Application of Three-Dimensional Filtering to Moving Target Detection

The standard approach to the detection of a stationary target immersed within an optically observed scene is to use integration to separate the target energy from the background clutter. When the target is nonstationary and moves with fixed velocity relative to the clutter, the procedure for integrating the target signal is no longer obvious. In this paper it is shown that the problem of tracking a target having a fixed velocity can be cast into a general framework of three-dimensional filter theory. From this point of view, the target detection problem reduces to the problem of finding optimal three-dimensional filters in the three-dimensional transform domain and processing the observed scene via this filtering. The design of these filters is presented, taking into account the target, clutter, and optical detection models. Performance is computed for a basic clutter model, showing the effective increase in detectability as a function of the target velocity. The three-dimensional transform approach is readily compatible with VLSI array processing technology.     

A Probabilistic Strongest Neighbor Filter Algorithm for m Validated Measurements

A new form of the probabilistically strongest neighbor filter (PSNF) algorithm taking into account the number of validated measurements is proposed. The probabilistic nature of the strongest neighbor (SN) measurement in a cluttered environment is shown to be varied with respect to the number of validated measurements. Incorporating the number of validated measurements into design of the PSNF produces a consistent and cost effective data association method. Simulation studies show that the new filter is less sensitive to the unknown spatial clutter density and is more reliable for practical target tracking in nonhomogeneous clutter than the existing PSNF. It has similar performances to the probabilistic data association filter amplitude information (PDAF-AI) with much less computational complexities.     

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     

MTI Optimization in a Multiple-Clutter Environment

A means of optimizing a moving target indicator (MTI) filter for rejecting several types of clutter, which are generated by different mechanisms such as by rain or the ground, is formulated. lt is found that the optimal performance of such a filter depends on the spectral density functions, average radar cross sections, and the relative mean Doppler frequencies of each type of clutter. lt is shown that the optimal improvement factor of such a filter is bounded by the weighted average (weighted in accordance with the radar cross sections of the clutter types) of the improvement factor for the individual clutter type. lt is also shown that the improvement factor of such a filter is a function of the relative mean Doppler frequency f0 between the clutter types. As f0 increases, the performance of the MTI system degrades. The worst improvement factor occurs when f0 is equal to half of the radar pulse-repetition frequency (PRF).     

Novel data association schemes for the probability hypothesis density filter

The probability hypothesis density (PHD) filter is a practical alternative to the optimal Bayesian multi-target Alter based on finite set statistics. It propagates the PHD function, a first-order moment of the full multi-target posterior density. The peaks of the PHD function give estimates of target states. However, the PHD filter keeps no record of target identities and hence does not produce track-valued estimates of individual targets. We propose two different schemes according to which PHD filter can provide track-valued estimates of individual targets. Both schemes use the probabilistic data-association functionality albeit in different ways. In the first scheme, the outputs of the PHD filter are partitioned into tracks by performing track-to-estimate association. The second scheme uses the PHD filter as a clutter filter to eliminate some of the clutter from the measurement set before it is subjected to existing data association techniques. In both schemes, the PHD filter effectively reduces the size of the data that would be subject to data association. We consider the use of multiple hypothesis tracking (MHT) for the purpose of data association. The performance of the proposed schemes are discussed and compared with that of MHT.     

Further results on radar pointing error reduction using discreteextended Kalman filtering

A recently proposed method of reducing target glint errors in radar systems using extended Kalman filtering is further extended with the inclusion of and compensation for clutter effects. A discrete target model and discrete Kalman filter (DKF) are used. Simulation results demonstrating the DKF are presented, and the limits on the effectiveness of the method are investigated. The major advantage of the DKF is that it can be implemented in software in the digital processor of the radar, offering flexibility over continuous time filters. The ability of the filter to reduce clutter effects further demonstrates the usefulness of this technique for radar pointing error reduction     

Multisensor tracking of a maneuvering target in clutter

An algorithm is presented for tracking a highly maneuvering target using two different sensors, a radar and an infrared sensor, assumed to operate in a cluttered environment. The nonparametric probabilist data association filter (PDAF) has been adapted for the multisensor (MS) case, yielding the MSPDAF. To accommodate the fact that the target can be highly maneuvering, the interacting multiple model (IMM) approach is used. The results of single-model-based filters and of the IMM/MSPDAF algorithm with two and three models are presented and compared. The IMM has been shown to be able to adapt itself to the type of motion exhibited by the target in the presence of heavy clutter. It yielded high accuracy in the absence of acceleration and kept the target in track during the high acceleration periods     

