Sensor scheduling over a packet-delaying network

We consider sensor scheduling for state estimation of a scalar system over a packet-delaying network. The current measurement data can be sent over a delay-free channel if the sensor uses larger communication energy; the data will be delayed for one time step if the sensor uses less communication energy. We consider a cost function consisting of a weighted average estimation error and a weighted terminal estimation error and explicitly construct optimal power schedules to minimize this cost function subject to communication energy constraint. Simulations are provided to demonstrate the key ideas of the paper.     

Robust Kalman filtering for uncertain discrete-time systems with probabilistic parameters bounded within a polytope

We consider the problem of finite horizon discrete-time Kalman filtering for systems with parametric uncertainties. Specifically, we consider unknown but deterministic uncertainties where the uncertain parameters are assumed to lie in a convex polyhedron with uniform probability density. The condition and a procedure for the construction of a suboptimal filter that minimizes an expected error covariance over-bound are derived.     

均方根嵌入式容积卡尔曼滤波

传统容积卡尔曼滤波(CKF)的基础是三阶球面-径向容积准则,该准则不仅要求计算n维超球体上的面积分,还需将容积准则与扩展高斯-拉盖尔准则配合使用,不易推导出高阶CKF滤波算法.此外,CKF推导所采用的三阶球面容积准则也存在缺陷,这极大地限制了CKF的滤波精度.为避免以上问题,本文基于嵌入式容积准则和均方根滤波技术,提出一种加性噪声环境下,用于非线性动态系统状态估计的全新容积卡尔曼滤波算法-三阶均方根嵌入式容积卡尔曼滤波(SICKF).SICKF具有滤波精度高、数值稳定性强等诸多优点,适用于动态目标跟踪、非线性系统控制等.仿真结果表明,SICKF的滤波精度显著优于传统的非线性滤波算法.     

Stability of Kalman filtering with Markovian packet losses

We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. Based on the sojourn time of each visit to the failure or successful packet reception state, we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, as an estimate of filtering deterioration caused by packet losses, which describes the upper envelope of the sequence of error covariance matrices {P_t,t?1} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case, and obtain a sufficient and necessary condition for the scalar case. Finally, the relationship between two different types of stability notions is discussed.     

Modified Kalman filter for networked monitoring systems employing a send-on-delta method

In this paper, we consider a networked estimation problem in which sensor data are transmitted only if their values change more than the specified value. When this send-on-delta method is used, no sensor data transmission implies that the sensor value does not change more than the specified value from the previously transmitted sensor value. Using this implicit information, we propose a modified Kalman filter algorithm. The proposed filter reduces sensor data traffic with relatively small estimation performance degradation. Through experiments, we demonstrate the feasibility of the proposed filter algorithm.     

An adaptive robustizing approach to kalman filtering

The performance of a linear Kalman filter will degrade when the dynamic noise is not Gaussian. A robust Kalman filter based on the m-interval polynomial approximation (MIPA) method for unknown non-Gaussian noise is proposed. Two situations are considered: (a) the state is Gaussian and the observation noise is non-Gaussian; (b) the state is non-Gaussian and the observation noise is Gaussian. It is shown, as compared with other non-Gaussian filters, the MIPA Kalman filter is computationally feasible, unbiased, more efficient and robust. For the scalar model, Monte Carlo simulations are given to demonstrate the ideas involved.     

Kalman filtering with partial Markovian packet losses

We consider the Kalman filtering problem in a networked environment where there are partial or entire packet losses described by a two state Markovian process. Based on random packet arrivals of the sensor measurements and the Kalman filter updates with partial packet, the statistical properties of estimator error covariance matrix iteration and stability of the estimator are studied. It is shown that to guarantee the stability of the Kalman filter, the communication network is required to provide for each of the sensor measurements an associated throughput, which captures all the rates of the successive sensor measurements losses. We first investigate a general discrete-time linear system with the observation partitioned into two parts and give sufficient conditions of the stable estimator. Furthermore, we extend the results to a more general case where the observation is partitioned into n parts. The results are illustrated with some simple numerical examples.     

Minimum entropy control of nonlinear ARMA systems over a communication network

In this paper, the entropy concept has been utilized to characterize the uncertainty of the tracking error for nonlinear ARMA stochastic systems over a communication network, where time delays in the communication channels are of random nature. A recursive optimization solution has been developed. In addition, an alternative algorithm is also proposed based on the probability density function of the tracking error, which is estimated by a neural network. Finally, a simulation example is given to illustrate the efficiency and feasibility of the proposed approach.     

Probabilistic performance of state estimation across a lossy network

We consider a discrete time state estimation problem over a packet-based network. In each discrete time step, a measurement packet is sent across a lossy network to an estimator unit consisting of a modified Kalman filter. Using the designed estimator algorithm, the importance of placing a measurement buffer at the sensor that allows transmission of the current and several previous measurements is shown. Previous pioneering work on Kalman filtering with intermittent observation losses is concerned with the asymptotic behavior of the expected value of the error covariance, i.e. as k→∞. We consider a different performance metric, namely a probabilistic statement of the error covariance , meaning that with high probability the error covariance is bounded above at any instant in time. Provided the estimator error covariance has an upper bound whenever a measurement packet arrives, we show that for any finite M this statement will hold so long as the probability of receiving a measurement packet is nonzero. We also give an explicit relationship between M and and provide examples to illustrate the theory.     

