An efficient algorithm for multisensor track fusion

An efficient algorithm for track-to-track fusion by incorporating cross-covariance between tracks created by dissimilar sensors is described. An analytical solution of this problem is complicated if cross-correlation between sensors tracking the same target is taken into account. An explicit solution of the cross-covariance matrix at steady state is derived in terms of an integral. It is shown that solution of this integral involves inversion of a matrix whose elements are functions of parameters of individual trackers. Structure of this matrix is analyzed. An efficient analytical solution for inversion of this matrix is obtained. For fusion of similar sensors, it is shown that this matrix is reduced to the Routh-Hurwitz matrix which arises in the study of steady state stability of linear systems. Numerical results showing the amount of reduction of fused track covariance by taking into account the effects of cross-correlation between candidate tracks for fusion is also presented     

Performance evaluation of track fusion with information matrixfilter

In a multisensor environment, each sensor detects multiple targets and creates corresponding tracks. Fusion of tracks from these, possibly dissimilar, sensors yields more accurate kinematic and attribute information regarding the target. Two methodologies have been employed for such purpose, which are: measurement fusion and state vector fusion. It is well known that the measurement fusion approach is optimal but computationally inefficient and the state vector fusion algorithms are more efficient but suboptimal, in general. This is so because the state vector estimates to be fused obtained from two sensors, are not conditionally independent in general due to the common process noise from the target being tracked. It is to be noted that there are three approaches to state vector fusion, which are: weighted covariance, information matrix, and pseudomeasurement. This research is restricted solely to performance evaluation of the information matrix form of state vector fusion. Closed-form analytical solution of steady state fused covariance has been derived as a measure of performance using this approach. Note that the results are derived under the assumptions that the two sensors are synchronized and no misassociation or merged measurement is considered in the study. Results are compared with those using Monte Carlo simulation, which was used in the past to predict fusion system performance by various authors. These results provide additional insight into the mechanism of track fusion and greatly simplify evaluation of fusion performance. In addition, availability of such a solution facilitates the trade-off studies for designing fusion systems under various operating conditions     

Performance limits of track-to-track fusion versus centralized estimation: theory and application [sensor fusion]

Track-to-track fusion is an important part in distributed multisensor-multitarget tracking. The centralized and distributed tracking configurations were studied in (H.Chen et al., Proc. of SPIE Conf. on Signal and Data Processing of Small Targets, vol. 4048, 2000) using simulated air-to-air scenarios, and in (K.C. Chang, et al, IEEE Transact. on Aerospace and Electronic Systems, vol. 33, no. 4, pp. 1271-1276, 1997) with analytical results based on /spl alpha/-/spl beta/ filters. The current work generalizes the results in the latter to the cases with more than 2 sensors. As the number of sensors increases, the performance of the distributed tracker is shown to degrade compared with the centralized estimation even when the optimal track-to-track fusion is used. An approximate track-to-track fusion is presented and compared with the optimal track-to-track fusion with performance curves for various numbers of sensors. These performance curves can be used in designing a fusion system where certain trade-offs need to be considered. Finally, these results are compared with simulation results for a realistic air-to-air encounter scenario.     

基于高斯混合模型的航迹抗差关联算法

针对雷达系统误差时变、上报目标不完全一致等复杂场景下目标航迹关联问题，采用高斯混合模型（GMM）与航迹间拓扑信息相结合的方法实现航迹抗差关联。将航迹关联问题转化为图像匹配中的非刚性点集匹配问题，建立对非同源航迹具有鲁棒性的高斯混合模型，根据航迹间的邻域拓扑信息决定高斯混合模型中各高斯组成部分的权重，利用期望最大值（EM）算法求解高斯混合模型的最优闭合解，在期望步（E-step）阶段求解航迹的对应关系，在最大化步（M-step）阶段求解非同源航迹比例，最后进行航迹关联判决以获得关联结果。仿真结果表明，该算法在不同系统误差、目标分布密度、探测概率等环境下具有较好有效性和鲁棒性。     

基于区实混合序列相似度的异步不等速率航迹关联算法

在分布式多目标跟踪系统中,由于局部传感器开机时间、采样频率以及通信延迟不同等原因,导致来自各传感器的局部航迹往往是异步不等速率的。目前一般的方法是先进行时域配准再进行航迹关联,但是在同步化的过程中,航迹估计值的误差会发生传播,影响航迹关联的性能。针对此问题,提出了一种基于区实混合序列相似度的异步不等速率航迹关联算法。算法首先通过区间数-实数混合序列变换(IRST)得到等长度的航迹行为序列,然后定义一种新的序列差异信息度量,得到混合序列的相似度,以此进行航迹关联判定。仿真实验表明,该算法可以有效地解决异步不等速率航迹关联问题,并且通信延迟和数据乱序对算法性能的影响不明显。     

