scholarly journals Distributed Robust Kalman Filtering with Unknown and Noisy Parameters in Sensor Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Donghua Chen ◽  
Ya Zhang ◽  
Cheng-Lin Liu ◽  
Yangyang Chen
Keyword(s):  
Kalman Filter ◽  
Sensor Networks ◽  
Kalman Filtering ◽  
Estimation Error ◽  
Measuring System ◽  
Mean Square ◽  
System Matrix ◽  
Estimation Errors ◽  
System Parameters ◽  
The Mean

This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor’s measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results.

Transmission rate conditions for distributed filtering in sensor networks against eavesdropper

2021 ◽  
pp. 014233122110056
Author(s):  
Bingya Zhao ◽  
Ya Zhang
Keyword(s):  
Sensor Networks ◽  
Topological Entropy ◽  
Kalman Filtering ◽  
Transmission Rate ◽  
Necessary Condition ◽  
Estimation Errors ◽  
Positive Role ◽  
Filtering Algorithm ◽  
Wiretap Channels ◽  
Kalman Filtering Algorithm

This paper studies the distributed secure estimation problem of sensor networks (SNs) in the presence of eavesdroppers. In an SN, sensors communicate with each other through digital communication channels, and the eavesdropper overhears the messages transmitted by the sensors over fading wiretap channels. The increasing transmission rate plays a positive role in the detectability of the network while playing a negative role in the secrecy. Two types of SNs under two cooperative filtering algorithms are considered. For networks with collectively observable nodes and the Kalman filtering algorithm, by studying the topological entropy of sensing measurements, a sufficient condition of distributed detectability and secrecy, under which there exists a code–decode strategy such that the sensors’ estimation errors are bounded while the eavesdropper’s error grows unbounded, is given. For collectively observable SNs under the consensus Kalman filtering algorithm, by studying the topological entropy of the sensors’ covariance matrices, a necessary condition of distributed detectability and secrecy is provided. A simulation example is given to illustrate the results.

A Rapid Computation Method for Kalman Filtering in Vehicular SINS/GPS Integrated System

2012 ◽  
Vol 182-183 ◽  
pp. 541-545 ◽  
Author(s):  
Qi Ju Zhu ◽  
Gong Min Yan ◽  
Peng Xiang Yang ◽  
Yong Yuan Qin
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Kalman Filtering ◽  
Integrated System ◽  
Computation Method ◽  
System Matrix ◽  
Computational Burden ◽  
Reduced Dimensions ◽  
Classic Method

A new rapid computation method for Kalman filtering is proposed. In this method, the prediction of state covariance matrix is expanded directly rather than computing by a looping program. Sequential filtering for measurement update is also applied. Furthermore, the subsidiary elements in system matrix are set to zero and a reduced-dimensions sub-optimal Kalman filter is presented. The proposed method greatly decreases computational burden and it is only 6.59% of the classic method. In the end, a vehicular test is carried out to prove the feasibility of the filtering.

scholarly journals Ground Reaction Force Estimation in Prosthetic Legs With Nonlinear Kalman Filtering Methods

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Seyed Fakoorian ◽  
Vahid Azimi ◽  
Mahmoud Moosavi ◽  
Hanz Richter ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Reaction Force ◽  
Force Estimation ◽  
Joint Angles ◽  
Estimation Errors ◽  
Reaction Forces

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.

Application of the Mean-Variance Theory and Resampling Technique for the Italian Energy Portfolio Settlement

2013 ◽  
Vol 869-870 ◽  
pp. 581-592
Author(s):  
Mauro Arnesano ◽  
Antonio Paolo Carlucci ◽  
Giovanni D'Oria ◽  
Alessio Guadalupi ◽  
Domenico Laforgia
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Estimation Error ◽  
Efficient Frontier ◽  
Energy Generation ◽  
Energy System ◽  
Estimation Errors ◽  
Energy Mix ◽  
The Mean ◽  
Mean Variance

