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- I am not able to reach convergence if I initialize the starting point with coordinates outside the stations net. The observations are Difference in Time of Arrival.

I'm computing the trajectory of a moving body and my net is composed by 5 stations.

My observations are DTOA: difference in time of Arrival (they have been linearized).

I am trying to use Least Squares with a linear model: Y = Ax + b, where Y are the observed measurements (DTOA), A the design matrix, b is the known terms vector and X is a vector of estimates. The algorithm processes data according to the epoch considered and iterate the process up to a value of 20 times, unless it reaches before a 1mm convergence.

Since it is an iterative process, the system requires an initialization at the starting point with approximated values for the unknowns, and here comes my problem: if I initialize the starting point with coordinates within the polygon formed by the five stations convergence is reached and the solution is successful, but if I initialize the point with coordinates outside the area formed by the stations the convergence is not reached and I’m not able to determine the trajectory.

Does anyone of you have an explanation for this?

My observations are DTOA: difference in time of Arrival (they have been linearized).

I am trying to use Least Squares with a linear model: Y = Ax + b, where Y are the observed measurements (DTOA), A the design matrix, b is the known terms vector and X is a vector of estimates. The algorithm processes data according to the epoch considered and iterate the process up to a value of 20 times, unless it reaches before a 1mm convergence.

Since it is an iterative process, the system requires an initialization at the starting point with approximated values for the unknowns, and here comes my problem: if I initialize the starting point with coordinates within the polygon formed by the five stations convergence is reached and the solution is successful, but if I initialize the point with coordinates outside the area formed by the stations the convergence is not reached and I’m not able to determine the trajectory.

Does anyone of you have an explanation for this?