21 August 1996 Information gained by pseudoredundant measurements
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Proceedings Volume 2784, Vision Systems: Sensors, Sensor Systems, and Components; (1996) https://doi.org/10.1117/12.248529
Event: Lasers, Optics, and Vision for Productivity in Manufacturing I, 1996, Besancon, France
Abstract
In order to extend the information contained in some nonlinearly mapped measurements we create additional measurements our of the really measured data by using the laws of physics. These auxiliary measurements provide extra information and thus lead to more exact estimates. Dealing with the state space model the information contained in the measurements can be measured by Fisher's information matrix, which can be obtained from the Cramer-Rao-inequality. The distribution function of the measurement noise is assumed to be gaussian and the observation model is given by y(k) equals h[y(k),k)] + v(k). We will show that additional measurements Ya(k) can provide additional information when they are nonlinear combinations of the really measured variables. In this case their distribution functions do not remain gaussian and they require an approximation, because any Kalman filter only deals with second order moments. This approximation can be achieved by means of minimum discrimination information. Thus we have created an extended measurement vector which consists of the really measured data and additional pseudoredundant data. We will then show that this extended measurement vector does contain extra information and therefore can be used to get more exact state estimates. The improvement will be shown in an application of an extended linearized Kalman filter to amplitude and phase modulation, where the measurements of the real and imaginary part of the signal are extended by a pseudoredundant phase measurement obtained from the available measurements by a tan-1 operation.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Christoph Arndt, Christoph Arndt, Otmar Loffeld, Otmar Loffeld, } "Information gained by pseudoredundant measurements", Proc. SPIE 2784, Vision Systems: Sensors, Sensor Systems, and Components, (21 August 1996); doi: 10.1117/12.248529; https://doi.org/10.1117/12.248529
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