: Identi#cation of model parameters can be viewed as a problem with multiple objectives and constraints derived from empirical data #dynamic and steadystate #, physical models and belief, empirical and qualitative belief, desired model properties etc. A fairly general approachtomulti-objective system identi#cation based on constrained optimization is suggested, and here we formalize the method for the identi#cation of FIR models. Particular attention is paid to the analysis and selection of tradeo#s between con#icting objectives and constraints. Keywords: Optimization, Parameter Estimation, Prior Knowledge, Linear Systems. 1. INTRODUCTION The main objective of system identi#cation is to identify a model with good prediction capabilities in the sense that it is able to accurately predict the system's response to a given class of excitations. Hence, a common identi#cation objectiveis to minimize some penalty on mismatch between model prediction and observed data, which is the u...