Table 1 RTR algorithm for matrix detector

Input: Covariance matrix manifold \({\mathcal{M}}\)of radar echo data in one CPI by formula (5); a metric \(g\) by (23); function f on \({\mathcal{M}}\)by formula (31); retraction R

Optimization problem: formula (32)

Output: sequence \(\{ { }W_{k} \}\)

Step 1: Calculate the mean of the reference cells matrix by formula (28);

Step 2: Set dimension n of parameter W in formula (32);

initialize \(W_{0} = I\);

Step 3: Riemannian gradient and Hessian of cost function by formula (33) (34) (36);

Step 4: Set Parameters of classical trust region algorithm;

Step 3: for k = 0, 1, 2,... do

Solve formula(40) with TCG method to obtain \(\xi_{k}\);

Computer \(\rho_{k}\) in (38);

Iteration according to classical trust region algorithm;

end for