Peformance of dynamic programming techniques forTrack-Before-Detect

“Track-Before-Detect” (TBD) is a target tracking technique where no threshold is applied at each measurement frame. Instead, data are processed over a number of frames before decisions on target existence are made. The track is returned simultaneously with the detection. A simple algorithm is presented and demonstrated via simulations. A detailed analysis enables detection and tracking performance to be predicted for particular algorithm parameters. Good performance is observed at low signal-to-noise ratio (SNR), with rapid degradation as SNR is reduced further. For some cases the detection performance does not improve regardless of how many frames of data are processed. Tracking performance may also be poor even though detection performance is good     

基于点集合并的修正Hough变换TBD算法

在低信噪比条件下,基于Hough变换的检测前跟踪算法是进行强杂波背景下目标航迹检测的一种手段。本文针对Hough变换后一个目标产生多条可能航迹以及航迹内可能存在杂波点的问题,提出了一种基于能量最大点和点集合并的修正Hough变换检测前跟踪算法。该算法利用量测点时序、能量信息及目标速度先验信息对Hough变换后点迹进行关联和剔除,能够有效的对目标原始航迹进行回溯。针对高斯噪声背景下的飞行目标,仿真结果表明该算法能够对微弱目标进行有效检测,在目标数目、杂波密度、信噪比发生变化的条件下仍能保持较高的检测概率。     

Maximum likelihood track-before-detect with fluctuating targetamplitude

An important problem in target tracking is the detection and tracking of targets in very low signal-to-noise ratio (SNR) environments. In the past, several approaches have been used, including maximum likelihood. The major novelty of this work is the incorporation of a model for fluctuating target amplitude into the maximum likelihood approach for tracking of constant velocity targets. Coupled with a realistic sensor model, this allows the exploitation of signal correlation between resolution cells in the same frame, and also from one frame to the next. The fluctuating amplitude model is a first order model to reflect the inter-frame correlation. The amplitude estimates are obtained using a Kalman filter, from which the likelihood function is derived. A numerical maximization technique avoids problems previously encountered in “velocity filtering” approaches due to mismatch between assumed and actual target velocity, at the cost of additional computation. The Cramer-Rao lower bound (CRLB) is derived for a constant, known amplitude case. Estimation errors are close to this CRLB even when the amplitude is unknown. Results show track detection performance for unknown signal amplitude is nearly the same as that obtained when the correct signal model is used     

Multiple model particle flter track-before-detect for range ambiguous radar

The middle pulse repetition frequency（MPRF）and high pulse repetition frequency（HPRF）modes are widely adopted in airborne pulse Doppler（PD）radar systems,which results in the problem that the range measurement of targets is ambiguous.The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio（SNR）is high enough.In this paper,a multiple model particle flter（MMPF）based track-beforedetect（TBD）method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment.By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number（PIN）as components of the target state vector,and modeling the incremental variable of the PIN as a three-state Markov chain,the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state fltering problem.At last,the hybrid fltering problem is implemented by a MMPF-based TBD method in the Bayesian framework.Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously,and succeeds in detecting and tracking weak targets with the range ambiguous radar.Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis（MH）method in low-SNR environment.     

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.     

基于邻帧差分近邻反相特征的红外运动点目标检测算法

基于运动点目标在邻帧差分图像中所具有的近邻反相特征,即运动点目标的两个位置相邻近、灰度值一正一负,提出一种在复杂背景下,基于红外序列图像的运动点目标检测算法.本算法利用该特征在邻帧差分图像中检测反相点对,进而构造反相点对矢量图,最后依据累积反相点对矢量图中多矢量首位相接的连续性检测出运动的点目标.文中给出并证明应用本算法能以概率1检测到运动点目标的收敛性定理.对典型复杂背景下10幅1000帧图像的仿真结果表明,当信噪比大于或等于1.5时,可以有效检测出运动点目标.     