Time-frequency method for detecting an accelerating target in sea clutter

The authors design a time-frequency (TF) method for use in high-frequency surface-wave radar (HFSWR) for detecting a small accelerating target in sea clutter. The clutter is modelled by pseudo targets moving with Bragg velocity towards and away from the radar. The design is based on the Wigner distribution (WD) defined by Chan (type-III WD, in our terminology) rather than the WD defined by Claasen and Mecklenbrauker (1980) (2times type-I WD, in our terminology). Like the type-I WD, the type-III WD also concentrates a chirp signal onto a straight line in the TF plane. The type-III WD has the following advantages: 1) Its range of unambiguously measurable frequencies (RUMF) is [-pi,pi] rad/s, whereas for the type-I WD the RUMF is [-pi/2,pi/2] rad/s. 2) It allows a target separated from the clutter by pi rad/s to be detected, whereas the type-I WD coalesces such a target with the clutter and thereby mask it. An ambiguity function (AF) was defined corresponding to the type-III WD and use it to derive a smoothed type-III WD that mitigates the clutter. The smoothed type-III WD method is applied to real radar data and shown to be superior to the conventional Fourier transform method. The advantages of the type-III WD over the type-I WD are also demonstrated. The design principles laid out in the paper can also be used to develop a TF method for use in air traffic control radar (ATCR) for detecting an accelerating target in land clutter     

密集杂波背景下的水下多目标跟踪方法

水下多目标跟踪是水声信号处理领域研究的热点和难点问题。高斯混合概率假设密度(Gaussian mixture probability hypothesis density, GM-PHD)滤波器以其高效的计算效率为解决水下多目标跟踪问题提供了保证。然而,GM-PHD滤波器在跟踪目标时需要先验已知新生目标的强度,否则其性能会出现严重退化。针对该问题,提出一种滑动窗两步初始化高斯混合概率假设密度(sliding window two step initialization GM-PHD, SWTSI-GMPHD)滤波器。将提出的滑动窗两步初始化方法嵌入GM-PHD滤波器,利用滑动窗两步初始化方法估计新生目标强度,减少杂波干扰导致跟踪结果中出现的虚假目标。仿真实验表明,在杂波密集环境下,相较于其他跟踪方法,提出方法将跟踪精度提高69.84%,52.62%和41.05%。     

Clutter Spectra of Low PRF AMTI Pulse-Doppler Radar

Approximate expressions are derived for the video clutter spectra in the receiver of a low pulse repetition frequency (PRF), airborne moving target indicator (AMTI), pulse-Doppler radar for both step-scanning and continuous-scanning antennas. The receiver is assumed to process the received waveform with a clutter-tracking oscillator and a window function is employed to obtain short-term spectra. Except for the broadening effects of the window function, it is shown that the clutter spectrum can be simply related to the antenna voltage-gain pattern. It is further shown, in the scanning antenna case, that the combined spectral broadening due to platform motion and antenna scanning cannot be assumed to be the result of the convolution of the separate effects unless the antenna gain pattern has a Gaussian shape. The approximate clutter expressions are illustrated by examples and are shown to agree well with the results of computer calculations.     

Clutter and jammer multipath cancellation in airborne adaptiveradar

Airborne surveillance radars must detect and localize targets in diverse interference environments consisting of ground clutter, conventional jamming, and terrain scattered jammer multipath. Multidimensional adaptive filtering techniques have been proposed to adaptively cancel this interference. However, a detailed analysis that includes the effects of multipath nonstationarity has been elusive. This work addresses the nonstationary nature of the jammer multipath and its impact on clutter cancellation and target localization. It is shown that the weight updating needed to track this interference will also modulate sidelobe signals. At the very least, this complicates the localization of targets. At the worst, it also greatly complicates the rejection of clutter. Several techniques for improving cancellation of jammer multipath and clutter are proposed, including 1) weight vector interpolation, extrapolation, and updating; 2) filter architecture, constraint, and beamspace selection; 3) prefilters; 4) 3-D STAP architectures; and 5) multidimensional sidelobe target editing     

Road-map assisted ground moving target tracking

Tracking ground targets with airborne GMTI (ground moving target indicator) sensor measurements proves to be a challenging task due to high target density, high clutter, and low visibility. The exploitation of nonstandard background information such as road maps and terrain information is therefore highly desirable for the enhancement of track quality and track continuity. The present paper presents a Bayesian approach to incorporate such information consistently. It is particularly suited to deal with winding roads and networks of roads. The target dynamics is modeled in quasi one-dimensional road coordinates and mapped onto ground coordinates using linear road segments taking road map errors into account. The case of several intersecting roads with different characteristics, such as mean curvature, slope, or visibility, is treated within an interacting multiple model (IMM) scheme. Targets can be masked both by the clutter notch of the sensor and by terrain obstacles. Both effects are modeled using a sensor-target state dependent detection probability. The iterative filter equations are formulated within a framework of Gaussian sum approximations on the one hand and a particle filter approach on the other hand. Simulation results for single targets taken from a realistic ground scenario show strongly reduced target location errors compared with the case of neglecting road-map information. By modeling the clutter notch of the GMTI sensor, early detection of stopping targets is demonstrated     

