DECONVOLUTION ALGORITHM
PACHNER, D.; KROUPA, .
Abstract
Deconvolution should be understood as the inverse operation to the convolution. It can be roughly described as the problem to guess the linear system input if its transfer function and the output are both known. This problem arises if a signal is measured through a dynamicaly distorting device. Such problems are often solved via the signal Fourier transform division by the filter frequency response. Our contribution presents a different approach defined rather in the time domain. We suppose the unknown input to be a random process realization. Then one can evaluate the conditional expectation of this process. The conditioning is understood with respect to all the data available. That is why the apporach is related to Kalman smoother rather than the filter. Compared to the frequency domain this approach has good both numerical and statistical properties. Except of the unknown input estimate, the smoothed filter initial condition is evaluated as well. This approach is easily applicable to the linear systems with multiple inputs and/or outputs. In this case the solution may happen not to be unique or it does not exist at all. These cases will be discussed. A number of deconvolution application examples will be shown. It will be demonstrated how the pilot control actions can be reconstructed from the aircraft positional angles.
Coresponding author e-mail: pachner[at]fel[dot]cvut[dot]cz
Session: Algorithms and Computing for Control
