The ekf for robot localization Prediction step Measurement step x+△cosb+q△cosb (2-x)+(2,-y+ y+Tsin 8+qAt sin 8 h(2,v) f(5,u,q) 0+△b+q△6 6+v A A 10-△ tsin e00 01△tcos00 H= r A=00 00 0 10 00 W 110 Pros and cons Pro: Very reliable Easy to implement if assumptions hold Gives very powerful framework for reasoning about quality of m Can be run on -or off-line Landmark representation somewhat intuitive to humans Con Very sensitive to data association errors Point features Linear-Gaussian world model Quadratic complexityThe EKF for Robot Localization ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ∆ − ∆ = 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 cos 0 0 1 0 sin 0 0 θ θ t t A W = [ ] 1 1 1 0 0 ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − − − − − − − = 2 1 2 1 2 1 2 1 1 1 1 1 1 0 r x r y r x r y r y r x r y r x H y x y x x y x y λ λ λ λ λ λ λ λ ( ) ( ) ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − − + − + = − θ θ λ λ λ λ ξ v x y x y v h v x y x y r 1 2 2 tan ( , ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 1 1 0 V Prediction step Measurement step ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + ∆ + ∆ + ∆ + ∆ + ∆ + ∆ = x x q y t q t x t q t f u q 1 1 sin sin cos cos ( , , ) λ λ θ θ θ θ θ θ θ ξ Pros and Cons ● Pro:● Very reliable ● Easy to implement if assumptions hold ● Gives very powerful framework for reasoning about quality of map ● Can be run on- or off-line ● Landmark representation somewhat intuitive to humans ● Con:● Very sensitive to data association errors ● Point features ● Linear-Gaussian world model ● Quadratic complexity