Symmetric Laplace transform and its application to parametric identification of linear systems

Properties of bilateral symmetric integral transform, which possesses useful features for identification of linear systems, are investigated. Relationships for covariance functions of stochastic stationary processes of measurement errors and disturbances are determined. The optimal solution is proposed to the identification problem for linear multivariable system with measured state coordinates in the transformation parameter domain, with account for restricted bandwidth of dynamic processes in the system at hand. The problem is solved for unknown initial state of the system and complex measurement errors including correlated noise, constant errors and linear trends.