Algorithms for position fixing using pulse arrival times

A general equation covering the calculation of position in synchronous, hyperbolic and bistatic fixing systems is derived. It is shown that the least-squares estimate of position for this quadratic problem is the solution of a system of linear equations depending on a parameter which satisfies a polynomial. For small errors, setting the parameter to zero gives a good approximation to the optimum solution. It is shown that this solution is equivalent to a previously published suboptimum linear solution. The performance of a three-receiver system in two dimensions is used to demonstrate the results