Effectiveness of track monitoring with multiple 2D passive sensors

An analytical technique is presented which can be used to evaluate the effectiveness of the track monitoring scheme presented by J.A. Roecker (see ibid., vol.27, no.6, p.872-6, Nov. 1991) in detecting false track-to-track (ghost track) assignments without the use of simulations. It is shown that when two tracks are traveling in parallel and in the direction of the inclination angle, it is impossible to determine which tracks to associate. However, track monitoring is effective under all other circumstances. A tracking algorithm designer can use this technique to determine the length of time before track-to-track initiation for good ghost track rejection. This technique also determines the probability of accepting ghost tracks during mature track monitoring.<>     

Diffusion analysis of track loss in clutter

In tracking a target through clutter, the selection of incorrect measurements for track updating causes track divergence and eventual loss of track. The plot-to-track association algorithm is modeled as a Markov process and the tracking error is modeled as a diffusion process in order to study the mechanism of track loss analytically, without recourse to Monte Carlo simulations, for nearest-neighbor association in two space dimensions. The time evolution of the error distribution is examined, and the connection of the approach with diffusion theory is discussed. Explicit results showing the dependence of various performance parameters, such as mean time to lose track and track half-life, on the clutter spatial density are presented. The results indicate the existence of a critical density region in which the tracking performance degrades rapidly with increasing clutter density. An optimal gain adaptation procedure that significantly improves the tracking performance in the critical region is proposed     

Evaluating a multiple-hypothesis multitarget tracking algorithm

The performance evaluation of multiple-hypothesis, multitarget tracking algorithm is presented. We are primarily interested in target-detection/track-initiation capabilities as measures of performance. Through Monte Carlo simulations, a multiple-hypothesis tracking algorithm was evaluated in terms of 1) probability of establishing a track from target returns and 2) false track density. A radar was chosen as the sensor, and a general multiple-hypothesis, multitarget tracking algorithm was used in the Monte Carlo simulations. The simulation results predict the probability of establishing a track from returns of a target as well as the false track density per scan volume per unit time. The effects of the target radar cross section and the radar power, measured through the mean signal-to-noise ratio (SNR) were studied, as were the effects of detection threshold and track quality threshold. Computational requirements were also investigated     

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.     

Track-before-detect for Infrared Maneuvering Dim Multi-target via MM-PHD

In this paper, we present a novel and efficient track-before-detect (TBD) algorithm based on multiple-model probability hypothesis density (MM-PHD) for tracking infrared maneuvering dim multi-target. Firstly, the standard sequential Monte Carlo probability hypothesis density (SMC-PHD) TBD-based algorithm is introduced and sequentially improved by the adaptive process noise and the importance re-sampling on particle likelihood, which result in the improvement in the algorithm robustness and convergence speed. Secondly, backward recursion of SMC-PHD is derived in order to ameliorate the tracking performance especially at the time of the multi-target arising. Finally, SMC-PHD is extended with multiple-model to track maneuvering dim multi-target. Extensive experiments have proved the efficiency of the presented algorithm in tracking infrared maneuvering dim multi-target, which produces better performance in track detection and tracking than other TBD-based algorithms including SMC-PHD, multiple-model particle filter (MM-PF), histogram probability multi-hypothesis tracking (H-PMHT) and Viterbi-like.     

Effectiveness of the likelihood function in logic-based trackformation

A logic-based track formation procedure was presented by C.B. Chang et al. (1984). In addition to the conventional gating logic, it utilized the negative log-likelihood function (goodness of fit or sum of residuals) to further reduce the false track acceptance probability. An analytical technique for the evaluation of the effectiveness of this reduction is presented. The exact solution in closed form and a Gaussian approximation are given and compared. It is shown that the goodness of fit provides an additional reduction of the false track acceptance probability by a factor of two to three     

