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.     

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。     

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.     

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     

Observer-type Kalman innovation filter for uncertain linear systems

An observer-type of Kalman innovation filtering algorithm to find a practically implementable "best" Kalman filter, and such an algorithm based on the evolutionary programming (EP) optima-search technique, are proposed, for linear discrete-time systems with time-invariant unknown-but-hounded plant and noise uncertainties. The worst-case parameter set from the stochastic uncertain system represented by the interval form with respect to the implemented "best" filter is also found in this work for demonstrating the effectiveness of the proposed filtering scheme. The new EP-based algorithm utilizes the global optima-searching capability of EP to find the optimal Kalman filter and state estimates at every iteration, which include both the best possible worst case Interval and the optimal nominal trajectory of the Kalman filtering estimates of the system state vectors. Simulation results are included to show that the new algorithm yields more accurate estimates and is less conservative as compared with other related robust filtering schemes     

多局部节点异步抗差航迹关联算法

为解决航迹异步与系统误差并存情况下的多局部节点航迹关联问题,提出一种基于区间序列离散度的多局部节点异步抗差航迹关联算法。定义区间型数据集的离散信息度量,给出系统误差下航迹序列区间化方法,通过累次积分计算离散度,结合多维分配进行关联判定。针对多局部节点上报目标不完全一致现象,设置零号航迹管理关联质量。与传统算法相比,无需时域配准,可在系统误差下对异步航迹直接关联。仿真结果表明,算法能在局部节点上报目标不完全一致场景下实现有效关联,且正确关联率随局部节点数目的增加或目标密集程度的增大而提高。     

基于区实序列变换的航迹关联算法

针对时变系统条件下的航迹关联问题,提出一种基于区实序列变换的关联算法。首先,利用线性最优化的方法,将上报航迹的不确定性描述为区间灰色序列;再在区实序列变换的基础上,利用实数序列间的灰关联度加权融合描述不同雷达上报航迹的关联相似度,通过判决给出关联结论。仿真结果显示了算法的有效性以及良好的抗差性能。     

基于傅里叶变换的航迹对准关联算法

研究了在组网雷达存在系统误差情况下的目标航迹关联问题,理论分析了雷达系统误差对目标航迹的影响,并将该影响表示为目标航迹的旋转和平移量。在此基础上,提出了一种基于傅里叶变换的系统误差配准前航迹对准关联算法,该算法将组网雷达的航迹数据看做为一种整体信息,采用傅里叶变换理论来估计和补偿组网雷达目标航迹数据到融合中心航迹数据的相对旋转量和平移量,将雷达网中雷达上报的目标航迹数据对准到融合中心,从而不依赖于估计雷达网系统误差,实现了误差配准前的航迹准确关联,能够为后端的系统误差配准提供可靠的关联目标航迹数据。     

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     

非线性系统中多传感器目标跟踪融合算法研究

 研究了在非线性系统中 ,基于转换坐标卡尔曼滤波器的多传感器目标跟踪融合算法。通过分析得出 :在非线性系统的多传感器目标跟踪中 ,基于转换坐标卡尔曼滤波器 ( CMKF)的分布融合估计基本可以重构中心融合估计。仿真实验也证明了此结论。由此可见分布的 CMKFA是非线性系统中较优的分布融合算法     

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.     

Track-to-track fusion with dissimilar sensors

An analysis is described of a kinematic state vector fusion algorithm when tracks are obtained from dissimilar sensors. For the sake of simplicity, it is assumed that two dissimilar sensors are equipped with nonidentical two-dimensional optimal linear Kalman filters. It is shown that the performance of such a track-to-track fusion algorithm can be improved if the cross-correlation matrix between candidate tracks is positive. This cross-correlation is introduced by noise associated with target maneuver that is common to the tracking filters in both sensors and is often neglected. An expression for the steady state cross-correlation matrix in closed form is derived and conditions for positivity of the cross-correlation matrix are obtained. The effect of positivity on performance of kinematic track-to-track fusion is also discussed     

Acoustic node calibration using a moving source

Acoustic nodes, each containing an array of microphones, can track targets in x-y space from their received acoustic signals, if the node positions and orientations are known exactly. However, it is not always possible to deploy the nodes precisely, so a calibration phase is needed to estimate the position and the orientation of each node before doing any tracking or localization. An acoustic node can be calibrated from sources of opportunity such as beacons or a moving source. We derive and compare several calibration methods for the case where the node can hear a moving source whose position can be reported back to the node. Since calibration from a moving source is, in effect, the dual of a tracking problem; methods derived for acoustic target trackers are used to obtain robust and high resolution acoustic calibration processes. For example, two direction-of-arrival-based calibration methods can be formulated based on combining angle estimates, geometry, and the motion dynamics of the moving source. In addition, a maximum likelihood (ML) solution is presented using a narrowband acoustic observation model, along with a Newton-based search algorithm that speeds up the calculation the likelihood surface. The Cramer-Rao lower bound (CRLB) on the node position estimates is also derived to show that the effect of position errors for the moving source on the estimated node position is much less severe than the variance in angle estimates from the microphone array. The performance of the calibration algorithms is demonstrated on synthetic and field data.     