Efficient target tracking using dynamic programming

A dynamic programming (DP) algorithm has been developed for the detection and tracking of subpixel-sized, low signal-to-noise ratio (SNR) targets observed by side-or forward-looking imaging sensors. A distinguishing feature of this approach is that target detection and tracking are combined into a single optimization procedure that takes into account statistical models of target motion, background noise, and clutter. Current work has led to a number of technical innovations that improve the performance and efficiency of the DP tracking algorithm, including the development of a new track scoring function, and an extension to the basic DP algorithm that reduces computation requirements by over an order of magnitude. A prototype infrared (IR) target tracking system incorporating these enhancements has been implemented for a step-starting IR camera application. Sensitivity improvements of several decibels over conventional sequential detection and tracking algorithms were realized     

Asymptotically Optimum Sample Size for Quickest Detection

A method is presented for selecting the asymptotically optimum sample size M for detecting a sudden change in the statistics of an observed process. The test statistic is assumed to be a sum of M consecutive values of some single sample detector and the optimization criterion is to minimize the mean time to detection MD for a given mean time between false alarms MF. It is shown that for large MF and MD the solution can be expressed as a function of the single variable ?MF? (or alternatively ?MD?) where ? is a measure of the signal-to-noise ratio (SNR).     

Pade approximations for detectability in K-clutter and noise

The Pade approximation (PA) method is used to analyze the detection performance of single and multiple pulse radar systems operating in K-distributed clutter and thermal noise. Simple approximations for false-alarm and detection probabilities are obtained, using lower order moments for the detection decision statistic. Both envelope and squaring detector laws are considered, with noncoherent integration, for independent and correlated K clutter. The target is assumed to be pulse-to-pulse Rayleigh fading. The methods are a substantial application of the PA methods we have previously published     

Formation tracking control for time-delayed multi-agent systems with second-order dynamics

In this paper, formation tracking control problems for second-order multi-agent systems (MASs) with time-varying delays are studied, specifically those where the position and velocity of followers are designed to form a time-varying formation while tracking those of the leader. A neigh-boring relative state information based formation tracking protocol with an unknown gain matrix and time-varying delays is presented. The formation tracking problems are then transformed into asymptotically stable problems. Based on the Lyapunov-Krasovskii functional approach, condi-tions sufficient for second-order MASs with time-varying delays to realize formation tracking are examined. An approach to obtain the unknown gain matrix is given and, since neighboring relative velocity information is difficult to measure in practical applications, a formation tracking protocol with time-varying delays using only neighboring relative position information is introduced. The proposed results can be used on target enclosing problems for MASs with second-order dynamics and time-varying delays. An application for target enclosing by multiple unmanned aerial vehicles (UAVs) is given to demonstrate the feasibility of theoretical results.     

EM-ML algorithm for track initialization using possibly noninformative data

Initializing and maintaining a track for a low observable (LO) (low SNR, low target detection probability and high false alarm rate) target can be very challenging because of the low information content of measurements. In addition, in some scenarios, target-originated measurements might not be present in many consecutive scans because of mispointing, target maneuvers, or erroneous preprocessing. That is, one might have a set of noninformative scans that could result in poor track initialization and maintenance. In this paper an algorithm based on the expectation-maximization (EM) algorithm combined with maximum likelihood (ML) estimation is presented for tracking slowly maneuvering targets in heavy clutter and possibly noninformative scans. The adaptive sliding-window EM-ML approach, which operates in batch mode, tries to reject or weight down noninformative scans using the Q-function in the M-step of the EM algorithm. It is shown that target features in the form of, for example, amplitude information (AI), can also be used to improve the estimates. In addition, performance bounds based on the supplemented EM (SEM) technique are also presented. The effectiveness of new algorithm is first demonstrated on a 78-frame long wave infrared (LWIR) data sequence consisting of an Fl Mirage fighter jet in heavy clutter. Previously, this scenario has been used as a benchmark for evaluating the performance of other track initialization algorithms. The new EM-ML estimator confirms the track by frame 20 while the ML-PDA (maximum likelihood estimator combined with probabilistic data association) algorithm, the IMM-MHT (interacting multiple model estimator combined with multiple hypothesis tracking) and the EVIM-PDA estimator previously required 28, 38, and 39 frames, respectively. The benefits of the new algorithm in terms of accuracy, early detection, and computational load are illustrated using simulated scenarios as well.     

Radar CFAR Thresholding in Clutter and Multiple Target Situations

Radar detection procedures involve the comparison of the received signal amplitude to a threshold. In order to obtain a constant false-alarm rate (CFAR), an adaptive threshold must be applied reflecting the local clutter situation. The cell averaging approach, for example, is an adaptive procedure. A CFAR method is discussed using as the CFAR threshold one single value selected from the so-called ordered statistic (this method is fundamentally different from a rank statistic). This procedure has some advantages over cell averaging CFAR, especially in cases where more than one target is present within the reference window on which estimation of the local clutter situation is based, or where this reference window is crossing clutter edges.     

