Algorithm 4: Recursive EKF algorithm with event based update

Input: uk,zk,xk−1,Pk−1,LGM

Output: x̂k,Pk

Data:f and h from model (6), Qk,Rk,ANXT

Initialization: x0,P0

for current time k do

Prediction Step EKF:

(same as Algorithm 1)

Correction Step EKF:

$K_k=P_k{H}_k^T{(H_k{P}_k{H}_k^T+V_k{R}_k{V}_k^T)}^{-1}$

x̂k = x̂k+Kk[zk−h(x̂k,0)]

Pk = (I−Kk Hk) Pk

3 − σ ellipsoid area Aellip

RA = Aellip/ANXT using (12)

if RA > RA,lim then

Global Correction Step:

xEKF = xEKF + ΔX

yEKF = yEKF + ΔY

θEKF = θGM

Pk,p = P0,x,y,θ

end

end