The UnScented QUaternion Estimator (USQUE) has been approved as a promising substitute for the extended Kalman filter when applied in the Standard Inertial Navigation Equations (SINE)-based inertial navigation system/global positioning system integration. However, the expensive computational burden makes it untenable in real time applications. In this paper, a computationally efficient filtering algorithm called Marginalised USQUE (MUSQUE) is derived by embedding the Marginalised Unscented Transformation (MUT) that is applicable to nonlinear systems with a linear substructure into the widely used USQUE. The contributions of the MUSQUE developed here are twofold. Firstly, the SINE are reconstructed to be only nonlinear in the attitude quaternion while linear in velocity and position, which makes the MUT potentially applicable in the USQUE. Secondly, the quaternion and generalised Rodrigues parameter-based sigma points are propagated simultaneously in the MUSQUE to deal with the dimensional mismatching hierarchy of the USQUE. Compared with the USQUE the number of sigma points can be decreased substantially, thereby making the applied MUSQUE computationally tenable. The experimental results show that the proposed MUSQUE has nearly identical performance with the USQUE but with much reduced computational burden.

The observability of error states in Inertial Navigation System/Global Positioning System (INS/GPS) integration is of great importance. Rank tests or null space tests of the observability matrix have been adopted by previous works, however, for a time-varying system with a high-dimension error state vector, it is very difficult to analyse the observability matrix by these traditional methods. In this paper, the decoupled observability analysis method is proposed for an 18-dimensional INS/GPS integration system. By reducing the dimension of coupling error states, several six-dimensional decoupled observability sub-matrices are obtained, which make the observability analyses easier. The observability results of error states are obtained by the proposed method. Covariance simulation with an Extended Kalman filter (EKF) and a flying test were performed which confirmed the theoretical results.

We develop a new frequency-domain dynamic response method to model integrated Inertial Navigation System (INS) and Global Positioning System (GPS) architectures and provide an accurate impulse-response-based INS-only navigation solution when GPS signals are denied (GPS outages). The input to such a dynamic system is the INS-only solution and the output is the INS/GPS integration solution; both are used to derive the transfer function of the dynamic system using Least Squares Frequency Transform (LSFT). The discrete Inverse Least Squares Frequency Transform (ILSFT) of the transfer function is applied to estimate the impulse response of the INS/GPS system in the time domain. It is shown that the long-term motion dynamics of a DQI-100 IMU/Trimble BD950 integrated system are recovered by 72%, 42%, 75%, and 40% for north and east velocities, and north and east positions respectively, when compared with the INS-only solution (prediction mode of the INS/GPS filter). A comparison between our impulse response model and the current state-of-the-art time-domain feed-forward neural network shows that the proposed frequency-dependent INS/GPS response model is superior to the neural network model by about 26% for 2D velocities and positions during GPS outages.

With the rapid developments in computer technology, the particle filter (PF) is becoming more attractive in navigation applications. However, its large computational burden still limits its widespread use. One approach for reducing the computational burden without degrading the system estimation accuracy is to combine the PF with other filters, i.e., the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). In this paper, the a posteriori estimates from an adaptive unscented Kalman filter (AUKF) are used to specify the PF importance density function for generating particles. Unlike the sequential importance sampling re-sampling (SISR) PF, the re-sampling step is not required in the algorithm, because the filter does not reuse the particles. Hence, the filter computational complexity can be reduced. Besides, the latest measurements are used to improve the proposal distribution for generating particles more intelligently. Simulations are conducted on the basis of a field-collected 3D UAV trajectory. GPS and IMU data are simulated under the assumption that a NovAtel DL-4plus GPS receiver and a Landmark™ 20 MEMS-based IMU are used. Navigation under benign and highly reflective signal environments are considered. Monte Carlo experiments are made. Numerical results show that the AUPF with 100 particles can present improved system estimation accuracy with an affordable computational burden when compared with the AEKF and AUKF algorithms.