This paper derives a novel initial alignment method for the strapdown inertial navigation system (SINS), which transforms the attitude alignment into an attitude estimation problem. The process model of the proposed initial alignment method by attitude estimation is established by decomposition of the attitude matrix. The measurement model is constructed based on a generalized velocity integration formula that can integrate the inertial measurements over certain fixed time intervals. The contributions of the work presented here are twofold. First, the attitude estimation-based structure enables the proposed method to estimate the gyroscope biases other than the attitude quaternion, which is celebrated for the low-cost SINS. The second is the application of the proposed generalized velocity integration formula to attenuate the accumulated errors in vector observations caused by the traditional velocity integration formula. Experimental road tests are performed with a low-cost SINS, which validate the efficacy of the proposed method.

This technical note concerns the deterministic sampling points construction strategy for unscented Kalman filter (UKF) and cubature Kalman filter (CKF). From the numerical-integration viewpoint, a new deterministic sampling points set is derived by orthogonal transformation on the cubature points. By embedding these points into the UKF framework, a modified nonlinear filter named transformed unscented Kalman filter (TUKF) is derived. The TUKF can address the nonlocal sampling problem inherent in CKF while maintaining the virtue of numerical stability for high dimensional problems. Moreover, the methodology proposed in this technical note can be used to construct nonlinear filters with improved accuracy for certain problems. The performance of the proposed algorithm is demonstrated through a nonlinear high dimensional problem.

This study concerns the unscented Kalman filter (UKF) for the non-linear dynamic systems with error statistics following non-Gaussian probability distributions. A novel robust unscented Kalman filter (NRUKF) is proposed. In the NRUKF the measurement information (measurements or measurements noise) is reformulated using Huber cost function, then the standard unscented transformation (UT) is applied to exact non-linear measurement equation. Compared with the conventional Huber-based unscented Kalman filter (HUKF) which is derived by applying the Huber technique to modify the measurement update equations of the standard UKF, the NRUKF, without linear (statistical linear) approximation, has much-improved performance and versatility with maintaining the robustness. Then the NRUKF is applied to the target tracking problem. The validity of the algorithm is demonstrated through numerical simulation study.

The integration of the inertial navigation system and the global positioning system (INS/GPS) is a widely used procedure for position and attitude determination applications. The Kalman type filter (KTF) is the primary mechanism to perform the integration. In the KTF, the process noise is always assumed to be Gaussian distribution, which may be violated by the vehicle's severe maneuver, resulting in a much degraded performance. In this paper, the Huber's M-estimation methodology is investigated to suppress the process uncertainty, founded on the cascaded form of the M-estimation-based Kalman filter. An iterated algorithm is designed to construct the weighted matrix to rescale the prior state estimate covariance. The proposed process uncertainty robust algorithm is embedded into the newly derived modified unscented quaternion estimator to perform the standard inertial navigation equations-based INS/GPS integration. The car-mounted experiments are carried out to validate the proposed method against the process uncertainty.

This paper proposes a modified unscented Kalman filter (UKF) with both adaptivity and robustness. In the proposed filter, the adaptivity is achieved by estimating the time-varying measurement noise covariance based on variational Bayesian (VB) approximation. The robustness is achieved by modifying the filter update based on Huber's M-estimation and Gaussian-Newton iterated method. In Gaussian assumptions, the proposed filter has a comparable filtering accuracy with the original UKF and better filtering consistency. When the measurement noise covariance is time-varying and there are outliers in the measurements, the proposed filter can outperform UKF and other adaptive or robust filters (such as VB-based UKF and Huber-based UKF) in terms of both filter accuracy and consistency. The efficacy of the proposed filter is demonstrated through the numerical simulation test and integrated navigation shipborne test.

This paper proposes an ingenious alignment scheme for a Doppler velocity log-aided strapdown inertial navigation system with only the initial velocity and position information. The proposed scheme decomposes the task into two tightly coupled subproblems. First, an optimization-based coarse alignment (OBCA) method is developed to derive the constant attitude at the very start of the alignment. During the OBCA process, the required velocity and position are all approximated using their initial values. Second, a nonlinear-filtering-based fine alignment (NFFA) is developed to refine the attitude and calculate the real-time velocity and position. In an NFFA, the standard inertial navigation equations are used directly as the process model, which, therefore, can track the vehicle maneuverability during the alignment period. The NFFA is carried out again from the very start, initialized with the roughly known attitude by OBCA and the known initial velocity and position information. This scheme necessitates the recording of the sensor data during the OBCA. The experimental results show that the proposed method can not only align the attitude to high precision within very short time, but also determine the velocity and position with satisfied accuracy.