A quantization architecture for track fusion

Many practical multi-sensor tracking systems are based on some form of track fusion, in which local track estimates and their associated covariances are shared among sensors. Communication load is a significant concern, and the goal of this paper is to propose an architecture for low-bandwidth track fusion. The scheme involves intelligent scalar and vector quantization of the local state estimates and of the associated estimation error covariance matrices. Simulation studies indicate that the communication saving can be quite significant, with only minor degradation of track accuracy.     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

Removal of Out-of-Sequence Measurements from Tracks

In multisensor tracking systems that operate in a centralized or distributed information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence due to system latencies. In order to avoid either a delay in the output or the need for reordering and reprocessing entire sequences of measurements, such latent measurements have to be processed by the tracking filter as out-of-sequence measurements (OOSM). Recent work developed a "one-step" procedure for incorporating OOSM with multiple-time-step latency into the tracking filter, which, while suboptimal, was shown to yield results very close to those obtained by reordering and reprocessing an entire sequence of measurements. The counterpart of this problem is the need to remove (revocate) measurements that have already been used to update a track state. This can happen in real-world systems when such measurements are reassigned to another track. Similarly to the problem of update with an OOSM, it is desired to carry out the removal of an earlier measurement without recomputing the track estimate (and the data association) using possibly a long sequence of subsequent measurements one at a time. A one-step algorithm is presented for this problem of removing a multistep OOSM.     

Reduced state estimator for systems with parametric inputs

A reduced state estimator is derived for systems with bounded parameters as inputs. Optimal filter gains are derived for minimizing the total covariance of the estimation error due to measurement noise and parameter uncertainty. It is shown that these filter gains for a two-state system with a Gaussian parameter satisfy the Kalata relation in steady state. Equations are also derived for optimally filtering measurements in arbitrary time order. This reduced state estimator offers novelties over a traditional Kalman filter in its application to the class of problems considered. The total error covariance, which is minimized, makes no use of plant noise. Furthermore, the filter is easier to optimize in high dimensional and multiple sensor applications as well as in processing out-of-sequence measurements.     

Update with out-of-sequence measurements in tracking: exact solution

In target tracking systems measurements are typically collected in "scans" or "frames" and then they are transmitted to a processing center. In multisensor tracking systems that operate in a centralized manner, there are usually different time delays in transmitting the scans or frames from the various sensors to the center. This can lead to situations where measurements from the same target arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting "negative-time measurement update" problem, which is quite common in real multisensor systems, was solved previously only approximately in the literature. The exact state update equation for such a problem is presented. The optimal and two suboptimal algorithms are compared on a number of realistic examples, including a GMTI (ground moving target indicator) radar case.     

Multiple model nonlinear filtering for low signal ground target applications

The design and implementation of a multiple model nonlinear filter (MMNLF) for ground target tracking using ground moving target indicator (GMTI) radar measurements is described. Like the well-known interacting multiple model Kalman filter (IMMKF), the MMNLF is based on the theory of hybrid stochastic systems. However, since it models the probability distribution for the target in a region, rather than just the distribution's first and second moments, a nonlinear filter is able to capture more fine-grained detail of the target motion and requires fewer models than typical IMMKF implementations. This is illustrated here with a two-model MMNLF in which one motion model incorporates terrain constraints while the second is a nearly constant velocity (CV) model. Another feature of the MMNLF is that it enables incorporation of prethresholded measurements. To implement the filter, the target state conditional probability density is discretized on a set of moving grids and recursively updated with sensor measurements via Bayes' formula. The conditional density is time updated between sensor measurements using alternating direction implicit (ADI) finite difference methods, generalized for this hybrid application. In simulation testing against low signal-to-interference-plus-noise ratio (SINR) targets, the MMNLF is able to maintain track in situations where single model filters based on either of the component models or filters that use thresholded data fail. Potential applications of this work include detection and tracking of foliage-obscured moving targets.     

