Optimal Filtering Over Uncertain Wireless Communication Channels

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.

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

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.

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.

A state estimation technique is developed for sensing inclination angles using relatively low cost sensors. A low bandwidth tilt sensor is used along with an inaccurate rate gyro to obtain the measurement. The rate gyro has an inherent bias along with sensor noise. The tilt sensor uses an internal pendulum and therefore has its own slow dynamics. These sensor dynamics were identified experimentally and combined to achieve high bandwidth measurements using an optimal linear state estimator. Potential uses of the measurement technique range from robotics, to rehabilitation, to vehicle control.

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.

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

Maneuver Detection and Reconstruction of Stationkeeping Spacecraft at GEO using the Optimal Control-Based Estimator

We consider the problem of estimating vector-valued variables from noisy “relative” measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. This type of measurement model appears in several sensor network problems, such as sensor localization and time synchronization. We consider the optimal estimate for the unknown variables obtained by applying the classical Best Linear Unbiased Estimator, which achieves the minimum variance among all linear unbiased estimators. We propose a new algorithm to compute the optimal estimate in an iterative manner, the Overlapping Subgraph Estimator algorithm. The algorithm is distributed, asynchronous, robust to temporary communication failures, and is guaranteed to converges to the optimal estimate even with temporary communication failures. Simulations for a realistic example show that the algorithm can reduce energy consumption by a factor of two compared to previous algorithms, while achieving the same accuracy.

State estimation is often a challenging task in distribution systems due to deploying a limited number of measurement devices. Moreover, the integration of precise distribution-level phasor measurement unites, a.k.a micro-PMUs, along with inaccurate pseudo-measurements in state estimation introduces another challenge. These issues might decrease the efficiency of traditional standard weighted least squares (WLS) for distribution system state estimation. This paper proposes a novel linear distribution system state estimation based on limited number of synchrophasor measurements and pseudo-measurements. To involve pseudo-measurements into the linear state estimation, Taylor's approximation is adopted to reformulate pseudo-measurement functions in a linear form. The results obtained via numerical simulations demonstrate that the proposed linear state estimation method performs as good as the standard nonlinear WLS estimator. Moreover, the sensitivity analyses results show that our method has a better performance compared to WLS once a limited number of highly precise micro-PMUs are accompanied with inaccurate pseudo-measurements in state estimation.

In this paper, the problem of convergence for the optimal linear estimator of discrete-time linear systems with multiplicative and time-correlated additive measurement noises is studied. By defining a new random vector that consists of the innovation, error, and part of the noise in the new measurement obtained from the measurement differencing method, we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose. It is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and, moreover, this fixed point can be obtained by solving a set of matrix equations.

This paper introduces a family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of the carrier phase and frequency offset of general quadrature amplitude modulated (QAM) transmissions. As an extension of the Viterbi and Viterbi (1983) estimator, a constellation-dependent optimal matched nonlinear estimator is derived such that its asymptotic (large sample) variance is minimized. A class of conventional monomial estimators is also proposed. The asymptotic performance of these estimators is established in closed-form expression and compared with the Cramer-Rao lower bound. A practical implementation of the optimal matched estimator, which is a computationally efficient approximation of the latter and exhibits negligible performance loss, is also derived. Finally, computer simulations are presented to corroborate the theoretical performance analysis and indicate that the proposed optimal matched nonlinear estimator improves significantly the performance of the classic fourth-power estimator.

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

The paper presents a model of a class of wireless network systems with delay and data dropout. The optimal state estimator is designed for the system by using time-varying Kalman filter on the basis of the presented model. Then, a design approach to feedback control of optimal state is presented. And the separation principle of state feedback controller and state observer is guaranteed by carrying the additional information in data packet. Finally, the stability of closed-loop NCSs is proven by applying MJLS theory.

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally, numerical examples are given to verify the proposed results.