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     

Closed-Form Expressions for Noncoherent Radar Integration Gain and Collapsing Loss

Closed-form formulas allow rapid determination of noncoherent integration gain and integration loss when the single-sample IF signal-to-noise ratio (SNR) is known. In addition, if the required SNR is known for any number of integrated pulses, the required SNR for any other number is easily determined. A closed-form expression is given for radar collapsing loss, expressed in terms of the equivalent integrated signal-to-noise ratio required to produce a given combination of false-alarm and detection probabilities. Alternatively, the single-sample signal-to-noise ratio of a set of samples may be used together with the closed-form expression for integration gain to get the equivalent integrated signal-to-noise ratio.     

Track-before-detect procedures for early detection of moving target from airborne radars

In this paper we present a family of track-before-detect (TBD) procedures for early detection of moving targets from airborne radars. Upon a sectorization of the coverage area, the received echoes are jointly processed in the azimuth-range-Doppler domain and in the time domain through a Viterbi-like algorithm that exploits the physically admissible target transitions between successive illuminations, in order to collect all of the energy back-scattered during the time on target (TOT). A reduced-complexity implementation is derived assuming, at the design stage, that the target does not change resolution cell during the TOT in each scan. The constant false alarm rate (CFAR) constraint is also englobed in the proposed procedures as well as the possibility of working with quantized data. Simulation results show that the proposed algorithms have good detection and tracking capabilities even for high target velocities and low quantization rates.     

Multiframe weak target track-before-detect based on pseudo-spectrum in mixed coordinates

Traditional multiframe Track-Before-Detect(TBD) may incur adverse integration loss resulting from model mismatch in sensor coordinates. Its suboptimal integration strategy may cause target envelope degradation. To address these issues, a pseudo-spectrum-based multiframe TBD in mixed coordinates is proposed firstly. The data search for energy integration is conducted based on an accurate model in the x-y plane while target energy is integrated based on pseudo-spectrum in sensor coordinates. The a...     

Frequency-Agile Radar Signal Processing

Modern radars may incorporate pulse-to-pulse carrier frequency modulation to increase probability of detection, to reduce Vulnerability to jamming, and to reduce probability of interception. However, if coherent processing is used for clutter rejection, the frequency of N consecutive pulses must be held constant for N-pulse clutter cancellation or Doppler filtering. If M pulses are transmitted during the time the antenna illuminates a target, there are M/N coherently integrated echoes available for noncoherent integration in the computer or the operator's display to further improve the signal-to-noise ratio (SNR). In this paper, analytical and simulation methods are employed to determine the balance between coherent and noncoherent integration that yields the greatest SNR improvement. Attention is focused upon a model using peak selection of fast Fourier transform (FFT) Doppler channels and is compared to a reference model involving only a single Doppler channel. Curves of detectable SNR as a function of M and N are presented for both models.     

Optimum array detector for a weak signal in unknown noise

We study the design of constant false-alarm rate (CFAR) tests for detecting a rank-one signal in the presence of background Gaussian noise with unknown spatial covariance. We look at invariant tests, i.e., those tests whose performance is independent of the nuisance parameters, like the background noise covariance. Such tests are shown to have the desirable CFAR property. We characterize the class of all such tests by showing that any invariant decision statistic can be written as a function of two basic statistics which are in fact the adaptive matched filter (AMF) statistic and Kelly's generalized likelihood ratio statistic. Further, we establish an optimum test in the limit of low signal-to-noise ratio (SNR), the locally most powerful invariant (LMPI) test. We also derive the bound for the probability of detection of any invariant detector, at a fixed false-alarm rate, and compare the LMPI and the published detectors (Kelly and AMF) to it     

Radar detection and preclassification based on multiple hypothesis

This work presents a single-scan-processing approach to the problem of detecting and preclassifying a radar target that may belong to different target classes. The proposed method is based on a hybrid of the maximum a posteriori (MAP) and Neyman-Pearson (NP) criteria and guarantees the desired constant false alarm rate (CFAR) behavior. The targets are modeled as subspace random signals having zero mean and given covariance matrix. Different target classes are discriminated based on their different signal subspaces, which are specified by their corresponding projection matrices. Performance is investigated by means of numerical analysis and Monte Carlo simulation in terms of probability of false alarm, detection and classification; the extra signal-to-noise power ratio (SNR) necessary to classify once target detection has occurred is also derived.