CFAR for homogeneous part of high-resolution imagery

In high-resolution imaging, weak target pixel amplifiers may not be detected in the presence of clutter containing strong nonhomogeneities, when conventional approaches are used. The authors describe a constant false alarm rate (CFAR) approach that avoids the elimination of these significant target returns. The nonhomogeneous clutter as well as the weak target components are detected with this approach. The targets could then be discriminated from the homogeneities by discrimination techniques. It is shown how the lower amplitude components of the background noise and homogeneous clutter (which have Rayleigh statistics) can be detected in the presence of strong homogeneous clutter and targets. The average level of the homogeneous component is then determined using these lower-amplitude components. This CFAR approach avoids having a CFAR on the strong nonhomogeneities as well as the homogeneous component. The avoidance is what yields the ability to detect weak target pixel amplitudes     

Design of MTI Radar on the Basis of Detection Probability

A single (quadrature) channel moving target indicator (MTI) radar system employing a tapped delay line filter is analyzed. The point of view taken is that of optimal clutter rejection in conjunction with subsequent receiver decision operations. The random nature of the spread of target Doppler shifts is taken into account. Based on the above, a procedure is presented by means of which the detection probability can be numerically evaluated for an optimized filter frequency response.     

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     

HRR Detector for Slow-Moving Targets in Sea Clutter

The radar detection of targets in the presence of sea clutter has historically relied upon the radial velocity of targets with respect to the radar platform either by exploiting the relative target Dopplers (for targets with sufficient radial velocity) or by discerning the paths targets traverse from scan to scan. For targets with little to no radial velocity component, though, it can become quite difficult to differentiate targets from the surrounding sea clutter. This paper addresses the detection of slow-moving targets in sea clutter using a high resolution radar (HRR) such that the target has perceptible extent in range. Under the assumption of completely random sea clutter spikes based on an epsiv-contaminated mixture model with the signal and clutter powers known, optimal detection performance results from using the likelihood ratio test (LRT). However, for realistic sea clutter, the clutter spikes tend to be a localized phenomenon. Based upon observations from real radar data measurements, a heuristic approach exploiting a salient aspect of the idealized LRT is developed which is shown to perform well when applied to real measured sea clutter.     

Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

PDAF with multiple clutter regions and target models

This paper presents the theory of a new multiple model probabilistic data association filter (PDAF). The analysis is generalized for the case of multiple nonuniform clutter regions within the measurement data that updates each model of the filter. To reduce the possibility of clutter measurements forming established tracks, the solution includes a model for a visible target. That is, a target that gives sensor measurements that satisfy one of the target models. Other features included in the algorithm are the selection of a fixed number of nearest measurements and the addition of signal amplitude to the target state vector. The nonuniform clutter model developed here is applicable to tracking signal amplitude. Performance of this algorithm is illustrated using experimentally recorded over-the-horizon radar (OTHR) data.     

Multi-Target Tracking in Clutter without Measurement Assignment

When tracking targets using radars and sonars, the number of targets and the origin of data is uncertain. Data may be false measurements or clutter, or they may be detections from an unknown number of targets whose possible trajectories and detection processes can only be described in a statistical manner. Optimal all-neighbor multi-target tracking (MTT) in clutter enumerates all possible joint measurement-to-track assignments and calculates the a posteriori probabilities of each of these joint assignments. The numerical complexity of this process is combinatorial in the number of tracks and the number of measurements. One of the key differences between most MTT algorithms is the manner in which they reduce the computational complexity of the joint measurement-to-track assignment process. We propose an alternative approach, using a form of soft assignment, that enables us to bypass this step entirely. Specifically, our approach treats possible detections of targets followed by other tracks as additional clutter measurements. It starts by approximating the a~priori probabilities of measurement origin. These probabilities are then used to modify the clutter spatial density at the location of the measurements. A suitable single target tracking (STT) filter then uses the modified clutter intensity for updating the track state. In effect, the STT filter is transformed into an MTT filter with a numerical complexity that is linear in the number of tracks and the number of measurements. Simulations show the effectiveness of this approach in a number of different multi-target scenarios.