Abstract: A method for providing an extended propagation ephemeris model for a satellite in Earth orbit, the method includes obtaining a satellite's orbital position over a first period of time, applying a least square estimation filter to determine coefficients defining osculating Keplarian orbital elements and harmonic perturbation parameters associated with a coordinate system defining an extended propagation ephemeris model that can be used to estimate the satellite's position during the first period, wherein the osculating Keplarian orbital elements include semi-major axis of the satellite (a), eccentricity of the satellite (e), inclination of the satellite (i), right ascension of ascending node of the satellite (?), true anomaly (?*), and argument of periapsis (?), applying the least square estimation filter to determine a dominant frequency of the true anomaly, and applying a Fourier transform to determine dominant frequencies of the harmonic perturbation parameters.

Abstract: A method of acquiring a signal includes generating a first set of acquired signal power values comprising an acquired signal power value for each of a plurality of Doppler bins over a first predetection integration time (PIT) interval, and generating a second set of acquired signal power values comprising an acquired signal power value for each of the plurality of Doppler bins over a second subsequent PIT interval. The first and the second sets are used to generate at least three additional sets of acquired signal power values. A new set is generated by selecting the maximum of the summations for each Doppler bin from the three additional sets, and a Doppler shift is identified from the Doppler bin having the maximum summation value. The output may be used to initialize a first and a second extended Kalman filters for tracking a carrier signal and a code signal, respectively.

Abstract: A method for providing an extended propagation ephemeris model for a satellite in Earth orbit, the method includes obtaining a satellite's orbital position over a first period of time, applying a least square estimation filter to determine coefficients defining osculating Keplarian orbital elements and harmonic perturbation parameters associated with a coordinate system defining an extended propagation ephemeris model that can be used to estimate the satellite's position during the first period, wherein the osculating Keplarian orbital elements include semi-major axis of the satellite (a), eccentricity of the satellite (e), inclination of the satellite (i), right ascension of ascending node of the satellite (?), true anomaly (?*), and argument of periapsis (?), applying the least square estimation filter to determine a dominant frequency of the true anomaly, and applying a Fourier transform to determine dominant frequencies of the harmonic perturbation parameters.