An Adaptive Two-Dimensional Kalman Tracking Filter

A continuously adaptive two-dimensional Kalman tracking filter for a low data rate track-while-scan (TWS) operation is introduced which enhances the tracking of maneuvering targets. The track residuals in each coordinate, which are a measure of track quality, are sensed, normalized to unity variance, and then filtered in a single-pole filter. The magnitude Z of the output of this single-pole filter, when it exceeds a threshold Z1 is used to vary the maneuver noise spectral density q in the Kalman filter model in a continuous manner. This has the effect of increasing the tracking filter gains and containing the bias developed by the tracker due to the maneuvering target. The probability of maintaining track, with reasonably sized target gates, is thus increased, The operational characteristic of q versus Z assures that the tracker gains do not change unless there is high confidence that a maneuver is in progress.     

A multipath data association tracker for over-the-horizon radar

A new algorithm, multipath probabilistic data association (MPDA), for initiation and tracking in over-the-horizon radar (OTHR) is described. MPDA is capable of exploiting multipath target signatures arising from discrete propagation modes that are resolvable by the radar. Nonlinear measurement models exhibiting multipath target signatures in azimuth, slant range, and Doppler are used. Tracking is performed in ground coordinates and therefore depends on the provision of estimates of virtual ionospheric heights to achieve coordinate registration. Although the propagation mode characteristics are assumed to be known, their correspondence with the detections is not required to be known. A target existence model is included for automatic track maintenance. Numerical simulations for four resolvable propagation modes are presented that demonstrate the ability of the technique to initiate and maintain track at probabilities of detection of 0.4 per mode in clutter densities for which conventional probabilistic data association (PDA) has a high probability of track loss, and suffers from track bias. A nearest neighbor version of MPDA is also presented     

Performance evaluation of a cascaded logic for track formation inclutter

The authors present a Markov-chain-based performance evaluation technique for two-stage sliding-window cascaded logic (2/2×m /n) for track formation in a cluttered environment. The main features of this technique are that it avoids the need for extensive simulations and it is more realistic than previous methods, accounting for the association gate size variation. The gates are obtained from a Kalman filter and fully account for the transient observed for the cascaded logic following the two-point initiation from its first stage. Numerical examples of performance evaluation are given along with a logic design example     

Integrated track maintenance for the PMHT via the hysteresis model

Unlike other tracking algorithms the probabilistic multi-hypothesis tracker (PMHT) assumes that the true source of each measurement is an independent realisation of a random process. Given knowledge of the prior probability of this assignment variable, data association is performed independently for each measurement. When the assignment prior is unknown, it can be estimated provided that it is either time independent, or fixed over the batch. This paper presents a new extension of the PMHT, which incorporates a randomly evolving Bayesian hyperparameter for the assignment process. This extension is referred to as the PMHT with hysteresis. The state of the hyperparameter reflects each model's contribution to the mixture, and thus can be used to quantify the significance of mixture components. The paper demonstrates how this can be used as a method for automated track maintenance in clutter. The performance benefit gained over the standard PMHT is demonstrated using simulations and real sensor data     

IMMPDAF for radar management and tracking benchmark with ECM

A framework is presented for controlling a phased array radar for tracking highly maneuvering targets in the presence of false alarms (FAs) and electronic countermeasures (ECMs). Algorithms are presented for track formation and maintenance; adaptive selection of target revisit interval, waveform and detection threshold; and neutralizing techniques for ECM, namely, against a standoff jammer (SOJ) and range gate pull off (RGPO). The interacting multiple model (IMM) estimator in combination with the probabilistic data association (PDA) technique is used for tracking. A constant false alarm rate (CFAR) approach is used to adaptively select the detection threshold and radar waveform, countering the effect of jammer-induced false measurements. The revisit interval is selected adaptively, based on the predicted angular innovation standard deviations. This tracker/radar-resource-allocator provides a complete solution to the benchmark problem for target tracking and radar control. Simulation results show an average sampling interval of about 2.5 s while maintaining a track loss less than the maximum allowed 4%     

Multitarget tracking using the joint multitarget probability density

This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as nonGaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR).     

