Bandwidth tilt measurement using low cost sensors

State estimators for systems with random parameter matrices, stochastic nonlinearities, fading measurements and correlated noises

In this letter, filtering over wireless communication channels subject to packet losses is considered. The packet losses are assumed to follow a Bernoulli distribution. The latter is interpreted as a special case of a Markov process for which hybrid filtering theory is shown to provide an exact solution. Unlike existing works where only the linear optimal state estimate is derived as a linear function of measurements, this paper shows that the optimal state estimate is in fact a nonlinear function of measurements. In addition, the optimal estimator is derived explicitly. Illustrative examples compare the performance of the linear optimal estimator and the optimal estimator, and show that the latter offer superior performance, in particular for unstable systems.

Chapter 12 - Application of mechanistic model-based nonlinear filtering and observation techniques for optimal state estimation of a catalytic tubular reactor with optimal sensor configuration

Efficient and accurate state estimation is essential for the optimal management of the future smart grid. However, to meet the requirements of deploying the future grid at a large scale, the state estimation algorithm must be able to accomplish two major tasks: 1) combining measurement data with different qualities to attain an optimal state estimate and 2) dealing with the large number of measurement data rendered by meter devices. To address these two tasks, we first propose a practical solution using a very short word length to represent a partial measurement of the system state in the meter device to reduce the amount of data. We then develop a unified probabilistic framework based on a Bayesian belief inference to incorporate measurements of different qualities to obtain an optimal state estimate. Simulation results demonstrate that the proposed scheme significantly outperforms other linear estimators in different test scenarios. These findings indicate that the proposed scheme not only has the ability to integrate data with different qualities but can also decrease the amount of data that needs to be transmitted and processed.

This letter is concerned with the problem of optimal linear exponential quadratic state estimation for discrete-time Gauss–Markov systems with intermittent observations. The optimal estimator and optimal cost are derived via an information state approach. The necessary and sufficient condition for the existence of the estimator is provided. For a special case when a scalar parameter in the exponential cost goes to zero, the derived estimator reduces to the corresponding Kalman filter. It is also interesting to note that the resulting estimator has the same form as that obtained from the $H_{\infty }$ setting.

Objective: State estimation is used as a necessary tool for online monitoring, analysis and control of power systems. The main objective of this paper is to deal with static state estimation using the snap shot data and dynamic state estimation which accounts for the time varying behaviour of power system states in to consideration. Methods/Analysis: Effects of inclusion of PMU measurements along with the available metered data have been explored using the weighted least square state estimation technique in this paper. A comparative analysis of static state estimation with and without bad data has been carried out and the bad data has been identified and eliminated by using largest normalized residue test. Findings: To investigate the time varying nature of the system states linear state estimator with second order approximation and kalman filter techniques has been proposed in this paper. Case studies are conducted on IEEE 14 bus test system and the test results obtained from non linear, linear first order, second order and kalman filter techniques have been compared. Application/Improvements: Correction of state variables are obtained using linear state estimation with first order and second order approximation and kalman filter techniques has been compared to get the better state estimation algorithm.

This chapter addresses the problem of time-varying nonlinear modeling and monitoring of a continuously stirred tank reactor (CSTR) process using state estimation techniques. These techniques include the extended Kalman filter (EKF), particle filter (PF), and the more recently the variational Bayesian filter (VBF). The objectives of this chapter are threefold. The first objective is to use the variational Bayesian filter with better proposal distribution for nonlinear states and parameters estimation. The second objective is to extend the state and parameter estimation techniques to better handle nonlinear and non-Gaussian processes without a priori state information, by utilizing a time-varying assumption of statistical parameters. The third objective is to apply the state estimation techniques EKF, PF and VBF for time-varying nonlinear modeling and monitoring of CSTR process. The estimation performance is evaluated on a synthetic example in terms of estimation accuracy, root mean square error and execution times.

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programing. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an enforced separation solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

An adaptive approach is presented for optimal estimation of a sampled stochastic process with finite-state unknown parameters. It is shown that for processes with an implicit generalized Markov property that the optimal (conditional mean) state estimates can be formed from (i) a set of optimal estimates based on known parameters, and (ii) a set of "learning" statistics which are recursively updated. The formulation thus provides a separation technique which simplifies the optimal solution of this class of nonlinear estimation problems. Examples of the separation technique are given for prediction of a non-Gaussian Markov process with unknown parameters and for filtering the state of a Gauss-Markov process with unknown parameters. General results are given on the convergence of optimal estimation systems operating in the presence of unknown parameters. Conditions are given under which a Bayes optimal (conditional mean) adaptive estimation system will converge in performance to an optimal system which is "told" the value of unknown parameters.

Optimal estimation of linear discrete-time systems with stochastic parameters

Optimal static state estimation using improved particle swarm optimization and gravitational search algorithm

—Fast and accurate state estimation has a crucial role in practical implementation of state feedback-based controllers. But most of the states are not accessible or economically feasible to measure and must be estimated. Although such controllers are normally designed offline, their dynamic performance is evaluated online. Hence, having high speed with acceptable accuracy is an essential feature for estimators. In this article, a state estimator based on an artificial neural network incorporated into a linear optimal regulator is introduced. First, an extended Kalman filter is designed, then an estimator based on a proposed feed-forward neural network structure is elaborated after much effort on promising neural network structures. Different neural networks are trained using the data collected from the extended Kalman filter, and a qualified and shapeable alternative for the extended Kalman filter in reducing its drawbacks is obtained. The optimum structure is identified when minimum state estimation error is achieved. Significant speed and sufficient accuracy are the main advantages of the proposed structure to be used online for state estimation. Dynamic performance of the system equipped with the linear optimal regulator plus different estimators is examined and compared to a single-machine/infinite-bus power system in MATLAB (The MathWorks, Natick, Massachusetts, USA).

The main purpose of this paper is the development of a constrained optimal boundary state estimation framework for the dissipative systems with boundary control and boundary observation operator. These dissipative systems will be described by an extended system which involves no unbounded operator except for the system's dynamics generator through the change of variables and Yosida approximation. Then, the constrained optimal state estimation problem is posed for the resulting extended system and the original system as well. Finally, an important and practically significant realization of constraints embedded in the structure of the optimal filter is realized. In addition, the explanation is provided as to how constraints fit in the optimal filter structure.

A Comparison of Multiple Imputation and Optimal Estimation for Missing and Uncertain Urban Air Toxics Data

Closed-form H-infinity optimal control for a class of infinite-dimensional systems