Rao-Blackwellized Gaussian Sum Particle Filtering for Multipath Assisted Positioning

Algorithm 1

RBGSPF for time instant .

Input:  , and for , , ,

Output:  , and for , ,

(1) for do

(2)draw new user particle using (33);

(3)if any new signal components detected then

(4)initialize the new transmitter(s) based on ;

(5)if track of any signal components lost then

(6)delete the corresponding transmitter(s);

(7)for do

(8)for do

(9)perform UKF prediction and update to calculate using the UKF equations in the Appendix;

(10)calculate the weight with (46);

(11)if then

(12)prune this Gaussian component: set ;

(13)calculate the weight with (45);

(14) for do

(15)for do

(16)normalize the weights for ;

(17) normalize the weights for ;

(18) resample the user particles [26];