Robust H-infinity filtering for time-delaysystems with missing measurements:a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

Estimation of spatially distributed processes using mobile sensor networks with missing measurements

This paper investigates the estimation problem for a spatially distributed process described by a partial differential equation with missing measurements.The randomly missing measurements are introduced in order to better reflect the reality in the sensor network.To improve the estimation performance for the spatially distributed process,a network of sensors which are allowed to move within the spatial domain is used.We aim to design an estimator which is used to approximate the distributed process and the mobile trajectories for sensors such that,for all possible missing measurements,the estimation error system is globally asymptotically stable in the mean square sense.By constructing Lyapunov functionals and using inequality analysis,the guidance scheme of every sensor and the convergence of the estimation error system are obtained.Finally,a numerical example is given to verify the effectiveness of the proposed estimator utilizing the proposed guidance scheme for sensors.

Modified robust finite-horizon filter for discrete-time systems with parameter uncertainties and missing measurements

A robust finite-horizon Kalman filter is designed for linear discrete-time systems subject to norm-bounded uncertainties in the modeling parameters and missing measurements.The missing measurements were described by a binary switching sequence satisfying a conditional probability distribution,the commonest cases in engineering,such that the expectation of the measurements could be utilized during the iteration process.To consider the uncertainties in the system model,an upperbound for the estimation error covariance was obtained since its real value was unaccessible.Our filter scheme is on the basis of minimizing the obtained upper bound where we refer to the deduction of a classic Kalman filter thus calculation of the derivatives are avoided.Simulations are presented to illustrate the effectiveness of the proposed approach.

Resilient Smart Power Grid Synchronization Estimation Method for System Resilience with Partial Missing Measurements

With the increasing demand for power system stability and resilience,effective real-time tracking plays a crucial role in smart grid synchronization.However,most studies have focused on measurement noise,while they seldom think about the problem of measurement data loss in smart power grid synchronization.To solve this problem,a resilient fault-tolerant extended Kalman filter(RFTEKF)is proposed to track voltage amplitude,voltage phase angle and frequency dynamically.First,a threephase unbalanced network’s positive sequence fast estimation model is established.Then,the loss phenomenon of measurements occurs randomly,and the randomness of data loss’s randomness is defined by discrete interval distribution[0,1].Subsequently,a resilient fault-tolerant extended Kalman filter based on the real-time estimation framework is designed using the timestamp technique to acquire partial data loss information.Finally,extensive simulation results manifest the proposed RFTEKF can synchronize the smart grid more effectively than the traditional extended Kalman filter(EKF).

Optimal filtering for uncertain systems with stochastic nonlinearities, correlated noises and missing measurements

The globally optimal recursive filtering problem is studied for a class of systems with random parameter matrices,stochastic nonlinearities, correlated noises and missing measurements. The stochastic nonlinearities are presented in the system model to reflect multiplicative random disturbances, and the additive noises, process noise and measurement noise, are assumed to be one-step autocorrelated as well as two-step cross-correlated.A series of random variables is introduced as the missing rates governing the intermittent measurement losses caused by unfavorable network conditions. The aim of the addressed filtering problem is to design an optimal recursive filter for the uncertain systems based on an innovation approach such that the filtering error is globally minimized at each sampling time. A numerical simulation example is provided to illustrate the effectiveness and applicability of the proposed algorithm.

Dark Energy from Kaluza-Klein Spacetime and Noether’s Theorem via Lagrangian Multiplier Method

The supposedly missing dark energy of the cosmos is found quantitatively in a direct analysis without involving ordinary energy. The analysis relies on five dimensional Kaluza-Klein spacetime and a Lagrangian constrained by an auxiliary condition. Employing the Lagrangian multiplier method, it is found that this multiplier is equal to the dark energy of the cosmos and is given by where E is energy, m is mass, c is the speed of light, and λ is the Lagrangian multiplier. The result is in full agreement with cosmic measurements which were awarded the 2011 Nobel Prize in Physics as well as with the interpretation that dark energy is the energy of the quantum wave while ordinary energy is the energy of the quantum particle. Consequently dark energy could not be found directly using our current measurement methods because measurement leads to wave collapse leaving only the quantum particle and its ordinary energy intact.

Recursive Filter with Partial Knowledge on Inputs and Outputs

This paper investigates the problem of state estimation for discrete-time stochastic linear systems, where additional knowledge on the unknown inputs is available at an aggregate level and the knowledge on the missing measurements can be described by a known stochastic distribution. Firstly, the available knowledge on the unknown inputs and the state equation is used to form the prior distribution of the state vector at each time step. Secondly, to obtain an analytically tractable likelihood function, the effect of missing measurements is broken down into a systematic part and a random part, and the latter is modeled as part of the observation noise. Then, a recursive filter is obtained based on Bayesian inference. Finally, a numerical example is provided to evaluate the performance of the proposed methods.