A Novel Probabilistic Approach for Vehicle Position Prediction in Free, Partial, and Full GPS Outages

Algorithm 1

Bayesian-Sparse Random Gaussian Prediction (B-SRGP) algorithm.

 Input: : predictor vectors; : measurement vectors; : covariance matrix of GPS;

 : number of iterations to obtain the Sparse Random Gaussian matrix.

 Output: the predicted measurement of the vehicle position .

(1) Initialization: At epoch :

(i) Set the initial vehicle position provided by GPS and ,

   the initial angular velocity and acceleration provided by INS;

(ii) Set initial values

(2) for   to   do

(3)   for   to   do

(4)   Compute the random Gaussian matrix according to (3);

(5)   

(6)   end for

(7)   Explore the measurement matrix based on RIP such that the optimization problem is resolved via [29];

(8)   Generate , , and using MLE (see (11), (13) and (14));

(9)   Calculate the likelihoods and according to (10) and (12);

(10)   Generate and evaluate the GPS weight according to (8);

(11)    if  , (Free GPS outage) then

(12)   Predict vehicle position such that based on (9) and (10);

(13)    end if

(14)    if   (Full GPS outage), then

(15)   Predict vehicle position such that based on (9) and (12);

(16)    Otherwise (, Partial GPS outage)

(17)   Compute according to (27);

(18)   Predict the vehicle position such that

(19) end if

(20) end for

(21) Return the predicted measurement of the vehicle position .