一种带随机偏差的分布式信息融合滤波算法

在通信、计算机、信号处理、自动控制中,对于带有未知的干扰和偏差的随机系统的状态估计已经广泛出现。在现实环境中,不同的传感器可能受到不同的干扰影响。研究随机系统的状态估计问题在实际应用中具有重要的意义。对带有随机偏差的线性随机系统,将系统转换为多模型结构的特殊情况。利用最小方差的最优加权融合估计算法,获得了分布式信息融合滤波算法。通过仿真可以看出,分布式信息融合算法要比局部估计算法具有更高的精度,算法具有分布式结构,这使其具有更好的鲁棒性和可靠性。     

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     

具有丢包补偿的分布式一致性融合估计器

研究了具有随机丢包的网络化分布式一致性估计问题。丢包现象存在于各节点间局部状态估计值的传输过程中,引入一组服从Bernoulli分布的随机变量来描述。当发生丢包时,以融合节点前一时刻融合估计值的一步预测值进行补偿。建立了以估计器增益为决策变量,以所有传感器有限时域下状态融合估计误差和为代价函数的优化问题。在给定一致性权重下,通过最小化代价函数的上界得到了一组次优的估计器增益,并给出了融合估计器渐进稳定的充分条件。最后,通过算例仿真验证了算法的有效性。     

Asynchronous distributed detection

Binary parallel distributed-detection architectures employ a bank of local detectors to observe a common volume of surveillance, and form binary local decisions about the existence or nonexistence of a target in that volume. The local decisions are transmitted to a central detector, the data fusion center (DEC), which integrates them to a global target or no target decision. Most studies of distributed-detection systems assume that the local detectors are synchronized. In practice local decisions are made asynchronously and the DFC has to update its global decision continually. In this study the number of local decisions observed by the central detector within any observation period is Poisson distributed. An optimal fusion rule is developed and the sufficient statistic is shown to be a weighted sum of the local decisions collected by the DFC within the observation interval. The weights are functions of the individual local detector performance probabilities (i.e., probabilities of false alarm and detection). In this respect the decision rule is similar to the one developed by Chair and Varshney for the synchronized system. Unlike the Chair-Varshney rule, however, the DFC's decision threshold in the asynchronous system is time varying. Exact expressions and asymptotic approximations are developed for the detection performance with the optimal rule. These expressions allow performance prediction and assessment of tradeoffs in realistic decision fusion architectures which operate over modern communication networks     

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.     

Blind adaptive decision fusion for distributed detection

We consider the problem of decision fusion in a distributed detection system. In this system, each detector makes a binary decision based on its own observation, and then communicates its binary decision to a fusion center. The objective of the fusion center is to optimally fuse the local decisions in order to minimize the final error probability. To implement such an optimal fusion center, the performance parameters of each detector (i.e., its probabilities of false alarm and missed detection) as well as the a priori probabilities of the hypotheses must be known. However, in practical applications these statistics may be unknown or may vary with time. We develop a recursive algorithm that approximates these unknown values on-line. We then use these approximations to adapt the fusion center. Our algorithm is based on an explicit analytic relation between the unknown probabilities and the joint probabilities of the local decisions. Under the assumption that the local observations are conditionally independent, the estimates given by our algorithm are shown to be asymptotically unbiased and converge to their true values at the rate of O(1/k/sup 1/2/) in the rms error sense, where k is the number of iterations. Simulation results indicate that our algorithm is substantially more reliable than two existing (asymptotically biased) algorithms, and performs at least as well as those algorithms when they work.     

A Self-organizing Bearings-only Target Tracking Algorithm in Wireless Sensor Network

In the bearings-only target tracking, wireless sensor network (WSN) collects observations of the target direction at various nodes and uses an adaptive filter to combine them for target tracking. An efficient network management is necessary to gain an optimal tradeoff between locating accuracy and energy consumption. This article proposes a self-organizing target tracking algorithm to select the most beneficial subset of nodes to track the target at every snapshot. Compared with traditional methods, this scheme avoids the need for keeping global position information of the network as in greedy selection. Each node judges its future usefulness depending on the knowledge of its own position and using simple mathematics computation. Simulations indicate that this scheme has locating accuracy comparable to the global greedy algorithm. Also, it has good robustness against node failure and autonomous adaptability to the change of the network scale. Furthermore, this algorithm consumes limited energy because only a portion of nodes partakes in the selection at every snapshot.