EKF SLAM vs. FastSLAM -- A comparison

Abstract

The two algorithms are described with a planar robot application in mind. Generalization is to any spatial SLAM scenarios is straightforward. For simplicity, we assume there is no control input. The pose consists of the robot’s position (x, y) ⊤ and its heading direction δ: st: = (x, y, δ) ⊤. The landmarks are denoted θi, simply consisting of a pair of planar coordinates. 1 Probabilistical EKF Formulation The Extended Kalman Filter (EKF) can be viewed as a variant of a Bayesian Filter; EKFs provide a recursive estimate of the state of a dynamic system, or more precise, solve an unobservable, nonlinear estimation problem. Roughly speaking, the state xt of a system at time t can be considered a random variable where the uncertainty about this state is represented by a probability distribution. One is interested in the posterior density p (xt |zt), where zt: = {z1,...,zt} is the set of measurements up to time t and xt: = ( s ⊤ t, θ ⊤ 0, θ ⊤ 1,..., θ ⊤ ) ⊤ K is the state vector. (Note that the superscript t refers to the set of variables at time t.) In general, the complexity of computing such a density grows exponentially with time; to make the computation tractable, the true state