rihaczek and Golden. A filter which completely suppresses the range sidelobes of a 13-element Barker sequence is only 0.2 dB worse than a matched filter in noise.     

A mean level adaptive detector using nonconcurrent data

Convergence results for a mean level adaptive detector (MLAD) are presented. The MLAD consists of an adaptive matched filter (for spatially correlated inputs) followed by a mean level detector (MLD). The optimal weights of the adaptive matched filter are estimated from one batch of data and applied to a statistically independent batch of nonconcurrent data. The threshold of the MLD is determined from the resultant data. Thereafter a candidate cell is compared against this threshold. Probabilities of false alarm and detection are derived as a function of the threshold factor, the order of the matched filter, the number of independent samples per channel used to calculate the adaptive matched filter weights, the number of samples used to set the MLD threshold, and the output signal-to-noise power ratio of the optimal matched filter. A number of performance curves are shown and discussed     

Estimation of Aircraft Target Motion Using Orientation Measurements

A new approach to estimating motion of a highly maneuverable aircraft target in an air-to-air tracking scenario is presented. An interactive filter system is developed that provides an improved estimate of target motion states by conditioning kinematic filter estimates on target aspect angle data. Pattern recognition techniques used with an electrooptical tracker are presumed to provide this target aspect information. A target orientation filter processes the aspect angle measurements by statistically weighting measured aspect angles with the current best estimate of target kinematics. The aerodynamic lift equation is used to relate approximate angle of attack to target velocity and acceleration. A novel statistical model for aircraft target normal acceleration is also developed to represent better the unknown target accelerations. Simulation results of realistic three-dimensional scenarios are presented to evaluate the performance of the interactive filter system.     

On detection using filter banks and higher order statistics

We suggest a method, based on the use of filter bank and higher order statistics (cumulants), for detection of transient signals. The method first uses a bandpass filter bank, which separates the spectrum of the observed signal into narrow frequency bands. Each subfilter of the filter bank is then followed by a cumulant estimator, and thereby suppressing colored noise. By selecting those subfilters that have large output energies, the filter bank can approximate the behavior of a matched filter. Moreover, no a priori information about the waveform of the signal is needed. The performance of the detector is evaluated by using a simulated signal as well as a measured signal. The presented detector is compared with the optimal matched filter detector.     

Interrelationship of single-filter and multiple-model adaptivealgorithms

An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model     

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.     

The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

Validation of windblown radar ground clutter spectral shape

We investigate the robustness of the linear matched filter (MF) operating in a Gaussian environment in the presence of a mismatch between the design clutter-power spectral density (PSD) shape and the actual one. The Gaussian, the power-law (PL), and the double-exponential spectral models have been considered with the goal of investigating which one fits best for windblown foliage. We analyze the MF performance in terms of improvement factor, probability of false alarm, and probability of detection by making use of the theoretical models and measured X-band ground clutter data. The numerical results validate the double-exponential spectral model for windblown foliage by showing that the differences in performance prediction between using measured clutter data and modeled clutter data of various spectral shapes (viz., Gaussian, FL, and double-exponential) are minimized when the spectral model employed is of double-exponential shape     

A Nonadaptive Processing of Radar Pulse Trains for Clutter Rejection

The problem of detecting coherent pulse trains with uniform amplitude in a clutter-plus-noise environment is considered. A radar processor for detecting targets moving radially with respect to the clutter is proposed. The minimum interpulse spacing of the transmitted signal is assumed long enough that returns are not received simultaneously from different ranges within a region of extended clutter, and the central frequency of the clutter power spectrum is postulated to be known. The processor is singled out as the linear filter, orthogonal to the clutter central frequency component, which yields the maximum ratio of peak signal power to average noise power. The filter can be implemented by slightly modifying the structure of the conventional matched filter. The performance of such a filter is compared with that achievable if full a priori knowledge of the input interference were available and with that of the conventional matched filter. This comparison is made on a signal-to-interference power ratio basis after assuming a transmitted signal consisting of equally spaced pulses and an interference characterized by an exponential covariance matrix.     

