Identification of linear systems using output measurements with only two possible values

Classical identification cannot be applied when no output measurements are available. In many situations however, discrete information on the unmeasured outputs can still be obtained and used to identify the underlying dynamics. An example is a moving object where an optical sensor can detect whether or not is in the sensors line of sight but whose position is not measured. Using these discrete data sources to estimate a model for the underlying dynamics is equivalent to the estimation of the linear parameters of a Wiener system, which has a known but non-invertible static non-linearity with two output levels. Techniques are derived to perform this estimation, using sequential quadratic programming to minimize a least squares goal function. Simulations are used to validate the proposed approach, yielding good convergence of the linear model parameters to their targets and a high prediction accuracy for the unmeasured variable of the Wiener system.