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     

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     

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     

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.     

Comparison of two measurement fusion methods forKalman-filter-based multisensor data fusion

Currently there exist two commonly used measurement fusion methods for Kalman-filter-based multisensor data fusion. The first (Method I) simply merges the multisensor data through the observation vector of the Kalman filter, whereas the second (Method II) combines the multisensor data based on a minimum-mean-square-error criterion. This paper, based on an analysis of the fused state estimate covariances of the two measurement fusion methods, shows that the two measurement fusion methods are functionally equivalent if the sensors used for data fusion, with different and independent noise characteristics, have identical measurement matrices. Also presented are simulation results on state estimation using the two measurement fusion methods, followed by the analysis of the computational advantages of each method     

Distributed state estimation for heterogeneous mobile sensor networks with stochastic observation loss

The problem of distributed fusion and random observation loss for mobile sensor networks is investigated herein. In view of the fact that the measured values, sampling frequency and noise of various sensors are different, the observation model of a heterogeneous network is constructed. A binary random variable is introduced to describe the drop of observation component and the topology switching problem caused by complete observation loss is also considered. A cubature information filtering algo...     

Ballistic missile track initiation from satellite observations

An algorithm is presented to initiate tracks of a ballistic missile in the initial exoatmospheric phase, using line of sight (LOS) measurements from one or more moving platforms (typically satellites). The major feature of this problem is the poor target motion observability which results in a very ill-conditioned estimation problem. The Gauss-Newton iterative least squares minimization algorithm for estimating the state of a nonlinear deterministic system with nonlinear noisy measurements has been previously applied to the problem of angles-only orbit determination using more than three observations. A major shortcoming of this approach is that convergence of the algorithm depends strongly on the initial guess. By using the more sophisticated Levenberg-Marquardt method in place of the simpler Gauss-Newton algorithm and by developing robust new methods for obtaining the initial guess in both single and multiple satellite scenarios, the above mentioned difficulties have been overcome. In addition, an expression for the Cramer-Rao lower bound (CRLB) on the error covariance matrix of the estimate is derived. We also incorporate additional partial information as an extra pseudomeasurement and determine a modified maximum likelihood (ML) estimate of the target state and the associated bound on the covariance matrix. In most practical situations, probabilistic models of the target altitude and/or speed at the initial point constitute the most useful additional information. Monte Carlo simulation studies on some typical scenarios were performed, and the results indicate that the estimation errors are commensurate with the theoretical lower bounds, thus illustrating that the proposed estimators are efficient     

Multisensor resource deployment using posterior Cramer-Rao bounds

The development of a general framework for the systematic management of multiple sensors in target tracking in the presence of clutter is described. The basis of the technique is to quantify, and subsequently control, the accuracy of target state estimation. The posterior Cramer-Rao lower bound (PCRLB) provides the means of achieving this aim by enabling us to determine a bound on the performance of all unbiased estimators of the unknown target state. The general approach is then to use optimization techniques to control the measurement process in order to achieve accurate target state estimation. We are concerned primarily with the deployment and utilization of limited sensor resources. We also allow for measurement origin uncertainty, with sensor measurements either target-generated or false alarms. An example in which the aim is to track a submarine by deploying a series of constant false-alarm rate passive sonobuoys is presented. We show that by making some standard assumptions, the effect of the measurement origin uncertainty can be expressed as a state-dependent information reduction factor which can be calculated off-line. This enables the Fisher information matrix (FIM) to be calculated quickly, allowing Cramer-Rao bounds to be utilized for real-time, dynamic sensor management. The sensor management framework is shown to determine deployment strategies that enable the target to be accurately localized, and at the same time efficiently utilize the limited sensor resources.     

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.     

