典型场景下EKF-SLAM估计一致性分析

Consistency Analysis of EKF-SLAM for a Basic Scenario

分析了典型场景下基于扩展卡尔曼滤波的同步定位和地图创建(EKF-SLAM)算法的估计一致性.通过理论分析证明了在移动机器人保持静止并持续对一个路标进行观测的场景下,如果机器人的初始位姿协方差矩阵为对角阵,则机器人位置估计的均值和协方差保持不变,而朝向估计将逐步失去一致性.此外,通过蒙特卡罗仿真给出了机器人朝向和路标估计下界的分布情况.结果表明,两者均服从正态分布,因此EKF-SLAM算法在概率意义下给出SLAM系统状态向量的无偏估计.

The consistency of the extended Kalman filter-based simultaneous localization and mapping （EKF-SLAM） is addressed in this article. It is theoretically proven that, for a basic scenario that the mobile robot is stationary and keeps observing a stationary landmark, the estimates of the position and its uncertainty of the robot remain the same as the initial values on condition that the initial covariance matrix of the robot pose is diagonal. The estimate of heading uncertainty will become inconsistent as the number of observation increases. The distributions of the lower bounds of robot heading and landmark position are obtained by Monte Carlo simulations. Simulation results show that both of two distributions follow a normal distribution, hence the EKF-SLAM algorithm provides unbiased estimates of the SLAM state vector in the sense of probability.