In general satellites guidance laws control the mean motion rather than the osculating motion of the satellite. Applying an on board osculating motion guidance law demands greater fuel budgets, requires uploading high precision orbit propagator, and for most of the missions this type of guidance is not required. An autonomous satellite, which does not rely on data from the ground station as a measurement in it's guidance law, would have to have means to measure the instantaneous orbit and calculate the mean motion. This Paper discusses the issue of obtaining mean orbital elements from GPS measurements. The method is applied to the Venμs satellite. Venμs has an experimental plasma thruster and uses GPS position vector measurements for its onboard autonomous guidance law. The problem of onboard orbital elements averaging is addressed in this paper. A two phase algorithm is suggested in order to calculate the full set of six orbital mean elements from instantaneous position vector measurements. Each phase comprises of a low order, easy to implement extended Kalman filter. The first filter estimates osculating orbital elements from position vector measurements (e.g. GPS measurements), and the second filter uses apriori knowledge of the harmonics of the osculating elements in order to estimate the mean elements. The filter calculates the phase and amplitude of the first few harmonics of the osculating elements, so the frequencies of those harmonics have to be well known. The need to know the dominant harmonics is not an obstacle, since those harmonics are the result of the oblateness of the Earth and the applied thrust. The number of harmonics to be estimated is a function of the chosen orbital element set and it is a trade-off between algorithm complexity and the required accuracy. The advantage of using the suggested filter, rather than computing the mean orbital elements using Brouwer's analytical artificial satellite theory [2], is that the filter can respond to thrust and it is less sensitive to measurement noise since it uses state covariance.
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