A Lagrangian Multiplier Method for TDOA and FDOA Positioning of Multiple Disjoint Sources with Distance and Velocity Correlation Constraints

Table 2

Process of proposed algorithm.

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Initialization and Input:

, initial value for Newton’s iteration.

, TDOA and FDOA measurements.

, positive multiplier vector.

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, 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).

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Preparation:

, initialize the value for comparison and save gradient vector and hessian matrix .

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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

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Output: as the optimal solution

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