Theoretical error modeling and analysis of strapdown inertial navigation system alignment under zero-velocity conditions

One of the important stages before the operation of an inertial navigation system is the initial alignment procedure, known as fine alignment under stationary conditions. This study analyzes the accuracy of the fine alignment algorithm, which uses zero-velocity updates to estimate and compensate navigation errors. Since the velocity-matching approach is not fully observable, an observability analysis identifies which error states cannot be estimated. The unobservable states and thus the ultimate alignment accuracy depend on both sensor precision and the orientation of the inertial measurement unit. This paper investigates the influence of attitude on fine alignment performance through analytical derivations and numerical simulations. New relationships are developed to predict alignment accuracy for arbitrary orientations, and their validity is demonstrated via extensive simulation results. Additionally, the impact of x-, y-, and z-channel sensors on the final accuracy of inertial alignment is examined statistically. The results reveal a differential sensitivity, indicating that alignment accuracy is predominantly influenced by sensors along the z-channel. This insight provides a practical strategy for sensor placement optimization, suggesting that allocating higher-accuracy sensors to the z-axis within a fixed budget can yield significant improvements in overall navigation system performance.