Track labeling and PHD filter for multitarget tracking

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approaches (as, e.g., MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter has been proposed and particle filtering techniques have been developed to implement the PHD filter. In the particle PHD filter, the track labeling problem is not considered, i.e., the PHD is obtained only for a frame at a time, and it is very difficult to perform the multipeak extraction, particularly in high clutter environments. A track labeling method combined with the PHD approach, as well as considering the finite resolution, is proposed here for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD in the resolution cell to get the estimated number and locations of the targets at each time step, and then perform the track labeling ("peak-to-track" association), whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard particle PHD filter. For example, in group target tracking, if we are interested in the motion of a specific target, we can track this target, which is not possible for the standard particle PHD filter, since the standard particle PHD filter does not keep track labels. Using our approach, multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging, and termination     

Sequential track extraction

Sensors like radar or sonar usually produce data on the basis of a single frame of observation: target detections. The detection performance is described by quantities like detection probability Pd and false alarm density f. A different task of detection is formation of tracks of targets unknown in number from data of multiple consecutive frames of observation. This leads to quantities which are of a higher level of abstraction: extracted tracks. This again is a detection process. Under benign conditions (high Pd, low f and well separated targets) conventional methods of track initiation are recommended to solve a simple task. However, under hard conditions the process of track extraction is known to be difficult. We here concentrate on the case of well separated targets and derive an optimal combinatorial method which can be used under hard operating conditions. The method relates to MHT (multiple hypothesis tracking), uses a sequential likelihood ratio test and derives benefit from processing signal strength information. The performance of the track extraction method is described by parameters such as detection probability and false detection rate on track level, while Pd and f are input parameters which relate to the signal-to-noise interference ratio (SNIR), the clutter density, and the threshold set for target detection. In particular the average test lengths are analyzed parametrically as they are relevant for a user to estimate the time delay for track formation under hard conditions     

Interacting multiple model tracking with target amplitude feature

A recursive tracking algorithm is presented which uses the strength of target returns to improve track formation performance and track maintenance through target maneuvers in a cluttered environment. This technique combines the interacting multiple model (IMM) approach with a generalized probabilistic data association (PDA), which uses the measured return amplitude in conjunction with probabilistic models for the target and clutter returns. Key tracking decisions can be made automatically by assessing the probabilities of target models to provide rapid and accurate decisions for both true track acceptance and false track dismissal in track formation. It also provides the ability to accurately continue tracking through coordinated turn target maneuvers     

多目标跟踪的概率假设密度粒子滤波

在多目标跟踪中,当目标数很大时,目标状态的联合分布的计算量会非常大。如果目标独立运动,可用各目标分别滤波来代替,但这要求考虑数据互联问题。文章介绍一种可以解决计算量问题的方法,只需计算联合分布的一阶矩——概率假设密度(PHD),PHD在任意区域S上的积分是S内目标数的期望值。因未记录目标身份,避免了数据互联问题。仿真中,传感器为被动雷达,目标观测值为距离、角度及速度时,对上述的PHD滤波进行了粒子实现,并对观测值是否相关的不同情况进行比较。PHD粒子滤波应用在非线性模型的多目标跟踪,实验结果表明,滤波可以稳健跟踪目标数为变数的情况,得到了接近真实情况的结果。     

Track segment association, fine-step IMM and initialization with Doppler for improved track performance

In this work we present a new track segment association technique to improve track continuity in large-scale target tracking problems where track breakages are common. A representative airborne early warning (AEW) system scenario, which is a challenging environment due to highly maneuvering targets, close target formations, large measurement errors, long sampling intervals, and low detection probabilities, provides the motivation for the new technique. Previously, a tracker using the interacting multiple model (IMM) estimator combined with an assignment algorithm was shown to be more reliable than a conventional Kalman filter based approach in tracking similar targets but it still yielded track breakages due to the difficult environment. In order to combine the broken track segments and improve track continuity, a new track segment association algorithm using a discrete optimization approach is presented. Simulation results show that track segment association yields significant improvements in mean track life as well as in position, speed, and course rms errors. Also presented is a modified one-point initialization technique with range rate measurements, which are typically ignored by other initialization techniques, and a fine-step IMM estimator, which improves performance in the presence of long revisit intervals. Another aspect that is investigated is the benefit of "deep" (multiframe or N-dimensional, with N > 2) association, which is shown to yield significant benefit in reducing the number of false tracks.     

