The additional information available in the form of linear or nonlinear constraints are often remain unexplored in the parameter identification problems related to linear dynamic systems. Our goal in this work is to explore the knowledge of the linear constraints to achieve significant improvement in the accuracy of the parameter estimates. In the class of problems being addressed here, the unknown boundary conditions appear as nuisance parameters. In practice, these nuisance parameters are eliminated from the loss function to get a variable projection optimization problem in the parameters of interest. In this work, we solve a constrained optimization problem instead, where the additional linear constraints are imposed in the form of partially known boundary conditions. In the process, we show how the accuracy of the estimates is improved by taking the constraints into account. The theoretical methodology is successfully applied also to numerical simulations as well as in real-world experiments. (C) 2004 Elsevier Ltd. All rights reserved.