Comparison of two-sensor tracking methods based on state vectorfusion and measurement fusion

There are two approaches to the two-sensor track-fusion problem. Y Bar-Shalom and L. Campo (ibid., vol.AES-22, 803-5, Nov. 1986) presented the state vector fusion method, which combines state vectors from the two sensors to form a new estimate while taking into account the correlated process noise. The measurement fusion method or data compression of D. Willner et al. (1976) combines the measurements from the two sensors first and then uses this fused measurement to estimate the state vector. The two methods are compared and an example shows the amount of improvement in the uncertainty of the resulting estimate of the state vector with the measurement fusion method     

Optimal Data Fusion in Multiple Sensor Detection Systems

There is an increasing interest in employing multiple sensors for surveillance and communications. Some of the motivating factors are reliability, survivability, increase in the number of targets under consideration, and increase in required coverage. Tenney and Sandell have recently treated the Bayesian detection problem with distributed sensors. They did not consider the design of data fusion algorithms. We present an optimum data fusion structure given the detectors. Individual decisions are weighted according to the reliability of the detector and then a threshold comparison is performed to obtain the global decision.     

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     

Optimal Decision Fusion in Multiple Sensor Systems

The problem of optimal data fusion in the sense of the Neyman-pearson (N-P) test in a centralized fusion center is considered. The fusion center receives data from various distributed sensors. Each sensor implements a N-P test individually and independently of the other sensors. Due to limitations in channel capacity, the sensors transmit their decision instead of raw data. In addition to their decisions, the sensors may transmit one or more bits of quality information. The optimal, in the N-P sense, decision scheme at the fusion center is derived and it is seen that an improvement in the performance of the system beyond that of the most reliable sensor is feasible, even without quality information, for a system of three or more sensors. If quality information bits are also available at the fusion center, the performance of the distributed decision scheme is comparable to that of the centralized N-P test. Several examples are provided and an algorithm for adjusting the threshold level at the fusion center is provided.     

Optimal distributed decision fusion

The problem of decision fusion in distributed sensor systems is considered. Distributed sensors pass their decisions about the same hypothesis to a fusion center that combines them into a final decision. Assuming that the sensor decisions are independent of each other for each hypothesis, the authors provide a general proof that the optimal decision scheme that maximizes the probability of detection at the fusion for fixed false alarm probability consists of a Neyman-Pearson test (or a randomized N-P test) at the fusion and likelihood-ratio tests at the sensors     

多传感器融合目标跟踪

分析了基于成象和雷达两种传感器对目标状态的测量模型及其融合模型。针对两种传感器之间测量信息的不同步问题,给出了一种基于最小二乘法的不同步信息之间的时间配准和融合方法,并设计了跟踪滤波器。     

Explicit solutions for some simple decentralized detection problems

A decentralized detection problem is considered in which a number of identical sensors transmit a finite-valued function of their observations to a fusion center which makes a final decision on one of M alternative hypotheses. The authors consider the case in which the number of sensors is large, and they derive (asymptotically) optimal rules for determining the messages of the sensors when the observations are generated from a simple and symmetrical set of discrete distributions. They also consider the tradeoff between the number of sensors and the communication rate of each sensor when there is a constraint on the total communication rate from the sensors to the fusion center. The results suggest that it is preferable to have several independent sensors transmitting low-rate (coarse) information instead of a few sensors transmitting high-rate (very detailed) information. They also suggest that an M-ary hypothesis testing problem can be viewed as a collection of M(M-1)/2 binary hypothesis testing problems. From this point of view the most useful messages (decision rules) are those that provide information to the fusion center that is relevant to the largest possible numbers of these binary hypothesis testing problems     

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     

基于改进D-S证据理论的航空发动机转子故障决策融合诊断研究

针对单一传感器的测量信息难以准确、全面地反映航空发动机转子、轴承和齿轮的工作状况,进而造成振动故障诊断难度大的问题,提出安装多个振动传感器组成传感器网络,建立基于多传感器信息的发动机转子故障决策融合诊断系统。由于多传感器系统不可避免地会存在各传感器信息不一致、信息冲突的情形,因此针对该融合诊断系统的信号测量、信息预处理、特征提取、故障诊断及决策融合5个环节,重点研究了决策融合环节的Dempster-Shafer（D-S）证据决策融合方法存在的冲突证据融合失效问题。通过分析原因,从避免“一票否决”现象和证据加权平均两个方面进行改进,提出了改进D-S证据融合方法,并应用于航空发动机转子的模拟故障决策融合诊断中。结果表明基于D-S证据理论对3个传感器的单一诊断结果进行决策融合,能得到比任一单个传感器更准确、可靠的结果;而改进D-S证据融合方法由于能在一定程度上克服冲突证据融合带来的失效问题,且能同时兼顾处理好非冲突证据的融合,故其对于证据冲突和非冲突情形都取得了较好的融合效果,因此总的分类正确率要高于常规D-S算法和PCR5算法。     

