Fangjun Qin

Transformed Unscented Kalman Filter

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.

Error analysis for SINS with different IMU rotation scheme

Influence on Strapdown Inertial Navigation System (SINS) error characteristics for different IMU (inertial measurement unit) rotation schemes was analyzed theoretically.Its indicated that, in single-axial and single-directed rotation scheme the gyros bias on rotational axis was not modulated, but a equivalent bias calculate by scale-factor error multiplying rotating velocity was introduced in rotational axis,which limit the position precision of the SINS. But in dual-axial and single-directed rotation scheme, both gyros bias and aforementioned equivalent bias were modulated, whenas another equivalent bias caused by coupling of the scale-factor error and the movement of vehicle were introduced and this bias also limited the position precision. The analysis in theory was proved by simulation.

Unscented type kalman filter: limitation and combination

This study investigates the shortcomings of existing unscented type Kalman filters (UTKFs) used for state estimation problem of non-linear stochastic dynamic systems. There are three kinds of UTKFs - the traditional unscented Kalman filter, the cubature Kalman filter and the transformed unscented Kalman filter. It was demonstrated in the past that these algorithms could capture the posterior mean and covariance accurately to the second order for any non-linearity when propagated through the true non-linear system. However, they yield different information on the higher order terms. Owing to the dualistic effect of higher order terms on the performance of these algorithms, it is desirable to come up with some solution to preserve the positive effect of this information in a single algorithm. Based on the assumption that the state measurements are Guassian, two methods are proposed in this work as the suitable candidates. The first one is an adaptive method that chooses the UTKF achieving the highest value of the likelihood function. The second method treats these algorithms as sub-filters and uses the partitioning approach to obtain an overall estimate. The numerical simulations show that the proposed methods can have comparable performances as one of the best UTKFs for the problems under consideration.

In-Motion Initial Alignment for Odometer-Aided Strapdown Inertial Navigation System Based on Attitude Estimation

This paper investigates the in-motion initial alignment for odometer-aided strapdown inertial navigation system with main focus on handling the severe disturbance inherent in the odometer. An attitude estimation-based alignment method is proposed through ingeniously attitude matrix decomposition and velocity rate equation reconstruction. The attitude estimation-based method can attenuate the disturbance in the odometer to a certain extent and can avoid some additional approximations. However, the severe disturbance in the odometer cannot be handled adequately by the attitude estimation structure. In this respect, a low-pass finite impulse response digital filter is used to attenuate the disturbance in the odometer preliminarily. Experimental results are reported to validate the effectiveness of the proposed alignment methods and the superiority of attitude estimation-based method over attitude determination-based method.

A Novel Backtracking Scheme for Attitude Determination-Based Initial Alignment

In this paper, a novel backtracking scheme is investigated to shorten the time of the attitude determination-based initial alignment. Based on the investigated backtracking scheme, the recorded data during the forward process is reversed and connected with the forward data, which is further used to construct the vector observations for the attitude determination based initial alignment. The investigated method can improve the accuracy and robustness of the initial alignment within only a very short period of time. The car-mounted experiment demonstrates the validity of the investigated method.

Improved precision of strapdown inertial navigation system brought by dual-axis continuous rotation of inertial measurement unit

When systemic rotation autocompensation technique is implemented in inertial navigation system (INS), inertial measurement unit (IMU) undergoes intentionally devised mechanical motions. This technique is one of the strategies of improving the system precision performance at the system level. A dual-axis continuous rotation scheme is introduced, and system error equation is derived. The behaviors of different errors are analyzed. It is concluded that the whole error of INS is attenuated effectively. The error model of the dual-axis continuous rotation INS is designed on digital computer, and the theoretical conclusion is validated.

Pseudo Open-Loop Unscented Quaternion Estimator for Attitude Estimation

In this paper, a novel attitude estimator called pseudo open-loop unscented quaternion estimator (PO-USQUE) is proposed for attitude estimation. In PO-USQUE, the attitude error estimate is used to construct the sigma points in the time update of the next filtering recursion, and therefore, the reset operation in current filtering recursion is no longer needed. The attitude update is achieved through the construction of the quaternion-based sigma points. Compared with the traditional USQUE, the attitude in PO-USQUE is updated more accurately due to the special structure, and the corresponding covariance is updated simultaneously in a nature way. The performance of the proposed PO-USQUE is assessed through two representative attitude estimation applications using simulation and field experiment data. The superiority of the PO-USQUE over USQUE in terms of accuracy, consistency, and efficiency is validated by the simulation and test results.

Genetic algorithm based fast alignment method for strap-down inertial navigation system with large azimuth misalignment.

In order to shorten the alignment time and eliminate the small initial misalignment limit for compass alignment of strap-down inertial navigation system (SINS), which is sometimes not easy to satisfy when the ship is moored or anchored, an optimal model based time-varying parameter compass alignment algorithm is proposed in this paper. The contributions of the work presented here are twofold. First, the optimization of compass alignment parameters, which involves a lot of trial-and-error traditionally, is achieved based on genetic algorithm. On this basis, second, the optimal parameter varying model is established by least-square polynomial fitting. Experiments are performed with a navigational grade fiber optical gyroscope SINS, which validate the efficiency of the proposed method.

Comment on “Highly Efficient Sigma Point Filter for Spacecraft Attitude and Rate Estimation”

In light of the intuition that a better symmetrical structure can further increase the numerical accuracy, the paper by Fan and Zeng (2009) developed a new sigma point construction strategy for the unscented Kalman filter (UKF), namely, geometric simplex sigma points (GSSP). This comment presents a different perspective from the standpoint of the numerical integration. In this respect, the GSSP constitutes an integration formula of degree 2 with equal weights. Then, we demonstrate that the GSSP can be derived through the orthogonal transformation from the basic points set of degree 2. Moreover, the method presented in this comment can be used to construct more accurate sigma points set for certain dynamic problems.

Indirect Kalman Filtering Based Attitude Estimation for Low-Cost Attitude and Heading Reference Systems

In this paper, a computational efficient attitude estimation method is proposed for the low-cost attitude and heading reference systems. In the proposed method, the velocity and position provided by the Global Positioning System and inertial sensors outputs are first used to construct the vector observations. With the constructed vector observations, an error equations based filtering model is established using the Euler angles as the attitude parameterization. If the attitude has been well initialized, the established model can reduce to a linear state-space model, which enables the application of standard Kalman filtering. For the established attitude estimation model, an indirect Kalman filter is detailedly designed. Car-mounted filed test results demonstrate that the proposed method possesses superiority over the existing methods with consideration of both accuracy and efficiency.