This paper presents detailed derivations and further explanations of the state transformation extended Kalman filter (ST-EKF) from the common frame error definition perspective. Both the system error and measurement models of strapdown inertial navigation system (SINS)/Odometer (OD) tightly-coupled navigation are derived based on the ST-EKF. Both theoretical analysis and test results indicate the effectiveness of the proposed velocity error definition on mitigating the covariance-inconsistency problem that is caused by the specific force calculation error in the EKF state transition matrix. The excellent covariance-consistency of the ST-EKF makes it not necessary to remove gyro and accelerometer bias errors from the initial alignment Kalman filter states. This phenomenon can ensure the subsequent integrated navigation performance. Single-position ground SINS alignment experiments by using a navigation grade inertial measurement unit (IMU) showed that the estimated yaw angle from the conventional 15-state EKF slowly diverged over time. Furthermore, this phenomenon became more distinct when the initial yaw angle error was larger. In contrast, the estimated yaw angle from the proposed 15-state ST-EKF was significantly more stable and less degraded by large initial yaw angle errors. Long- distance land-vehicle SINS/OD integrated navigation tests also exhibited the ST-EKF's higher positioning and heading accuracy than the EKF.

In-motion alignment of Strapdown Inertial Navigation Systems (SINS) without any geodetic-frame observations is one of the toughest challenges for Autonomous Underwater Vehicles (AUV). This paper presents a novel scheme for Doppler Velocity Log (DVL) aided SINS alignment using Unscented Kalman Filter (UKF) which allows large initial misalignments. With the proposed mechanism, a nonlinear SINS error model is presented and the measurement model is derived under the assumption that large misalignments may exist. Since a priori knowledge of the measurement noise covariance is of great importance to robustness of the UKF, the covariance-matching methods widely used in the Adaptive KF (AKF) are extended for use in Adaptive UKF (AUKF). Experimental results show that the proposed DVL-aided alignment model is effective with any initial heading errors. The performances of the adaptive filtering methods are evaluated with regards to their parameter estimation stability. Furthermore, it is clearly shown that the measurement noise covariance can be estimated reliably by the adaptive UKF methods and hence improve the performance of the alignment.

With the development of high-accuracy inertial navigation system inertial sensors, such as ring laser gyroscopes and atomic spin gyroscopes, it is increasingly important to improve the strapdown inertial navigation algorithms to match such high-accuracy inertial sensors. For example, the existing inertial navigation algorithms have not taken into account the triple-cross-product term of noncommutativity error. However, theoretical analysis demonstrates that the ignored triple-cross-product term is nonignorable under coning motion with constant angular rate precession environments. In this paper, a new high-accuracy rotation vector algorithm is proposed for strapdown inertial navigation. The Taylor series about time is used for error analysis and optimization of the new algorithm. General maneuvers and coning motion with constant angular rate precession environments are considered in establishing the coefficient equations in the proposed algorithm. Error drift equations are given after the error compensation. Normalized quaternion under coning motion with constant angular rate precession environments and Savage's severe integrated angular-rate profiles are used to numerically verify the new algorithm. The results indicate that the new high-order attitude updating algorithm can improve inertial navigation accuracy.

In the integrated navigation system using extended Kalman filter (EKF), the state error conventionally uses linear approximation to tackle the commonly nonlinear problem. However, this error definition can diverge the filter in some adverse situations due to significant distortion of the linear approximation. By contrast, the nonlinear state error defined in the Lie group satisfies the autonomous equation, which thus has distinctively better convergence property. This work proposes a novel strapdown inertial navigation system (SINS) nonlinear state error defined in the Lie group and derives the SINS equations of the Lie group EKF (LG-EKF) for the MIMU/GNSS/magnetometer integrated navigation system. The corresponding measurement equations are also derived. A land vehicle field test has been conducted to evaluate the performance of EKF, ST-EKF (state transformation extended Kalman filter) and LG-EKF, which verifies LG-EKF's superior estimation accuracy of the heading angle as well as the other two horizontal angles (pitch and roll). The LG-EKF proposed in this paper is unlimited in the choice of sensors, which means it can be applied with both high-end and low-end inertial sensors.

Since the drifts of Inertial Navigation System (INS) solutions are inevitable and also grow over time, a Doppler Velocity Log (DVL) is used to aid the INS to restrain its error growth. Therefore, INS/DVL integration is a common approach for Autonomous Underwater Vehicle (AUV) navigation. The parameters including the scale factor of DVL and misalignments between INS and DVL are key factors which limit the accuracy of the INS/DVL integration. In this paper, a novel parameter calibration method is proposed. An iterative implementation of the method is designed to reduce the error caused by INS initial alignment. Furthermore, a simplified INS/DVL integration scheme is employed. The proposed method is evaluated with both river trial and sea trial data sets. Using 0.03°/h(1σ) ring laser gyroscopes, 5 × 10⁻⁵ g(1σ) quartz accelerometers and DVL with accuracy 0.5% V ± 0.5 cm/s, INS/DVL integrated navigation can reach an accuracy of about 1‰ of distance travelled (CEP) in a river trial and 2‰ of distance travelled (CEP) in a sea trial.