Abstract

A Kalman filter is commonly used for state estimation. It is optimal in that the variance of the error is minimized by the estimator. In this paper the problem of optimal sensor location is combined with estimator design to obtain a sensor placement that minimizes the error variance. The question of whether of a larger number of inaccurate sensors, that is those with large noise variance, can provide as good an estimate as a single highly accurate (but probably more expensive) sensor. This question can be investigated with the assumption that all the selected sensors are placed optimally. Estimation of the state of a one-dimensional diffusion equation with three different disturbances is examined in this context. Despite the difference among disturbances, similar proportional relations between the sensor noise variance and the estimation error are observed in numerical simulations. Furthermore, it appears that multiple low quality sensors can lead to better estimation than a single high quality sensor, provided that enough sensors are used.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.