Robustness of the Quadratic Antiparticle Filter for Robot Localization

Robot localization using odometry and feature measurements is a nonlinear estimation problem. An efficient solution is found using the extended Kalman filter, EKF. The EKF however suffers from divergence and inconsistency when the nonlinearities are significant. We recently developed a new type of filter based on an auxiliary variable Gaussian distribution which we call the antiparticle filter AF as an alternative nonlinear estimation filter that has improved consistency and stability. The AF reduces to the iterative EKF, IEKF, when the posterior distribution is well represented by a simple Gaussian. It transitions to a more complex representation as required. We have implemented an example of the AF which uses a parameterization of the mean as a quadratic function of the auxiliary variables which we call the quadratic antiparticle filter, QAF. We present simulation of robot feature based localization in which we examine the robustness to bias, and disturbances with comparison to the EKF.