The problem of solution uniqueness to the task of determining unknown parameters of mathematical models from input-output observations is studied. This problem is known as structural identifiability problem. We offer a new approach for testing structural identifiability of linear state space models. The approach compares favorably with numerous methods proposed by other authors for two main reasons. First, it is formulated in obvious mathematical form. Secondly, the method does not involve unfeasible symbolic computations and thus allows to test identifiability of large-scale models. In case of non-identifiability, when there is a set of solutions to the task, we offer a method of computing functions of the unknown parameters which can be determined uniquely from input-output observations and later used as new parameters of the model. Such functions are called parametric functions capable of estimation. To develop the method of computation of these functions we use Lie group transformation theory. Illustrative example is given to demonstrate applicability of presented methods.