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     

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     

Particle filters for tracking with out-of-sequence measurements

An extension is presented to the particle filtering toolbox that enables nonlinear/non-Gaussian filtering to be performed in the presence of out-of-sequence measurements (OOSMs) with arbitrary lag, without the need to adopt linearising approximations in the filter and without the degradation of performance that would occur if the OOSMs were simply discarded. An estimate of the performance of the OOSM particle filter (OOSM-PF) is obtained for bearings-only tracking scenarios with a single target and a small number of sensors. These performance estimates are then compared with the posterior Cramer-Rao lower bound (CRLB) for the state estimate rms error and similar performance estimates obtained from the oosm extended Kalman filter (OOSM-EKF) algorithms recently introduced in the literature. For a mildly nonlinear bearings-only tracking problem the OOSM-PF and OOSM-EKF are shown to achieve broadly similar performance.     

Radar Measurement Noise Variance Estimation with Several Targets of Opportunity

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. A method is presented of determining the measurement noise variances of a sensor, assumed to be constant, by using multiple IMM estimators while tracking targets whose motion is not known---targets of opportunity. Combining techniques outlined in [2] and [6], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out over a varying grid of IMMs to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.     

One-step solution for the multistep out-of-sequence-measurement problem in tracking

In multisensor target tracking systems measurements from the same target can arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting problem - how to update the current state estimate with an "older" measurement - is a nonstandard estimation problem. It was solved first (suboptimally, then optimally) for the case where the OOSM lies between the two last measurements, i.e, its lag is less than a sampling interval - the 1-step-lag case. The real world has, however, OOSMs with arbitrary lag. Subsequently, the suboptimal algorithm was extended to the case of an arbitrary (multistep) lag, but the resulting algorithm required a significant amount of storage. The present work shows how the 1-step-lag algorithms can be generalized to handle an arbitrary (multistep) lag while preserving their main feature of solving the update problem without iterating. This leads only to a very small (a few percent) degradation of MSE performance. The incorporation of an OOSM into the data association process is also discussed. A realistic example with two GMTI radars is presented. The consistency of the proposed algorithm is also evaluated and it is found that its calculated covariances are reliable.     

Tracking of crossing targets with imaging sensors

The authors present an algorithm for the tracking of crossing targets using the centroid measurement and the centroid offset measurement of the distributed image formed by the targets. The measurements are obtained by a forward-looking infrared (FLIR) imaging sensor. The joint probabilistic data association merged-measurement coupled filter (JPDAMCF) is used for state estimation which performs filtering in a coupled manner for the targets with common measurements. Two filters are examined: one assuming the displacement noise white and the other one modeling it correctly as autocorrelated. The latter is shown to yield substantially better performance. The proposed algorithm demonstrates the usefulness of the JPDAMCF for tracking crossing targets in combination with the models for the centroid and offset measurements. Even though the centroid offset measurement requires more computations and a more complex model for estimation, it yields significantly better results if the filter accounts for its colored measurement noise     

Event-triggered cooperative target tracking in wireless sensor networks

Since the issues of low communication bandwidth supply and limited battery capacity are very crucial for wireless sensor networks, this paper focuses on the problem of event-triggered cooperative target tracking based on set-membership information filtering. We study some fundamental properties of the set-membership information filter with multiple sensor measure-ments. First, a sufficient condition is derived for the set-membership information filter, under which the boundedness of the outer ellipsoidal approximation set of the estimation means is guaranteed. Second, the equivalence property between the parallel and sequential versions of the set-membership information filter is presented. Finally, the results are applied to a 1D event-triggered target tracking scenario in which the negative information is exploited in the sense that the measurements that do not satisfy the triggering conditions are modelled as set-membership mea-surements. The tracking performance of the proposed method is validated with extensive Monte Carlo simulations.     

Speech Data Rate Reduction Part I: Applicability of Modern Estimation Theory

Efficient coding of continuous speech signals for digital representation has attracted much interest in recent years. The underlying aim of efficient coding methods is to reduce the channel capacity required to represent a signal to meet a specific reconstruction fidelity criterion. To achieve this objective, modern speech data compression techniques rely on two very similar procedures. One procedure uses predictive deconvolution which subtracts from the current signal value that portion which can be predicted from its past and thus removes redundancy in the speech by removing sequential correlation. The signal thus requires fewer bits for equivalent quantization error. The second procedure involves identification of a complete mathematical model of the speech producing mechanism. This involves determination of the characteristics of the source that drives this transfer function. Data reduction is again achieved since the rate of change of the parameters of the speech model is much smaller than the rate of change of the speech waveform. This paper develops these data reduction procedures in terms of modern estimation theory, specifically a Kalman filter model, and illustrates the utility of this model as an analysis tool by means of an example based on a uniform tube which provides a qualitative assessment of the potential of the technique for application to real speech signals.     

