Multi-sensor optimal information fusion Kalman filter

This paper presents a new multi-sensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, it is equivalent to the maximum likelihood fusion criterion under the assumption of normal distribution. Based on this optimal fusion criterion, a general multi-sensor optimal information fusion decentralized Kalman filter with a two-layer fusion structure is given for discrete time linear stochastic control systems with multiple sensors and correlated noises. The first fusion layer has a netted parallel structure to determine the cross covariance between every pair of faultless sensors at each time step. The second fusion layer is the fusion center that determines the optimal fusion matrix weights and obtains the optimal fusion filter. Comparing it with the centralized filter, the result shows that the computational burden is reduced, and the precision of the fusion filter is lower than that of the centralized filter when all sensors are faultless, but the fusion filter has fault tolerance and robustness properties when some sensors are faulty. Further, the precision of the fusion filter is higher than that of each local filter. Applying it to a radar tracking system with three sensors demonstrates its effectiveness.     

Linear minimum variance estimation fusion

This paper shows that a general multisensor unbiased linearly weighted estimation fusion essentially is the linear minimum variance (LMV) estimation with linear equality constraint, and the general estimation fusion formula is developed by extending the Gauss-Markov estimation to the random parameter under estimation. First, we formulate the problem of distributed estimation fusion in the LMV setting. In this setting, the fused estimator is a weighted sum of local estimates with a matrix weight. We show that the set of weights is optimal if and only if it is a solution of a matrix quadratic optimization problem subject to a convex linear equality constraint. Second, we present a unique solution to the above optimization problem, which depends only on the covariance matrix Ck.Third, if a priori information, the expectation and covariance, of the estimated quantity is unknown, a necessary and sufficient condition for the above LMV fusion becoming the best unbiased LMV estimation with known prior informatio     

多传感器分布式区间估计融合

考虑了对未知参数θ的多传感器分布式区间估计融合问题. 建立了一种最优区间估计融合模型———凸线性组合融合, 并给出搜索最优权系数的Gauss Seidel迭代算法, 另外, 给出了一种近似的区间估计融合, 它能减少大量的计算量, 并且在某些情况下可以达到最优的估计性能. 最后采用计算机数值模拟, 用以上方法得到的融合区间估计均优于每个传感器的区间估计的性能.     

An efficient sensor quantization algorithm for decentralized estimation fusion

In this paper, we consider the design problem of optimal sensor quantization rules (quantizers) and an optimal linear estimation fusion rule in bandwidth-constrained decentralized random signal estimation fusion systems. First, we derive a fixed-point-type necessary condition for both optimal sensor quantization rules and an optimal linear estimation fusion rule: a fixed point of an integral operation. Then, we can motivate an iterative Gauss–Seidel algorithm to simultaneously search for both optimal sensor quantization rules and an optimal linear estimation fusion rule without Gaussian assumptions on the joint probability density function (pdf) of the estimated parameter and observations. Moreover, we prove that the algorithm converges to a person-by-person optimal solution in the discretized scheme after a finite number of iterations. It is worth noting that the new method can be applied to vector quantization without any modification. Finally, several numerical examples demonstrate the efficiency of our method, and provide some reasonable and meaningful observations how the estimation performance is influenced by the observation noise power and numbers of sensors or quantization levels.     

基于伪测量的分布式最优单步延迟航迹融合估计

融合中心如何处理无序局部数据,对分布式多传感器系统的运行品质至关重要．本文将系统中的局部估计转化为伪测量,将分布式融合估计转化为二级集中式融合估计．将所得的伪测量兼分布式融合估计算法与单步延迟的无序测量数据（out-of-sequencemeasurements,OOSM）最优滤波-A1算法进行组合,得出了分布式多传感器系统的最优单步延迟无序航迹（out-of-sequence tacks,OOST）估计算法,适用于航迹无序局部数据融合估计．该算法具有最优估计性能．     

基于信息融合估计的离散系统最优跟踪控制

针对期望输出和未来干扰无预见的离散线性系统最优跟踪问题,提出一种基于信息融合最优估计的控制方法.若将当前给定值和可测干扰值分别看作系统未来输出和干扰的预见值,则跟踪控制问题可转化为具有无限预见步数的预见控制问题,并将无限预见信息融合成一步等效预见信息,进而获得近似最优融合控制律.对线性直流电机系统和宏观经济系统的仿真结果均验证了该控制器在提高系统跟踪精度和抑制干扰等方面的有效性.     