A three-dimensional probabilistic fuzzy control system for network queue management

A novel probabilistic fuzzy control system is proposed to treat the congestion avoidance problem in transmission control protocol （TCP） networks. Studies on traffic measurement of TCP networks have shown that the packet traffic exhibits long range dependent properties called self-similarity, which degrades the network performance greatly. The probabilistic fuzzy control （PFC） system is used to handle the complex stochastic features of self-similar traffic and the modeling uncertainties in the network system. A three-dimensional （3-D） membership function （MF） is embedded in the PFC to express and describe the stochastic feature of network traffic. The 3-D MF has extended the traditional fuzzy planar mapping and further provides a spatial mapping among ＂fuzziness-randomness-state＂. The additional stochastic expression of 3-D MF provides the PFC an additional freedom to handle the stochastic features of self-similar traffic. Simulation experiments show that the proposed control method achieves superior performance compared to traditional control schemes in a stochastic environment.     

Sensor data scheduling for optimal state estimation with communication energy constraint

In this paper, we consider sensor data scheduling with communication energy constraint. A sensor has to decide whether to send its data to a remote estimator or not due to the limited available communication energy. We construct effective sensor data scheduling schemes that minimize the estimation error and satisfy the energy constraint. Two scenarios are studied: the sensor has sufficient computation capability and the sensor has limited computation capability. For the first scenario, we are able to construct the optimal scheduling scheme. For the second scenario, we are able to provide lower and upper bounds of the minimum error and construct a scheduling scheme whose estimation error falls within the bounds.     

一种基于卡尔曼滤波和模糊控制的RBF神经网络新型学习算法

提出了基于Kalman滤波最优估计和模糊控制的径向基函数（Radical Basis Function, RBF）神经网络学习算法,用实例进行了仿真实验。结果表明,与传统的RBF网络学习算法比较,该算法具有明显快速的学习效率和较高的识别精度.     

A convex optimization approach to filtering in jump linear systems with state dependent transitions

We introduce a new methodology to construct a Gaussian mixture approximation to the true filter density in hybrid Markovian switching systems. We relax the assumption that the mode transition process is a Markov chain and allow it to depend on the actual and unobservable state of the system. The main feature of the method is that the Gaussian densities used in the approximation are selected as the solution of a convex programming problem which trades off sparsity of the solution with goodness of fit. A meaningful example shows that the proposed method can outperform the widely used interacting multiple model (IMM) filter and GPB2 in terms of accuracy at the expenses of an increase in computational time.     

The problem of optimal robust Kalman state estimation via limited capacity digital communication channels

This paper considers a state estimation problem for a continuous-time uncertain system via a digital communication channel with bit-rate constraints. The estimated state must be quantized, coded and transmitted via a limited capacity digital communication channel. Optimal and suboptimal recursive coder–decoder state estimation schemes are proposed and investigated.     

A new watermarking approach based on probabilistic neural network in wavelet domain

A novel scheme of digital image watermarking based on the combination of dual-tree wavelet transform (DTCWT) and probabilistic neural network is proposed in this paper. Firstly, the original image is decomposed by DTCWT, and then the watermark bits are added to the selected coefficients blocks. Because of the learning and adaptive capabilities of neural networks, the trained neural networks can recover the watermark from the watermarked images. Experimental results show that the proposed scheme has good performance against several attacks.     

A note on estimation algebras on nonlinear filtering theory

The idea of using estimation algebras to construct finite dimensional nonlinear filters was first proposed by Brockett and Mitter independently. It turns out that the concept of estimation algebra plays a crucial role in the investigation of finite dimensional nonlinear filters. In his talk at the International Congress of Mathematicians in 1983, Brockett proposed to classify all finite dimensional estimation algebras. In this paper we consider some filtering systems. In a special filtering system: (1) We have some structure results. (2) For any arbitrary finite dimensional state space, under the condition that the drift term is a linear vector field plus a gradient vector field, we classify all finite dimensional estimation algebras with maximal rank. (3) We classify all finite dimensional estimation algebras with maximal rank if the dimension of the state space is less than or equal to three. A more general filtering system is considered. The above three results can be ‘used’ locally. Therefore from the algebraic point of view, we have now understood generically some finite dimensional filters.     

Kalman filter-based identification for systems with randomly missing measurements in a network environment

We consider the problem of parameter estimation and output estimation for systems in a transmission control protocol (TCP) based network environment. As a result of networked-induced time delays and packet loss, the input and output data are inevitably subject to randomly missing data. Based on the available incomplete data, we first model the input and output missing data as two separate Bernoulli processes characterised by probabilities of missing data, then a missing output estimator is designed, and finally we develop a recursive algorithm for parameter estimation by modifying the Kalman filter-based algorithm. Under the stochastic framework, convergence properties of both the parameter estimation and output estimation are established. Simulation results illustrate the effectiveness of the proposed algorithms.     

Optimal control of LTI systems over unreliable communication links

In this paper, optimal control of linear time-invariant (LTI) systems over unreliable communication links is studied. The motivation of the problem comes from growing applications that demand remote control of objects over Internet-type or wireless networks where links are prone to failure. Depending on the availability of acknowledgment (ACK) signals, two different types of networking protocols are considered. Under a TCP structure, existence of ACK signals is assumed, unlike the UDP structure where no ACK packets are present. The objective here is to mean-square (m.s.) stabilize the system while minimizing a quadratic performance criterion when the information flow between the controller and the plant is disrupted due to link failures, or packet losses. Sufficient conditions for the existence of stabilizing optimal controllers are derived.