Lagrange Polynomial Fitting for Satellite Precise Ephemeris Data
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Lagrange polynomials serve as a fundamental mathematical tool for curve fitting between discrete data points. Satellite precise ephemeris provides accurate orbital position and velocity information, primarily utilized in navigation systems and geophysical research. The application of Lagrange polynomial fitting to satellite ephemeris data involves interpolating scattered position and velocity measurements into continuous smooth curves, thereby enhancing the accuracy and reliability of navigation solutions and scientific analyses. Implementation typically involves constructing basis polynomials for each data point using the formula L_i(x) = Π (x - x_j)/(x_i - x_j) where j≠i, and combining them through weighted summation. Key computational considerations include handling equidistant/non-equidistant nodes and implementing barycentric interpolation for optimal numerical stability when processing large ephemeris datasets.
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