A criterion for the degree of observability of state variables in linear time-varying systems is considered. The qualitative characteristics of the observability of the errors in inertial navigation systems are studied with a change in the aircraft flight altitude, the step of computation and in depending with the type of inertial navigation system, that are characterized by the values of the mean frequency of the random change in the drift of the gyroplatform. The results of simulation of navigation system errors, their degree of observability and estimation by the non-stationary Kalman filter are presented. The problem of determining the achievable accuracy of corrected inertial navigation systems in aircraft is investigated. In the models of the estimation algorithms, different values of the average frequency of the change in drift of the gyroplatform are used. A method for studying the achievable accuracy of corrected navigation systems has been developed, which makes it possible to make an informed decision on the use of the system in the design of the aircraft avionics. Based on the analysis of the state variable observability characteristics of navigation systems, it can be concluded that the accuracy of the estimation is dependent on the variable parameters of the inertial navigation system error model.