Mixture Reduction Algorithms for Point and Extended Object Tracking in Clutter

The Bayesian solution to the problem of tracking a target with measurement association uncertainty gives rise to mixture distributions, which are composed of an ever increasing number of components. To produce a practical tracking filter, the growth of components must be controlled by approximating the mixture distribution. Two mixture reduction schemes (a joining algorithm and a clustering algorithm) have been derived for this purpose. If significant well spaced mixture components are present, these techniques can provide a useful improvement over the probabilistic data association filter (PDAF) approach, which reduces the mixture to a single Gaussian component at each time step. For the standard problem of tracking a point target in uniform random clutter, a Monte Carlo simulation study has been employed to identify the region of the problem parameter space where significant performance improvement is obtained over the PDAF. In the second part of this paper, the formal Bayesian filter is derived for an extended target consisting of an array of measurement sources with association uncertainty. A practical multiple hypothesis filter is implemented using mixture reduction and simulation results are presented.     

Kalman Filter Compensation for a Special Class of Systems

Filter compensation techniques for several special but practical cases are discussed. A general set of bias and covariance equations for linear filters with modeling errors is first summarized. A method for relating the modeling errors to the selection of the covariance of "process noise" for model error compensation is suggested. A performance ordering for cases when the true system becomes a subsystem of the model used for the filter construction is given. A bias correcting filter is derived for the case when the filter is matched only to a subsystem of the actual system.     

Compensating a Recursive MTI Filter for Missing Pulses

Four methods of compensating a recursive, double-delay movingtarget indictor (MTI) cltter-cancellation filter for missing pulses were simulated and compared. One technique involving feedback from the delay outputs gave an average frequency response closely approximating that of the unperturbed filter.     

Multiple target tracking using products of position measurements

The continued development of the symmetric measurement equation (SME) filter for track maintenance in multiple target tracking (MTT) is considered, focusing on the case in which the SMEs are generated by forming sums of products of the original position measurements. The SME filter is developed for the case of N targets whose motions consist of random perturbations about constant-velocity trajectories. It is assumed that measurements of x-coordinate positions are available, and that the number of measurements is equal to the number of targets. Various analytical properties of the SME filter are studied. It is shown that under a very weak condition, the estimation error equation is locally exponentially stable. The performance of the SME filter is investigated by comparing it with an optimal (minimum-variance) estimator and by generating a computer simulation in the six-target case     

High-Resolution Imaging of Tropospheric Radio Scatterers

A two-dimensional matched filter technique is described for processing ing the signal from a pulsed coherent troposcatter link to obtain high crosspath resolution "maps" showing the relative positions of individual scatterers. For a typical tropolink (station displacement 200 km; midpath beam halfwidth 2 km; wavelength 0.3 meters) crosspath resolution is about 4.5 meters under perfect conditions. Vertical resolution is inversely proportional to scatterer height, but even for wide bandwidth signals is never better than hundreds of meters. Slight velocity mismatches between the signal and filter degrade crosspath resolution considerably so that the scatterers' velocity must be known accurately a priori. Crosspath resolution is relatively insensitive to mismatch in signal and filter record lengths. Random fluctuations of the velocity of a scatterer seriously degrade crosspath resolution. For the typical tropolink parameters and with a 10 m/s scatterer crosspath velocity and a 0.2 m/s standard deviation ion fluctuation the crosspath resolution degrades by an order of magnitude. It is concluded that the matched filter imaging scheme will produce images of individual scatterers if specific atmospheric conditions ions exist. The best results are obtained if the received signal comes from a single scattering layer at a known height, with scatterers moving at a known constant horizontal velocity, with no along-path or vertical components. Such a layer would be observed during night time or early morning when convective and mixing processes are at a minimum.