基于PTE的多雷达航迹融合算法

针对杂波背景下的多雷达航迹融合时局部估计误差互协方差矩阵未知的问题，提出基于目标存在概率（PTE）的航迹融合算法，提升了正确航迹率和跟踪精度。首先，通过综合概率数据关联得到单接收站的目标航迹估计集合和对应的目标存在概率。然后，在局部估计误差互协方差矩阵未知的条件下，基于PTE信息提出不带记忆的综合广义凸组合航迹融合算法。进而将前一帧的融合状态进行反馈，提出带记忆的综合广义凸组合航迹融合算法。仿真验证了所提算法的有效性。     

Architectures and algorithms for track association and fusion

Target tracking using multiple sensors can provide better performance than using a single sensor. One approach to multiple target tracking with multiple sensors is to first perform single sensor tracking and then fuse the tracks from the different sensors. Two processing architectures for track fusion are presented: sensor to sensor track fusion, and sensor to system track fusion. Technical issues related to the statistical correlation between track estimation errors are discussed. Approaches for associating the tracks and combining the track state estimates of associated tracks that account for this correlation are described and compared by both theoretical analysis and Monte Carlo simulations     

组合导航系统中一种基于特征值分解的自适应信息融合滤波算法

基于分散滤波理论的联合滤波算法,可以有效地降低组合导航系统的计算负担,并且增强系统的容错性能。给出了一种联合滤波算法中信息分配系数的自适应计算方法,能够使联合系统根据导航过程中各传感器的信息质量的变化合理地反馈全局信息。仿真结果表明,该算法可以有效地降低由于导航子系统降级带来的滤波误差。     

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.<>     

On optimal track-to-track fusion

Track-to-track fusion is an important part in multisensor fusion. Much research has been done in this area. Chong et al. (1979, 1986, 1990) among others, presented an optimal fusion formula under an arbitrary communication pattern. This formula is optimal when the underlying systems are deterministic, i.e., the process noise is zero, or when full-rate communication (two sensors exchange information each time they receive new measurements) is employed. However, in practice, the process noise is not negligible due to target maneuvering and sensors typically communicate infrequently to save communication bandwidth. In such situations, the measurements from two sensors are not conditionally (given the previous target state) independent due to the common process noise from the underlying system, and the fusion formula becomes an approximate one. This dependence phenomena was also observed by Bar-Shalom (1981) where a formula was derived to compute the cross-covariance of two track estimates obtained by different sensors. Based on this results a fusion formula was subsequently derived (1986) to combine the local estimates which took into account the dependency between the two estimates. Unfortunately, the Bayesian derivation made an assumption that is not met. This work points out the implicit approximation made and shows that the result turns out to be optimal only in the ML (maximum likelihood) sense. A performance evaluation technique is then proposed to study the performance of various track-to-track fusion techniques. The results provide performance bounds of different techniques under various operating conditions which can be used in designing a fusion system.     

Performance evaluation for MAP state estimate fusion

This paper presents a quantitative performance evaluation method for the maximum a posteriori (MAP) state estimate fusion algorithm. Under ideal conditions where data association is assumed to be perfect, it has been shown that the MAP or best linear unbiased estimate (BLUE) fusion formula provides the best linear minimum mean squared estimate (LMMSE) given local estimates under the linear Gaussian assumption for a static system. However, for a dynamic system where fusion is recursively performed by the fusion center on local estimates generated from local measurements, it is not obvious how the MAP algorithm will perform. In the past, several performance evaluation methods have been proposed for various fusion algorithms, including simple convex combination, cross-covariance combination, information matrix, and MAP fusion. However, not much has been done to quantify the steady state behavior of these fusion methods for a dynamic system. The goal of this work is to present analytical fusion performance results for MAP state estimate fusion without extensive Monte Carlo simulations, using an approach developed for steady state performance evaluation for track fusion. Two different communication strategies are considered: fusion with and without feedback to the sensors. Analytic curves for the steady state performance of the fusion algorithm for various communication patterns are presented under different operating conditions.     

Fusion of sensors with dissimilar measurement/tracking accuracies

The case of data fusion of sensors dissimilar in their measurement/tracking errors is considered. It is shown that the fused track performance is similar whether the sensor data are fused at the track level or at the measurement level. The case of a cluster of targets, resolved by one sensor but not the other, is also considered. Under certain conditions the fused track may perform worse than the worst of the sensors. A remedy to this problem through modifications of the association algorithm is presented     

Performance evaluation of multi-sensor classification systems

A common problem in classification is to use one/more sensors to observe repeated measurements of a target's features/attributes, and in turn update the targets' posterior classification probabilities to aid in target identification. This paper addresses the following questions: 1. How do we quantify the classification performance of a sensor? 2. What happens to the posterior probabilities as the number of measurements increase? 3. Will the targets be classified correctly? While the Kalman filter allows for off-line estimation of kinematic performance (covariance matrix), a comparable approach for studying classification accuracy has not been done previously. We develop a new analytical approach for computing the long-run classification performance of a sensor and also present recursive formulas for efficient calculation of the same. We show that, under a minimal condition, a sensor will eventually classify all targets perfectly. We also develop a methodology for evaluating the classification performance of multi-sensor fusion systems involving sensors of varying quality. The contributions of this paper are 1. A simple metric to quantify a sensor's ability to discriminate between the targets being identified, and its use in comparing multiple sensors, 2. An approximate formula based on this metric to compute off-line estimates of the rate of convergence toward perfect classification, and the number of measurements required to achieve a desired level of classification accuracy, and 3. The use of this metric to evaluate classification performance of multi-sensor fusion systems.     