Tracking in Clutter using IMM-IPDA?Based Algorithms

We describe three single-scan probabilistic data association (PDA) based algorithms for tracking manoeuvering targets in clutter. These algorithms are derived by integrating the interacting multiple model (IMM) estimation algorithm with the PDA approximation. Each IMM model a posteriori state estimate probability density function (pdf) is approximated by a single Gaussian pdf. Each algorithm recursively updates the probability of target existence, in the manner of integrated PDA (IPDA). The probability of target existence is a track quality measure, which can be used for false track discrimination. The first algorithm presented, IMM-IPDA, is a single target tracking algorithm. Two multitarget tracking algorithms are also presented. The IMM-JIPDA algorithm calculates a posteriori probabilities of all measurement to track allocations, in the manner of the joint IPDA (JIPDA). The number of measurement to track allocations grows exponentially with the number of shared measurements and the number of tracks which share the measurements. Therefore, IMM-JIPDA can only be used in situations with a small number of crossing targets and low clutter measurement density. The linear multitarget IMM-IPDA (IMM-LMIPDA) is also a multitarget tracking algorithm, which achieves the multitarget capabilities by integrating linear multitarget (LM) method with IMM-IPDA. When updating one track using the LM method, the other tracks modulate the clutter measurement density and are subsequently ignored. In this fashion, LM achieves multitarget capabilities using the number of operations which are linear in the: number of measurements and the number of tracks, and can be used in complex scenarios, with dense clutter and a large number of targets.     

N-fold Bernoulli probability based adaptive fast-tracking algorithm and its application to autonomous aerial refuelling

Recently, deep learning has been widely utilized for object tracking tasks. However, deep learning encounters limits in tasks such as Autonomous Aerial Refueling (AAR), where the target object can vary substantially in size, requiring high-precision real-time performance in embedded systems. This paper presents a novel embedded adaptiveness single-object tracking framework based on an improved YOLOv4 detection approach and an n-fold Bernoulli probability theorem. First, an Asymmetric Convolutional Network (ACNet) and dense blocks are combined with the YOLOv4 architecture to detect small objects with high precision when similar objects are in the background. The prior object information, such as its location in the previous frame and its speed, is utilized to adaptively track objects of various sizes. Moreover, based on the n-fold Bernoulli probability theorem, we develop a filter that uses statistical laws to reduce the false positive rate of object tracking. To evaluate the efficiency of our algorithm, a new AAR dataset is collected, and extensive AAR detection and tracking experiments are performed. The results demonstrate that our improved detection algorithm is better than the original YOLOv4 algorithm on small and similar object detection tasks; the object tracking algorithm is better than state-of-the-art object tracking algorithms on refueling drogue tracking tasks.     

Tracking in clutter with nearest neighbor filters: analysis andperformance

The measurement that is “closest” to the predicted target measurement is known as the “nearest neighbor” (NN) measurement in tracking. A common method currently in wide use for tracking in clutter is the so-called NN filter, which uses only the NN measurement as if it were the true one. The purpose of this work is two fold. First, the following theoretical results are derived: the a priori probabilities of all three data association events (updates with correct measurement, with incorrect measurement, and no update), the probability density functions (pdfs) of the NN measurement conditioned on the association events, and the one-step-ahead prediction of the matrix mean square error (MSE) conditioned on the association events. Secondly, a technique for prediction without recourse to expensive Monte Carlo simulations of the performance of tracking in clutter with the NN filter is presented. It can quantify the dynamic process of tracking divergence as well as the steady-state performance. The technique is a new development along the line of the recently developed general approach to the performance prediction of algorithm with both continuous and discrete uncertainties