OS-CFAR thresholding in decentralized radar systems

In a decentralized detection scheme, several sensors perform a binary (hard) decision and send the resulting data to a fusion center for the final decision. If each local decision has a constant false alarm rate (CFAR), the final decision is ensured to be CFAR. We consider the case that each local decision is a threshold decision, and the threshold is proportional, through a suitable multiplier, to a linear combination of order statistics (OS) from a reference set (a generalization of the concept of OS thresholding). We address the following problem: given the fusion rule and the relevant system parameters, select each threshold multiplier and the coefficients of each linear combination so as to maximize the overall probability of detection for constrained probability of false alarm. By a Lagrangian maximization approach, we obtain a general solution to this problem and closed-form solutions for the AND and OR fusion logics. A performance assessment is carried on, showing a global superiority of the OR fusion rule in terms of detection probability (for operating conditions matching the design assumptions) and of robustness (when these do not match). We also investigate the effect of the hard quantization performed at the local sensors, by comparing the said performance to those achievable by the same fusion rule in the limiting case of no quantization     

Local SNR considerations in decentralized CFAR detection

We consider the decentralized detection problem, involving N sensors and a central processor, in which the sensors transmit unquantized data to the fusion center. Assuming a homogeneous background for constant false-alarm rate (CFAR) analysis, we obtain the performances of the system for the Swerling I and Swerling III target models. We demonstrate that a simple nonparametric fusion rule at the central processor is sufficient for nearly optimum performance. The effect of the local signal-to-noise ratios (SNRs) on the performances of the optimum detector and two suboptimum detectors is also examined. Finally, we obtain a set of conditions, related to the SNRs, under which better performance may be obtained by using decentralized detection as compared with centralized detection     

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     

一种基于相邻模块化加权D-S的融合诊断方法

常规D-S (Dempster-Shafter)决策融合方法由于其自身理论不足,不能很好直接处理决策结果偏差大、冲突大的传感器融合问题,因而对于信息高冲突情况下的转子微弱故障融合诊断存在着失效问题。针对该类问题与不足,借鉴复杂网络的舆论传播、社会学习理论及多智能体一致性决策的相关概念与思路,从避免决策结果冲突大的传感器直接进行融合的角度进行改进,提出相邻模块化加权D-S融合方法。该方法首先根据初步结果进行相邻节点与模块划分,只有决策距离在相邻界限值范围内的相邻模块节点才能进行决策融合;对于同一模块内相邻节点,根据各节点决策权重及初步决策结果采用加权D-S融合方法进行决策融合;针对融合结果再进行相邻节点模块划分与融合,依此步骤进行循环划分与融合,直到所有模块与节点均不相邻;最后采用专家权威决策方法确定权重和最大的模块融合结果作为最终的传感器网络一致性决策结果。通过多传感器网络的转子故障模拟实验对所提方法进行验证,应用结果表明:所提方法可以较好解决少数传感器诊断正确、而多数诊断错误的信息高冲突条件下的局部微弱故障融合诊断问题。     

Decentralized linear estimation in correlated measurement noise

Some results and perspectives are provided on the problem of optimally combining estimates from different sensors when the measurement noise processes are correlated. The authors consider only the static estimation problem and limit the discussion to fusion with two sensors. A necessary and sufficient condition for optimality of the decentralized estimator in the presence of correlated measurement noise processes is presented. The result ties together previously reported work, and yields additional insights.<>     

Predetection fusion: resolution cell grid effects

If members of a suite of sensors from which fusion is to be carried out are not colocated, it is unreasonable to assume that they share a common resolution cell grid; this is generally ignored in the data fusion community. We explore the effects of such “noncoincidence”, and we find that what at first seems to be a problem can in fact be exploited. The idea is that a target is known to be confined to an intersection of overlapping resolution cells, and this overlap is generally small. We examine noncoincidence from two viewpoints: tracking and detection. With respect to tracking our analysis is first static, by which is meant that we establish the decrease in measurement error; and then dynamic, meaning that the overall effect in the tracking problem is quantified. The detection viewpoint considers noncoincidence as it has impact on a predetection fusion system. Specifically, the role of the fusion rule is examined, and the use of noncoincidence to improve detection performance (rather than that of tracking) is explored     

Decision fusion rules in multi-hop wireless sensor networks

The decision fusion problem for a wireless sensor network (WSN) operating in a fading environment is considered. In particular, we develop channel-aware decision fusion rules for resource-constrained WSNs where binary decisions from local sensors may need to be relayed through multi-hop transmission in order to reach a fusion center. Each relay node employs a binary relay scheme whereby the relay output is inferred from the channel impaired observation received from its source node. This estimated binary decision is subsequently transmitted to the next node until it reaches the fusion center. Under a flat fading channel model, we derive the optimum fusion rules at the fusion center for two cases. In the first case, we assume that the fusion center has knowledge of the fading channel gains at all hops. In the second case, we assume a Rayleigh fading model, and derive fusion rules utilizing only the fading channel statistics. We show that likelihood ratio (LR) based optimum decision fusion statistics for both cases reduce to respective simple linear test statistics in the low channel signal-to-noise ratio (SNR) regime. These suboptimum detectors are easy to implement and require little a priori information. Performance evaluation, including a study of the robustness of the fusion statistics with respect to unknown system parameters, is conducted through simulations.     

基于庞加莱映射的多站数据融合算法

针对目前单目标跟踪数据融合中存在的伪数据问题,研究了基于庞加莱映射的补充条件定位引导算法和多站抗野值数据融合算法,建立了适应实际传感器数量变化的数据融合体系。理论分析和仿真结果均证明,该方法可行有效。     

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     

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     

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.