Kinematic deformation scheme for multilayer thin structures with significantly dissimilar layers

An improved kinematic scheme of elastic deformation for multilayer thin structures with significantly dissimilar layers is proposed as well as a problem solution algorithm; the algorithm is based on a priori calculation of kinematic relations that represent a nature of variation of elastic displacements over the layer packet thickness and do not result in a considerable increase of the problem dimension.     

Joint sensor registration and track-to-track fusion for distributed trackers

Sensor registration deals with the correction of registration errors and is an inherent problem in all multisensor tracking systems. Traditionally, it is viewed as a least squares or a maximum likelihood problem independent of the fusion problem. We formulate it as a Bayesian estimation problem where sensor registration and track-to-track fusion are treated as joint problems and provide solutions in cases 1) when sensor outputs (i.e., raw data) are available, and 2) when tracker outputs (i.e., tracks) are available. The solution to the latter problem is of particular significance in practical systems as band limited communication links render the transmission of raw data impractical and most of the practical fusion systems have to depend on tracker outputs rather than sensor outputs for fusion. We then show that, under linear Gaussian assumptions, the Bayesian approach leads to a registration solution based on equivalent measurements generated by geographically separated radar trackers. In addition, we show that equivalent measurements are a very effective way of handling sensor registration problem in clutter. Simulation results show that the proposed algorithm adequately estimates the biases, and the resulting central-level trucks are free of registration errors.     

Efficient multisensor fusion using multidimensional dataassociation

We present the development of a multisensor fusion algorithm using multidimensional data association for multitarget tracking. The work is motivated by a large scale surveillance problem, where observations from multiple asynchronous sensors with time-varying sampling intervals (electronically scanned array (ESA) radars) are used for centralized fusion. The combination of multisensor fusion with multidimensional assignment is done so as to maximize the “time-depth” in addition to “sensor-width” for the number S of lists handled by the assignment algorithm. The standard procedure, which associates measurements from the most recently arrived S-1 frames to established tracks, can have, in the case of S sensors, a time-depth of zero. A new technique, which guarantees maximum effectiveness for an S-dimensional data association (S⩾3), i.e., maximum time-depth (S-1) for each sensor without sacrificing the fusion across sensors, is presented. Using a sliding window technique (of length S), the estimates are updated after each frame of measurements. The algorithm provides a systematic approach to automatic track formation, maintenance, and termination for multitarget tracking using multisensor fusion with multidimensional assignment for data association. Estimation results are presented for simulated data for a large scale air-to-ground target tracking problem     

基于序贯关联算法的多目标无源跟踪

基于序贯关联算法,对多目标无源跟踪问题进行了研究。在只有角度信息可以利用的情况下,首先,利用波门技术对各个无源传感器角度测量数据进行关联和滤波,形成参数航迹;然后,将各个无源传感器的参数航迹送到融合中心进行关联配对,并在关联过程中通过构造关联质量函数对参数航迹的关联历史情况进行度量,解决参数航迹关联模糊问题;最后,通过对关联成功的参数航迹进行交叉定位,给出多个不同目标的位置信息,实现分布式无源系统对多目标的数据关联和跟踪,并通过仿真分析,对算法的有效性和可行性进行验证。     

The modeling and estimation of asynchronous multirate multisensor dynamic systems

An asynchronous data fusion problem based on a kind of multirate multisensor dynamic system is studied. The system is observed by multirate sensors independently, with the state model known at the finest scale. Under the assumption that the sampling rates of sensors decrease successively by any positive integers, the discrete dynamic system models are established based on each single sensor and an asynchronous multirate multisensor state fusion estimation algorithm is presented. Theoretically, the estimate is proven to be unbiased and the optimal in the sense of linear minimum covariance, the fused estimate is better than the Kalman filtering results based on each single sensor, and the accuracy of the fused estimate will decrease if any of the sensors' information is neglected. The feasibility and effectiveness of the algorithm are shown through simulations.     

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.     

On hierarchical tracking for the real world

Several information processing configurations for hierarchical tracking and their performances are described in a concise manner, and the selection of one of them is discussed. It is shown that the performance of the "track-to-track fusion without memory" configuration, which, while suboptimal, is simple from the point of view of both computation and communication requirements, is remarkably close to the optimum