# An Enhanced Fusion Strategy for Reliable Attitude Measurement Utilizing Vision and Inertial Sensors
## 1 Introduction  
Attitude measurement has received considerable attention from the research community due to its significant importance in navigation, positioning, tracking and control [1; 2; 3; 4], where measurement precision and stability are also important requirements. The main purpose of attitude measurement is to dynamically obtain the spatial attitude angles of the measured object using one or more sensors installed onto it in engineering measurement, military, controlling and locating robots [5; 6; 7]. However, the development of an effective attitude measurement strategy that performs well while ensuring stability and precision is still a significant challenge due to the following important reasons. (i) The single sensor has limited performance due to its own measurement characteristics. (ii) To use an integrated system, the data fusion algorithm, such as the filtering method, can only operate when at least two types of data are available. That is, there is always a sampling frequency discrepancy among heterogeneous sensors. All the aforementioned factors pose multiple handicaps in implementing a high-performance attitude measurement system. For common single measurement techniques [8; 9], such as inertial measurement and visual measurement, their applications are fairly limited due to their inherent measurement characteristics. Focusing on the low cost and widely used micro-electromechanical systems (MEMS) inertial sensor [10; 11], its sampling frequency is high, but the measurement errors accumulate quickly with time due to bias error drift and scale factor instability [12; 13; 14]. The vision measurement can provide relatively stable results. However, compared to the inertial sensor, it has a significantly lower frequency, which may not be sufficient for fast moving object tracking. Thus, the single attitude measurement technique may fail to meet the practical attitude measurement requirements, which promote the development of the fusion measurement system. Considering the advantages and limitations of a single sensor, a vision sensor and an inertial sensor are frequently deployed together where data are fused to enhance measurement performance by fully utilizing the complementary properties of each sensor to overcome the shortcomings inherent with a single sensor. For attitude measurement, the combination of vision and inertial sensors [15] can enhance the accuracy, fault detection and confidence in decision making. To fuse data from heterogeneous sensors, such as the vision sensor and inertial sensor together, a common strategy is nonlinear Kalman filter (KF) [16], such as the extended KF (EKF) [17], unscented KF (UKF) [18; 19], and cubature KF (CKF) [20]. In general applications, the EKF relies only on the first order linearization of nonlinear system models. Thus, the EKF may provide particularly poor performance if the dynamic systems are highly nonlinear. To better treat the nonlinearity, the UKF has been developed to address nonlinear state estimation in the context of the control theory. Unlike the conventional EKF, the UKF can obtain second order accuracy of the posterior mean and covariance. Under the Bayesian filtering framework, the CKF provides a new direction to realize the nonlinear filter [21]. CKF is more preferred over the UKF for its more stable performance. Therefore, CKF is used to fuse inertial and visual data, and its performance is compared with those of other filter methods. Actually, in a vision and inertial integrated system, the attitude measurement performance does not only depend on the selection of the filtering methods. Other factors may also need to be considered. Among them, the multi-frequency is an important problem in theory and practice. As the sampling frequency of the inertial sensor is high and that of visual sensor is low, an inconsistent sampling frequency always exists in a vision and inertial integrated attitude measurement system [22]. Correspondingly, a degradation of measurement performance is unavoidable in the intersampling of slow vision data.