Distributed optimal component fusion weighted by scalars for fixed-lag Kalman smoother

Based on the optimal fusion criterion in the linear minimum variance sense, a distributed optimal fusion fixed-lag Kalman smoother with a three-layer fusion structure is given for the discrete time-varying linear stochastic control systems with multiple sensors and correlated noises. Its components are estimated by scalar weighting fusion, respectively. It only requires in parallel a series of computations of the weighted scalars, and avoids the computations of the weighted matrices, so that the computational burden can obviously be reduced. Further, the steady-state fusion smoother is also given for the discrete time-invariant linear stochastic control systems. The scalar weights can be obtained by fusing once after all local estimations reach steady state. It can reduce the online computational burden. Also, the computation formulas of smoothing error cross-covariance matrices are given. Two simulation examples show the performance.     

Robust weighted fusion Kalman predictors with uncertain noise variances

In this paper, the problem of designing weighted fusion robust time-varying Kalman predictors is considered for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle and the unbiased linear minimum variance (ULMV) rule, based on the worst-case conservative system with the conservative upper bounds of noise variances, the local and five weighted fused robust time-varying Kalman predictors are designed, which include a robust weighted measurement fuser, three robust weighted state fusers, and a robust covariance intersection (CI) fuser. Their actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equation approach. The concept of the robust accuracy is presented, and the robust accuracy relations are proved. The corresponding steady-state robust local and fused Kalman predictors are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman predictors is proved by the dynamic error system analysis (DESA) method and the dynamic variance error system analysis (DVESA) method. Simulation results show the effectiveness and correctness of the proposed results.     

不受约束的全局最优加权观测融合估计

利用矩阵满秩分解方法,基于加权最小二乘理论提出了一种不受各传感器观测阵是否相同、观测噪声是否相关约束限制的加权观测融合估计算法。证明了其估计结果每时刻恒同于集中式融合Kalman估计结果,因而具有全局最优性,且可明显减小计算负担,便于实时应用。通过对GPS目标跟踪系统的两种方案进行仿真说明了它的功能等价性、快速性以及最优性。     

Estimation of the disturbance structure from data using semidefinite programming and optimal weighting

Designing a state estimator for a linear state-space model requires knowledge of the characteristics of the disturbances entering the states and the measurements. In [Odelson, B. J., Rajamani, M. R., & Rawlings, J. B. (2006). A new autocovariance least squares method for estimating noise covariances. Automatica, 42(2), 303-308], the correlations between the innovations data were used to form a least-squares problem to determine the covariances for the disturbances. In this paper we present new and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates. We also formulate the optimal weighting to be used in the least-squares objective in the covariance estimation problem to ensure minimum variance in the estimates. A modification to the above technique is then presented to estimate the number of independent stochastic disturbances affecting the states. This minimum number of disturbances is usually unknown and must be determined from data. A semidefinite optimization problem is solved to estimate the number of independent disturbances entering the system and their covariances.     

集中式与分布式鲁棒状态融合估计

研究不确定多传感器系统的鲁棒估计问题是多传感器融合估计理论的一个重要研究方向.本文以鲁棒滤波理论为基础,给出了不确定多传感器系统的多胞型描述模型,并利用LMI方法给出集中式鲁棒状态融合估计问题的解,证明了将集中式鲁棒融合估计转化为相同估计性能的分布式融合估计算法的条件.最后给出了分布式不确定多传感器系统的状态融合估计的一个算例.     

Integrated optimization methods in multisensor decision and estimation fusion

This paper presents a significant integrated optimization point of view behind the following three successful decision and estimation fusion results: 1) a unified fusion rule for networked sensor decision systems; 2) optimal sensor data quantization for estimation fusion and 3) integrated multi-target data association tracking systems. More precisely speaking, the integrated optimization method in 1) derives a unified objective function optimizing only sensor rules given a unified fusion rule; the method in 2) derives a unified objective function optimizing both the sensor quantization rule and the final estimation in the MSE sense, and the method in 3) integrates all associated targets and their valid observations into a whole random measurement matrix dynamic system so that the optimal random matrix Kalman filtering can be applied to estimate the states of all associated targets.     

