Inertial navigation system positioning error analysis and Cramér-Rao lower bound

Self-contained inertial navigation system (INS) has generated enough attention inside indoor positioning and navigation sector in recent years. However stand-alone low-cost INS suffers severe position drift after using for a short period of time due to the noises in both gyroscope and accelerometer. This paper presents the theoretical analysis of INS's position root mean squared error (RMSE) caused by white Gaussian noise within body frame sensors. Standard deviations of Gaussian noise in tri-axial accelerometer and tri-axial gyroscope are acquired through Allan Variance analysis. Up to second order of Taylor expansion is considered when approximating transformation matrix formed by gyroscope values from beginning, which is used to project acceleration collected from body frame onto local navigation frame. No particular IMU mounting position is assumed for the derivation. In addition, Cramér-Rao Lower Bound (CRLB) for INS perturbed by the same white Gaussian noise is derived for comparison with RMS error on the same route to test our proposed methodology. Monte Carlo simulation is performed to compare with derived RMS error and CRLB. The plot of RMS error is shown to be close to CRLB especially at the early stage of the route. Our proposed RMS error analysis proves to be efficient by staying close to CRLB along the route where CRLB serves as a lower benchmark of position error growth. It can also provide insight of performance for any other INS if the mean and variances of sensors noises are known. In conclusion, the main contribution of this paper is that our proposed position RMS error methodology can serve as an efficient alternative to CRLB.