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 a new 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 there is a trade-off between two desirable properties, accuracy and computational stability.