Discrete identification of continuous non-linear andnon-stationary dynamical systems that is insensitive to noise correlation and measurement outliers

The paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned ‘integrating filters’ of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization and can be identified, for example, by the classical least squares procedure. Since in the presence of correlated noise, the estimated parameter values are burdened with an unavoidable systematic error (manifested by asymptotic bias of the estimates), in order to significantly improve the identification consistency, the method of instrumental variables is used here. In our research we use an estimation algorithm based on the least absolute values (LA) criterion of the least sum of absolute values, which is optimal in identifying linear and non-linear systems in the case of sporadic measurement errors. In the paper, we propose a procedure for determining the instrumental variable for a continuous model with non-linearity (related to the Wienerian system) in order to remove the evaluation bias, and a recursive sub-optimal version of the LA estmator. This algorithm is given in a simple (LA) version and in an instrumental variable version (IV-LA), which is robust to outliers, removes evaluation bias, and is suited to the task of identifying processes with non-linear dynamics (semi-Wienerian/NLID). In conclusion, the effectiveness of the proposed algorithmic solutions has been demonstrated by numerical simulations of the mechanical system, which is an essential part of the suspension system of a wheeled vehicle.