Lightweight hybrid visual-inertial odometry with closed-form zero velocity update

Visual-Inertial Odometry (VIO) fuses measurements from camera and Inertial Measurement Unit (IMU) to achieve accumulative performance that is better than using individual sensors. Hybrid VIO is an extended Kalman filter-based solution which augments features with long tracking length into the state vector of Multi-State Constraint Kalman Filter (MSCKF). In this paper, a novel hybrid VIO is proposed, which focuses on utilizing low-cost sensors while also considering both the computational efficiency and positioning precision. The proposed algorithm introduces several novel contributions. Firstly, by deducing an analytical error transition equation, one-dimensional inverse depth parametrization is utilized to parametrize the augmented feature state. This modification is shown to significantly improve the computational efficiency and numerical robustness, as a result achieving higher precision. Secondly, for better handling of the static scene, a novel closed-form Zero velocity UPdaTe (ZUPT) method is proposed. ZUPT is modeled as a measurement update for the filter rather than forbidding propagation roughly, which has the advantage of correcting the overall state through correlation in the filter covariance matrix. Furthermore, online spatial and temporal calibration is also incorporated. Experiments are conducted on both public dataset and real data. The results demonstrate the effectiveness of the proposed solution by showing that its performance is better than the baseline and the state-of-the-art algorithms in terms of both efficiency and precision. A related software is open-sourced to benefit the community.^①     

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.     

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.     

Tracking a 3D maneuvering target with passive sensors

A novel application of the interacting multiple models (IMM) algorithm in which passive infrared sensors are fused for tracking a target maneuvering in three dimensions is discussed. More accurate models of target motion are proposed to improve performance. When the general models are used to describe the maneuvering periods, it is shown that the IMM behaviour is not satisfactory, in that the innovations associated with the different models do not discriminate between the corresponding target maneuvering regimes. The turning of the Markov chain transition matrix, i.e., a priori information, is then crucial to obtaining the correct ordering of the a posteriori regime probabilities. On the contrary, a more satisfactory behavior of the IMM algorithm is obtained by carefully selecting the target motion models in the different regimes     

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。     

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.     

Optimal sensor selection strategy for discrete-time stateestimators

A novel sensor selection strategy is introduced, which can be implemented on-line in time-varying discrete-time system. We consider a case in which several measurement subsystem are available, each of which may be used to drive a state estimation algorithm. However, due to practical implementation constraints (such as the ability of the on-board computer to process the acquired data), only one of these subsystems can actually by utilized at a measurement update. An algorithm is needed, by which the optimal measurement subsystem to be used is selected at each sensor selection epoch. The approach described is based on using the square root V-Lambda information filter as the underlying state estimation algorithm. This algorithm continuously provides its user with the spectral factors of the estimation error covariance matrix, which are used in this work as the basis for an on-line decision procedure by which the optimal measurement strategy is derived. At each sensor selection epoch, a measurement subsystem is selected, which contributes the largest amount of information along the principal state space direction associated with the largest current estimation error. A numerical example is presented, which demonstrates the performance of the new algorithm. The state estimation problem is solved for a third-order time-varying system equipped with three measurement subsystem, only one of which can be used at a measurement update. It is shown that the optimal measurement strategy algorithm enhances the estimator by substantially reducing the maximal estimation error     

基于CDKF的快速协方差交叉融合跟踪算法研究

随着目标抗干扰能力的增强，单一寻的制导方式很难完成对目标的稳定跟踪和精确打击，需采用多种探测器作为传感器，提供多种观测数据以实现对目标的稳定跟踪和精确打击。建立了适当的目标运动模型和观测模型，利用中心差分卡尔曼滤波（CDKF）变换处理模型的非线性问题，避免了求解复杂的雅克比矩阵。对于分布式多传感器融合，传统的方法多采用协方差交叉（CI）融合方法，但是这类方法需要寻优求解。而快速协方差交叉（FCI）则不需要进行寻优过程，且计算量小。在此基础上，提出了用于多传感器目标跟踪的CDKF-FCI融合算法。最后，对算法进行了仿真分析，并进一步验证了提出算法的有效性。     

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.