Recursive Sensor Allocation For A Class Of Distributed Parameter Systems (original) (raw)

Optimization of measurements for state estimation in parabolic distributed systems

Kybernetika, 1984

The aim of this paper is to consider the optimal, from the viewpoint of a state estimation accuracy, measurement location problem in linear distributed-parameter systems with white Gaussian noises. In contrary to earlier works the proposed approach consists of two steps. Namely, to find closed form solution for the optimal measurement weighting function (MWF), assuming measurements continuous in space, and then to approximate this solution using point sensors. At the first step it was also shown that the Green function of the system can be used as a suboptimal MWF. State estimation in one-dimensional heat transfer problem illustrates the results.

Optimal sensor allocation for parameter estimation in distributed systems

jiip, 2001

Some fundamental results of the modern theory of optimum experimental design are extended here to address the problem of determining the optimal measurement scheduling, encountered while estimating unknown parameters in mathematical models described by partial differential equations from observations of the underlying physical phenomenon being modelled. Special emphasis is put on measurements realized by optimal motion of spatially-movable sensors for which we generalize the approach advanced by Rafaj lowicz in his seminal paper [16] to the case of minimizing a general performance index defined on the Fisher information matrix related to the parameters to be identified. Since only the measurability of the resulting trajectories can be guaranteed, we also show how to ease this inconvenience by introducing a suitable parametrization of the set of admissible solutions. In the latter case, we also detail how to adapt standard sequential numerical algorithms of optimum experimental design so that they could be employed for computation of trajectories in particular situations.

Optimum choice of moving sensor trajectories for distributed-parameter system identification

International Journal of Control, 1986

The problem is considered of the optimal choice of moving sensor trajectories from the viewpoint of distributed-parameter system identification accuracy. The determinant of the information matrix of parameter estimates is taken as a measure of identification accuracy. Necessary and sufficient conditions for the trajectories to be optimal are derived. It is shown that the optimum trajectories can be found by solving a sequence of optimal sensor allocation problems. A number of examples illustrated the proposed approach.

Optimal sensor location problem for a linear distributed parameter system

IEEE Transactions on Automatic Control, 1978

ing a solution of the optimal filtering error covariance function for the pointwise observation case is considered. 'Ihen by using the existence and equations of R i d type is proved. By osing the ttteoremsl obtained here, the existence theorem concerning a sdution of the optimal sensor location problem is proved and the oecessary and sufficient conditions for optimality are derived. Finally, some numerical examples for the optimal sensor location problem are Wdmted. uniqueness theorem, the I x q m i m l theorem for the partial differential

The Hypothesizing Distributed Kalman Filter

2012 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI), 2012

This paper deals with distributed information processing in sensor networks. We propose the Hypothesizing Distributed Kalman Filter that incorporates an assumption of the global measurement model into the distributed estimation process. The procedure is based on the Distributed Kalman Filter and inherits its optimality when the assumption about the global measurement uncertainty is met. Recursive formulas for local processing as well as for fusion are derived. We show that the proposed algorithm yields the same results, no matter whether the measurements are processed locally or globally, even when the process noise is not negligible. For further processing of the estimates, a consistent bound for the error covariance matrix is derived. All derivations and explanations are illustrated by means of a new classification scheme for estimation processes.

On robust design of sensor trajectories for parameter estimation of distributed systems

IFAC Proceedings Volumes, 1999

This paper deals with the optimal parameter estimation of a distributed-parameter process, for which the observation subject to additive noise is realized by poinrwise sensors which are allowed to move in the spatial domain and are driven by some control inputs. The global design criterion is the expectation of a general local design criterion defined on the Fisher information matrix, given a priori distribution of the parameters to be identified. A stochastic-gradient algorithm is used for its Inaximization, which makes it possible to reduce significantly the required computational burden. A technique to tackle minimax-optinlality criteria is also indicated.

Linear Estimation for Distributed Parameter Systems with Uncertain Observations

IFAC Proceedings Volumes, 1997

This paper considers the least mean squared error linear estimation problem in distributed parameter systems with uncertain observations. The recursive equations for the optimal linear estimator are obtained using a orthogonal projection approach. The resolution of the infinite-dimensional algorithm is also presented here. For this, the expansion of the estimators into eigenfunction series is considered and an algorithm for the coefficients of the series is derived.

Distributed and Recursive Parameter Estimation

Sensor Networks, 2009

Parametric estimation is a canonical problem in sensor networks. The intrinsic nature of sensor networks requires regression algorithms based on sensor data to be distributed and recursive. Such algorithms are studied in this chapter for the problem of (conditional) least squares regression when the data collected across sensors is homogeneous, i.e., each sensor observes samples of the dependent and independent variable in the regression problem. The chapter is divided into three parts. In the first part, distributed and recursive estimation algorithms are developed for the nonlinear regression problem. In the second part, a distributed and recursive algorithm is designed to estimate the unknown parameter in a parametrized state-space random process. In the third part, the problem of identifying the source of a diffusion field is discussed as a representative application for the algorithms developed in the first two parts.