Extended solution to multiple maneuvering target tracking

An improved algorithm for tracking multiple maneuvering targets is presented. This approach is implemented with an approximate adaptive filter consisting of the one-step conditional maximum-likelihood technique together with the extended Kalman filter and an adaptive maneuvering compensator. In order to avoid the extra computational burden of considering events with negligible probability, a validation matrix is defined in the tracking structure. With this approach, data-association and target maneuvering problems can be solved simultaneously. Detailed Monte Carlo simulations of the algorithm for many tracking situations are described. Computer simulation results indicate that this approach successfully tracks multiple maneuvering targets over a wide range of conditions     

Data fusion and tracking using HMMs in a distributed sensor network

This work deals with the problem of multiple target tracking, from the measurements made on a field of passive sonars activated by an active sonar (multistatic network). The difficulties encountered then are of two kinds: each sensor alone does not provide full observability of a target, and multiple, possibly maneuvering targets moving in a cluttered environment must be dealt with. The algorithm presented here is based on a discrete Markovian modelization of the targets evolution in time. It starts with a fusion of the detections obtained at each measurement time. Tracking and target motion analysis (TMA) are next achieved thanks to dynamic programming (DP). This approach leads to multiple and maneuvering target tracking, with few assumptions; for instance, the use of deterministic target state models are avoided. Simulation results are presented and discussed.     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.     

Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

The probability hypothesis density (PHD) filter has been recognized as a promising tech-nique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation (APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter (PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking mul-tiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches.     

残差滤波及其在密集多回波环境下机动多目标跟踪中的应用

 修正概率数据关联滤波（MPDAF）是目前解决密集多回波环境下机动多目标跟踪较为有效的方法,但当回波密度增高时,该方法容易失跟。本文针对此特点,在MPDAF基础上,提出了残差滤波（RF）方法,分别从理论和Monte carlo仿真两方面揭示了RF与数据关联的内在机理,结果表明该方法能大幅度提高跟踪滤波器捕捉目标和剔除关联域内多余回波的能力以及跟踪的性能,是一种解决高密集多回波环境下机动多目标跟踪的有效方法。     

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     

A class of near optimal JPDA algorithms

The crucial problem in multiple target tracking is the hit-to-track data association. A hit is a received signal from a target or background clutter which provides positional information If an incorrect hit is associated with a track, that track could diverge and prematurely terminate or cause other tracks to also diverge. Most methods for hit-to-track data association fall into two categories: multiple hypothesis tracking (MHT) and joint probabilistic data association (JPDA). Versions of MHT use all or some reasonable hits to update a track and delay the decision on which hit was correct. JPDA uses a weighted sum of the reasonable hits to update a track. These weights are the probability that the hit originated from the target in track. The computational load for the joint probabilities increases exponentially as the number of targets increases and therefore, is not an attractive algorithm when expecting to track many targets. Reviewed here is the JPDA filter and two simple approximations of the joint probabilities which increase linearly in computational load as the number of targets increase. Then a new class of near optimal JPDA algorithms is introduced which run in polynomial time. The power of the polynomial is an input to the algorithm. This algorithm bridges the gap in computational load and accuracy between the very fast simple approximations and the efficient optimal algorithms     

An improved multiple model GM-PHD filter for maneuvering target tracking

In this paper, an improved implementation of multiple model Gaussian mixture probability hypothesis density (MM-GM-PHD) filter is proposed. For maneuvering target tracking, based on joint distribution, the existing MM-GM-PHD filter is relatively complex. To simplify the filter, model conditioned distribution and model probability are used in the improved MM-GM-PHD filter. In the algorithm, every Gaussian components describing existing, birth and spawned targets are estimated by multiple model method. The final results of the Gaussian components are the fusion of multiple model estimations. The algorithm does not need to compute the joint PHD distribution and has a simpler computation procedure. Compared with single model GM-PHD, the algorithm gives more accurate estimation on the number and state of the targets. Compared with the existing MM-GM-PHD algorithm, it saves computation time by more than 30%. Moreover, it also outperforms the interacting multiple model joint probabilistic data association (IMMJPDA) filter in a relatively dense clutter environment.     

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%。     

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。     

Multiple-Model Probability Hypothesis Density Filter for Tracking Maneuvering Targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.     

基于均值漂移算法的冷空炽热体红外目标跟踪

Mean Shift（均值漂移）算法对彩色序列图像目标跟踪是有效的,而对红外目标跟踪是不稳健的。本文对Mean Shift算法做适当改进,将其用于冷空炽热体红外目标跟踪。先对红外图像做伽马变换,把目标从背景中分离出来;用直方图非均匀量化改进传统Mean Shift算法量化方式,提高目标定位准确性。仿真结果表明,该方法对冷空炽热体红外目标跟踪是有效的和稳健的。     

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.     

Multiple ground target tracking

For current GMTI trackers, one of the most common contextual information used is road network information. In this paper, we present our approach using the road network information in tracking ground targets and in solving some ambiguities that can arise at road intersections or following a target manoeuvre leaving the road. For this we examine the performances of an adapted algorithm for tracking manoeuvring ground targets on road and off road in a cluttered environment using the map information.     

改进的MMPHD机动目标跟踪方法

基于序列蒙特卡罗方法的经典多模概率假设密度滤波方法及其各种衍生方法,在预测过程中依据多个并行的状态转移模型,通过将大量粒子散布到下一时刻目标所有可能出现的状态空间实现目标状态的捕获,造成计算量大、目标跟踪精度差。为此,提出一种改进的多模粒子概率假设密度机动目标跟踪方法。该方法利用最新量测信息估计目标运动模型概率及模型参数,并将估计得到的目标模型应用到粒子概率假设密度滤波方法的预测过程中生成预测粒子,从而将大部分粒子聚合在目标最可能出现的状态空间邻域中,实现粒子的有效利用。数值仿真表明,所提方法不仅显著地减少了目标丢失个数,而且提高了目标跟踪精度。     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

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.     

一种密集多回波环境下的机动多目标跟踪起始算法

 本文研究密集多回波环境下的机动多目标跟踪起始问题。文中首先提出主跟踪子空间和边缘跟踪子空间的定义与性质,接着修正Bayes轨迹确定方法BTC,并将其与具有残差滤波的修正概率数据关联滤波算法MPDAF-RF有机地结合起来,提出一种适合高密集多回波环境的机动多目环跟踪起始方法——“全邻”Bayes跟踪起始算法ABTI。Monte Carlo仿真表明,本文所给出的算法不仅克服了一类概率数据关联滤波方法没有跟踪起始机理的缺陷,而且辨别目标与虚警的能力很强,不失为解决高密集多回波环境下机动多目标跟踪起始的有效方法。     

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.     

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).