Localization with TOA as a Constrained Robust Stochastic Least Squares Problem

Localizing a source given range measurements from base stations with fixed locations is a nonlinear optimization problem. A typical solution to such a problem is to run iterative algorithms which do not guarantee convergence or use maximum likelihood with grid searches. An alternative is then to transform the problem to anew one for which we know the solution is simple and computationally stable. We formulate the time-of-arrival base localization problem as a constrained robust stochastic least squares problem. While we can solve such problems efficiently The price paid for computational stability is positioning accuracy. Hence then is a trade-off between two desirable properties, accuracy and computational stability.