In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions.

The cubature Kalman filter (CKF) is widely used in the application of GPS/INS integrated navigation systems. However, its performance may decline in accuracy and even diverge in the presence of process uncertainties. To solve the problem, a new algorithm named improved strong tracking seventh-degree spherical simplex-radial cubature Kalman filter (IST-7thSSRCKF) is proposed in this paper. In the proposed algorithm, the effect of process uncertainty is mitigated by using the improved strong tracking Kalman filter technique, in which the hypothesis testing method is adopted to identify the process uncertainty and the prior state estimate covariance in the CKF is further modified online according to the change in vehicle dynamics. In addition, a new seventh-degree spherical simplex-radial rule is employed to further improve the estimation accuracy of the strong tracking cubature Kalman filter. In this way, the proposed comprehensive algorithm integrates the advantage of 7thSSRCKF’s high accuracy and strong tracking filter’s strong robustness against process uncertainties. The GPS/INS integrated navigation problem with significant dynamic model errors is utilized to validate the performance of proposed IST-7thSSRCKF. Results demonstrate that the improved strong tracking cubature Kalman filter can achieve higher accuracy than the existing CKF and ST-CKF, and is more robust for the GPS/INS integrated navigation system.

In previous research, a semi-strapdown inertial navigation system (SSINS), based on micro-electro-mechanical system (MEMS) sensors, was able to realize over-range measurement of the attitude information of high-rotation missiles by constructing a single axis “spin reduction” platform. However, the MEMS sensors in SSINS were corrupted by significant sensor errors. In order to further improve SSINS measurement accuracy, a rotational modulation technique has been introduced to compensate for sensor errors. The ideal modulation angular velocity is changed sharply to achieve a constant speed, while in practical applications, the angular rate of the rotating mechanism’s output needs to go through an acceleration-deceleration process. Furthermore, the stability of the modulation angular rate is difficult to achieve in a high-speed rotation environment. In this paper, a novel rotation scheme is proposed which can effectively suppress the residual error in the navigation coordinate system caused by the modulation angular rate error, including the acceleration-deceleration process and instability of angular rate. The experiment results show that the position and attitude accuracy of the new rotation scheme was increased by more than 56%. In addition, the proposed scheme is applicable to navigation accuracy improvement under various dynamic conditions.

The optimization-based alignment (OBA) methods, which are implemented by the optimal attitude estimation using vector observations—also called double-vectors—have proven to be effective at solving the in-flight alignment (IFA) problem. However, the traditional OBA methods are not applicable for the low-cost strap-down inertial navigation system (SINS) since the error of double-vectors will be accumulated over time due to the substantial drift of micro-electronic- mechanical system (MEMS) gyroscope. Moreover, the existing optimal estimation method is subject to a large computation burden, which results in a low alignment speed. To address these issues, in this article we propose a new fast IFA method based on modified double-vectors construction and the gradient descent method. To be specific, the modified construction method is implemented by reducing the integration interval and identifying the gyroscope bias during the construction procedure, which improves the accuracy of double-vectors and IFA; the gradient descent scheme is adopted to estimate the optimal attitude of alignment without complex matrix operation, which results in the improvement of alignment speed. The effect of different sizes of mini-batch on the performance of the gradient descent method is also discussed. Extensive simulations and vehicle experiments demonstrate that the proposed method has better accuracy and faster alignment speed than the related traditional methods for the low-cost SINS/global positioning system (GPS) integrated navigation system

The Semi-Strapdown Inertial Navigation System (SSINS) provides a new solution to attitude measurement of a high-speed rotating missile. However, micro-electro-mechanical-systems (MEMS) inertial measurement unit (MIMU) outputs are corrupted by significant sensor errors. In order to improve the navigation precision, a rotation modulation technology method called Rotation Semi-Strapdown Inertial Navigation System (RSSINS) is introduced into SINS. In fact, the stability of the modulation angular rate is difficult to achieve in a high-speed rotation environment. The changing rotary angular rate has an impact on the inertial sensor error self-compensation. In this paper, the influence of modulation angular rate error, including acceleration-deceleration process, and instability of the angular rate on the navigation accuracy of RSSINS is deduced and the error characteristics of the reciprocating rotation scheme are analyzed. A new compensation method is proposed to remove or reduce sensor errors so as to make it possible to maintain high precision autonomous navigation performance by MIMU when there is no external aid. Experiments have been carried out to validate the performance of the method. In addition, the proposed method is applicable for modulation angular rate error compensation under various dynamic conditions.

Alignment technology plays an important role in navigation, and is used extensively throughout military and civilian applications. However, the existing in-flight alignment methods cannot be applied to the low-cost based strap-down inertial navigation system/global positioning system integrated navigation system, used in short-endurance and high-speed rotation flight bodies, since they cannot quickly obtain alignment results to meet the accuracy requirements of a flight body with special movement characteristics of short-endurance and high-speed rotation. In this paper, in order to solve this challenging problem of alignment for flight body with short-endurance and high-speed rotation, a fast in-flight alignment method based on the Lie group is proposed. First, an in-flight alignment model based on vector observations was established by using the Lie group. Second, addressing the problem that the alignment accuracy is greatly affected by the low-cost inertial sensor bias, an improved unscented Kalman filter was constructed in the Lie group on the basis of fully considering the characteristics of the system equations to estimate and feedback the correlated errors. Finally, a trajectory simulation of high-speed flight body and field semi-physical test was carried out to evaluate the proposed method. Evaluation of the system performance in comparison with existing state-of-the-art methods indicated that the proposed in-flight alignment method has better alignment accuracy and faster alignment velocity for a low-cost strap-down inertial navigation system/global positioning system integrated navigation system.