| Initialization and Input: | , initial value for Newton’s iteration. | , TDOA and FDOA measurements. | , positive multiplier vector. |
| , positive penalty parameter which are fixed in iteration. | , the maximum number of iterations.( in this paper) | , initial step for iterations, attenuation factor. | , threshold, a sufficiently small and positive value ( in this paper). |
| Preparation: | , initialize the value for comparison and save gradient vector and hessian matrix . |
| Iteration process: | For: | Step 1: Update the estimate by | and turn to step 2. | Step 2: if , renew , and update the multipliers by using (42), then , record the updated and , turn to step 4. | Step 3: if , , then | , turn to step 4. | Step 4: when , output , otherwise, turn to step 1. | End |
| Output: as the optimal solution |
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