Precise determination of orbital parameters in system with slowly drifting phases: application to the case of XTE J1807-294

We describe a timing technique that allows to obtain precise orbital parameters of an accreting millisecond pulsar in those cases in which intrinsic variations of the phase delays (caused e.g. by proper variation of the spin frequency) with characteristic timescale longer than the orbital period do not allow to fit the orbital parameters over a long observation (tens of days). We show under which conditions this method can be applied and show the results obtained applying this method to the 2003 outburst observed by RXTE of the accreting millisecond pulsar XTE J1807-294 which shows in its phase delays a non-negligible erratic behavior. We refined the orbital parameters of XTE J1807-294 using all the 90 days in which the pulsation is strongly detected and the method applicable. In this way we obtain the orbital parameters of the source with a precision more than one order of magnitude better than the previous available orbital solution, a precision obtained to date, on accreting millisecond pulsars, only for XTE J1807-294 analyzing several outbursts spanning over seven years and with a much better statistics.