In mobile robotics, position-sensing is crucial to a robot. We investigate a type of online position estimations based on visual and inertial sensor fusion. Being different from the traditional state estimation, our position estimation is a linear state estimation with implicit observation equations. To this end, an implicit Kalman filter is proposed and designed in details for this position estimation. Furthermore, a state augmentation method is employed in which the accelerometer bias is taken as a state of the filter to compensate for its effect to the position estimation results. Simulation results show that the implicit Kalman filter is convergent, and the effect of the accelerometer bias is eliminated from the position estimation.%机器人对自身位置的实时感知在机器人技术中非常重要.本文主要研究机器人技术中一类基于视觉与惯性传感器的位置估计问题.与传统的状态估计问题不同的是,所研究位置估计问题为带有隐式观测方程的线性状态估计问题.为此提出一种能够解决此类估计问题的隐式卡尔曼滤波器,并给出了详细的滤波器设计过程.另外采用扩展变量法将加速度信息中的偏移量作为滤波器状态来估计,以补偿其对位置估计结果的影响.仿真结果显示,所给出的隐式卡尔曼滤波器收敛,加速度偏移带来的影响被有效的补偿.
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