基于均值漂移无味粒子滤波的地面运动目标变结构交互多模型跟踪(英文)

为了跟踪地面运动目标,本文提出在变结构交互多模型基础上使用均值漂移无味粒子滤波的算法。模型滤波中,通过均值漂移将无味粒子滤波产生的采样粒子向目标状态最大后验密度估计方向移动。"停止"模型基础上,提出了"遮蔽"模型:出现地形遮蔽时,使用上一时刻的预测代替下一时刻的测量,且保持道路模型与遮蔽前一致。仿真实验采用地面运动目标指示雷达,考虑地面运动目标的三种常见场景:进入或离开道路、经过道路交叉点以及无测量值。使用了RMSE和ANEES两种评价指标,实验结果表明本文算法有效地提高了目标改变行驶道路时的跟踪精度;且目标速度过低或被遮蔽时,可以避免轨迹中断。     

A passive tracking filter for missile capture

A practical filter is suggested for ground-based missile tracking in a capture-guidance mode utilizing angle-only measurements from a passive missile sensor, and its performance is evaluated by a realistic system-simulation study. A missile-acceleration model that provides inputs to the filter is also suggested. The filter has a decoupled structure of independent azimuth and elevation channels, which requires fewer computations in solving the filter gain compared to a coupled structure. Simulation results show good tracking performance of the filter when used in association with the proposed missile-acceleration model     

A multi-rate sensor fusion approach using information filters for estimating aero-engine performance degradation

Gas-path performance estimation plays an important role in aero-engine health management, and Kalman Filter(KF) is a well-known technique to estimate performance degradation. In previous studies, it is assumed that different kinds of sensors are with the same sampling rate, and they are used for state estimation by the KF simultaneously. However, it is hard to achieve state estimation using various kinds of sensor measurements at the same sampling rate due to a complex network and physical characteristic differences between sensors, especially in an advanced multisensor architecture. For this purpose, a multi-rate sensor fusion using the information filtering approach is proposed based on the square-root cubature rule, which is called Multi-rate Squareroot Cubature Information Filter(MSCIF) to track engine performance degradation. Soft measurement synchronization of the MSCIF is designed to provide a sensor fusion condition for multiple sampling rates of measurement, and a fault sensor is isolated by maximum likelihood validation before state estimation. The contribution of this paper is to supply a novel multi-rate informationfilter approach for sensor fault tolerant health estimation of an aero-engine in a multi-sensor system. Tests are conducted for aero-engine performance degradation estimation with multiple sampling rates of sensor measurement on both digital simulation and semi-physical experiment.Experimental results illustrate the superiority of the proposed algorithm in terms of degradation estimation accuracy and robustness to sensor failure in a multi-sensor system.     

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 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     

A measurement-driven adaptive probability hypothesis density filter for multitarget tracking

This paper studies the dynamic estimation problem for multitarget tracking. A novel gating strategy that is based on the measurement likelihood of the target state space is proposed to improve the overall effectiveness of the probability hypothesis density(PHD) filter. Firstly, a measurement-driven mechanism based on this gating technique is designed to classify the measurements. In this mechanism, only the measurements for the existing targets are considered in the update step of the existing targets while the measurements of newborn targets are used for exploring newborn targets. Secondly, the gating strategy enables the development of a heuristic state estimation algorithm when sequential Monte Carlo(SMC) implementation of the PHD filter is investigated, where the measurements are used to drive the particle clustering within the space gate.The resulting PHD filter can achieve a more robust and accurate estimation of the existing targets by reducing the interference from clutter. Moreover, the target birth intensity can be adaptive to detect newborn targets, which is in accordance with the birth measurements. Simulation results demonstrate the computational efficiency and tracking performance of the proposed algorithm.