The energy planning based on Mean - Variance theory, guides the investors in investment decisions, trying to maximize the return and minimize the risk of investment. However, this theory is based on strong hypotheses and, in addition, input data are often affected by estimation errors. Moreover, this theory determines poor diversification increasing return and risk of the portfolio, and strong variability of the outputs when inputs are varied.In the first part of the paper, the Mean - Variance theory was applied to the energy generation in Italy; in particular, the analysis was on the actual energy mix, but also assuming the use of nuclear technology and taking into account verisimilar improvement, of technologies in the future.On the other hand, in the second part of the paper, a methodology has been applied in order to limit the problems of Mean-Variance theory applied to the energy mix settlement. In particular, the input variables have been calculated using Monte Carlo simulation, in order to reduce the estimation error, and the Resampled EfficiencyTMtechnique has been applied in order to calculate the resulting new “average” efficient frontier. This methodology has been applied either not limiting or limiting the minimum and maximum percentage for every energy generation technology, in order to simulate constraints due, for example, to the technological characteristics of the plant, the availability of the sources and eventually to norms, to the territorial characteristics and to the socio-political choices. The application of Mean - Variance theory allowed to obtain energy portfolio, alternative to the actual, characterized by higher values of expected returns an lower values of risk.It was also shown that the application of the Resampled EfficiencyTMtechnique with data originated with the Monte Carlo simulation effectively tackles the problems of Mean - Variance theory; in this way, the decision maker is helped in making decisions in the energy system policy and development.Thanks to this approach, applied in particular to the Italian energy contest, it was also possible to evaluate the effectiveness of the introduced modifications to the Italian actual energy mix to achieve the 2020 European Energy Directive targets in particular concerning the reduction of CO2levels.

scholarly journals Diffusion Strategies for Distributed Kalman Filter with Dynamic Topologies in Virtualized Sensor Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shujie Yang ◽  
Tao Huang ◽  
Jianfeng Guan ◽  
Yongping Xiong ◽  
Mu Wang
Keyword(s):  
Wireless Sensor Networks ◽  
Kalman Filter ◽  
Sensor Networks ◽  
Network Virtualization ◽  
Physical Layer ◽  
Wireless Sensor ◽  
Kalman Filter Algorithm ◽  
The Mean ◽  
Improved Performance ◽  
Filter Algorithms

Network virtualization has become pervasive and is used in many applications. Through the combination of network virtualization and wireless sensor networks, it can greatly improve the multiple applications of traditional wireless sensor networks. However, because of the dynamic reconfiguration of topologies in the physical layer of virtualized sensor networks (VSNs), it requires a mechanism to guarantee the accuracy of estimate values by sensors. In this paper, we focus on the distributed Kalman filter algorithm with dynamic topologies to support this requirement. As one strategy of distributed Kalman filter algorithms, diffusion Kalman filter algorithm has a better performance on the state estimation. However, the existing diffusion Kalman filter algorithms all focus on the fixed topologies. Considering the dynamic topologies in the physical layer of VSNs mentioned above, we present a diffusion Kalman filter algorithm with dynamic topologies (DKFdt). Then, we emphatically derive the theoretical expressions of the mean and mean-square performance. From the expressions, the feasibility of the algorithm is verified. Finally, simulations confirm that the proposed algorithm achieves a greatly improved performance as compared with a noncooperative manner.

Random Response Relationships to Transfer Function and State-Space Properties

2007 ◽  
Vol 129 (5) ◽  
pp. 672-677
Author(s):  
Robin C. Redfield
Keyword(s):  
Transfer Function ◽  
State Space ◽  
Dynamic Systems ◽  
System Response ◽  
Mean Square ◽  
System Matrix ◽  
Matrix Transfer Function ◽  
Mean Square Response ◽  
The Mean ◽  
Insight Into

Output variables of dynamic systems subject to random inputs are often quantified by mean-square calculations. Computationally for linear systems, these typically involve integration of the output spectral density over frequency. Numerically, this is a straightforward task and, analytically, methods exist to find mean-square values as functions of transfer function (frequency response) coefficients. These formulations offer analytical relationships between system parameters and mean-square response. This paper develops further analytical relationships in calculating mean-square values as functions of transfer function and state-space properties. Specifically, mean-square response is formulated from (i) system pole-zero locations, (ii) as a spectral decomposition, and (iii) in terms of a system matrix transfer function. Direct, closed-form relationships between response and these properties are afforded. These new analytical representations of the mean-square calculation can provide significant insight into dynamic system response and optimal design/tuning of dynamic systems.