Drift-free attitude estimation for accelerated rigid bodies

In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long-term stable even in the presence of gyro drift.     

有限时间信息融合线性二次型最优控制

针对有限时间线性二次型最优控制问题, 提出了一种新的求解方法—–信息融合估计方法. 基于线性最小方差估计准则下的融合估计理论, 通过融合期望状态轨迹、理想控制策略等软约束信息, 分别采用集中式融合和序贯式融合两种信息处理方法, 求得最优状态调节器问题的最优融合控制序列. 进一步从理论上论证了序贯式融合控制方法与传统最优控制方法的一致性, 并通过直流电机系统的数值仿真也验证了集中式和序贯式融合控制方法 与传统最优控制方法的等效性, 从而统一了最优估计与最优控制问题, 并为最优控制问题提供了一种新的求解方法.     

Optimal sequential and distributed fusion for state estimation in cross-correlated noise

This paper is concerned with the optimal state estimation for linear systems when the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. We derive the optimal linear estimation in a sequential form and for distributed fusion. They are both compared with the optimal batch fusion, suboptimal batch fusion, suboptimal sequential fusion, and the suboptimal distributed fusion where the cross-correlation between the noises are neglected. The comparison is in terms of theoretical filter mean square error and the real root mean square error. Simulation on a target tracking example is given to show the effectiveness of the presented algorithms.     

Multi-rate optimal state estimation

This article formulates a multi-rate linear minimum mean squared error (LMMSE) state estimation problem, which includes four rates as follows: the state updating rate in the model, the measurement sampling rate, the estimate updating rate and the estimate output rate. This formulation is unique in two ways. First, the rate ratio between state measurement and state estimate is more general (a rational number), instead of just an integer or its reciprocal as considered in the existing literature. Second, state estimates are produced in blocks, which have never been considered before in the multi-rate estimator design. The multi-rate LMMSE estimation problem is solved by examining several distinctive cases for single-rate state estimation, obtained through the lifting technique. Also, sufficient conditions are given for asymptotic stability of the proposed multi-rate LMMSE estimators. An example in tracking a manoeuvering target is given to illustrate the proposed multi-rate state estimators.     

Extension of minimum variance estimation for systems with unknown inputs

In this paper, we address the problem of minimum variance estimation for discrete-time time-varying stochastic systems with unknown inputs. The objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs. It extends the results of Darouach and Zasadzinski (Automatica 33 (1997) 717) where the unknown inputs are only present in the model. The main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises, this fact leads generally to suboptimal filters. Necessary and sufficient conditions for the unbiasedness of this filter are established. Then conditions under which the estimation error and the system noises are uncorrelated are presented, and an optimal estimator and a predictor filters are derived. Sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time-invariant case. A numerical example is given in order to illustrate the proposed method.     

基于快速清晰度估计的多聚焦图像融合

为了准确地估计源图像的清晰区域,提高多聚焦图像融合的效率,本文提出了一种新的基于清晰度估计的图像融合方法。首先,利用基于离散小波的清晰度估计方法获取源图像的聚焦区域,然后使用均值滤波和空洞填充进一步优化该聚焦区域,最后结合清晰度估计和相似性特性,将不同聚焦区域合并生成融合图像。该方法获得的融合图像在客观评价和主观质量上都优于以往基于清晰度的图像融合方法。     

离散线性信息融合最优跟踪控制

提出一种有限时间离散线性最优跟踪控制问题的新解法--信息融合估计解法.基于信息融合估计理论,推导出协状态融合滤波方程和控制量融合估计值,由此获得最优融合控制律及二次性能指标最小值.从理论上证明了信息融合估计解法与传统解法的等同性,从信息融合的角度建立了有限时间离散线性最优跟踪控制系统,从而统一了最优控制问题和最优估计问题,电机系统的控制仿真结果验证了该解法的有效性以及与传统解法的等同性.