Application of Interval Kalman Filtering Algorithm in Integrated Navigation Data Fusion

2012 ◽  
Vol 433-440 ◽  
pp. 4059-4064
Author(s):  
Yun Feng Ma
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Interval Matrix ◽  
Uncertain Parameters ◽  
Integrated Navigation ◽  
System Matrix ◽  
Inversion Algorithm ◽  
Filtering Algorithm ◽  
Kalman Filtering Algorithm ◽  
Time Accuracy

The traditional Kalman filter cannot be used directly when some system parameters such as certain elements of the system matrix are not precisely known or gradually change with time. Some uncertain parameters can be described as an interval model. An interval Kalman filtering algorithm is studied in this paper, which can be used to process a system with uncertain parameters. A simple inversion algorithm of interval matrix has been applied and its statistic performances and iterative form are similar to those of traditional Kalman filter. Simulation results show that such filtering algorithm can provide the real time accuracy error estimation and can be applied to such kind of low-cost integrated navigation system.

Incorporation of Neural Network State Estimator for GPS Attitude Determination

2004 ◽  
Vol 57 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Dah-Jing Jwo ◽  
Chun-Fan Pai
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Least Squares ◽  
Kalman Filtering ◽  
Attitude Determination ◽  
Least Squares Method ◽  
State Estimator ◽  
Estimation Errors ◽  
Network State ◽  
The Neural Network

The Global Positioning System (GPS) can be employed as a free attitude determination interferometer when carrier phase measurements are utilized. Conventional approaches for the baseline vectors are essentially based on the least-squares or Kalman filtering methods. The raw attitude solutions are inherently noisy if the solutions of baseline vectors are obtained based on the least-squares method. The Kalman filter attempts to minimize the error variance of the estimation errors and will provide the optimal result while it is required that the complete a priori knowledge of both the process noise and measurement noise covariance matrices are available. In this article, a neural network state estimator, which replaces the Kalman filter, will be incorporated into the attitude determination mechanism for estimating the attitude angles from the noisy raw attitude solutions. Employing the neural network estimator improves robustness compared to the Kalman filtering method when uncertainty in noise statistical knowledge exists. Simulation is conducted and a comparative evaluation based on the neural network estimator and Kalman filter is provided.

scholarly journals Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory

Sensors ◽  
2019 ◽  
Vol 19 (1) ◽  
pp. 149 ◽  
Author(s):  
Pablo Bernal-Polo ◽  
Humberto Martínez-Barberá
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Attitude Estimation ◽  
Performance Metric ◽  
Unit Quaternions ◽  
The Mean ◽  
Correction Step ◽  
Manifold Theory ◽  
Multiplicative Update ◽  
Natural Way

The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric.

An Application of the Kalman Filter in a Laser Tracking Measurement System

2005 ◽  
Vol 295-296 ◽  
pp. 245-252
Author(s):  
X.R. Chen ◽  
P. Cai ◽  
Wen Ku Shi
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Measurement System ◽  
Tracking System ◽  
Measuring System ◽  
Filter Method ◽  
Laser Tracking ◽  
Filtering Algorithm ◽  
Kalman Filtering Algorithm ◽  
Tracking Measurement

Flexible coordinate measuring system based on laser tracking measurement system (LTS) is an effective method to detect 3D coordinates of moving target. However, the system suffers from various interferences resulting in low accuracy. This paper extends the application of a Kalman filtering algorithm in LTS to solve the problem. The laser tracking system is introduced. The state model of the laser tracking measurement system is developed and the linearization method of the model is analyzed. A Kalman filtering algorithm is used for the system. The result of the simulation shows that the proposed Kalman filter method works well for the improvement of accuracy of LTS.

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