M

Now that the inverse of the line of sight unit matrix (L^-1) and the ECI matrix (R_ECI) of the observation location have been determined, we need to multiply them together to determine an intermediate matrix (M), some of whose components will be used to determine the coefficients that will be used to estimate the second geocentric radial distance of the satellite.

As a result, matrix multiplication will be required. The equation below shows exactly how the two matrices will be multiplied:

M = L^-1 R_ECI

More specifically, the individual components of the M matrix are provided by the following equations:

M₁₁ = (L^-1₁₁)(R_ECI11) + (L^-1₁₂)(R_ECI21) + (L^-1₁₃)(R_ECI31)
M₁₂ = (L^-1₁₁)(R_ECI12) + (L^-1₁₂)(R_ECI22) + (L^-1₁₃)(R_ECI32)
M₁₃ = (L^-1₁₁)(R_ECI13) + (L^-1₁₂)(R_ECI23) + (L^-1₁₃)(R_ECI33)
M₂₁ = (L^-1₂₁)(R_ECI11) + (L^-1₂₂)(R_ECI21) + (L^-1₂₃)(R_ECI31)
M₂₂ = (L^-1₂₁)(R_ECI12) + (L^-1₂₂)(R_ECI22) + (L^-1₂₃)(R_ECI32)
M₂₃ = (L^-1₂₁)(R_ECI13) + (L^-1₂₂)(R_ECI23) + (L^-1₂₃)(R_ECI33)
M₃₁ = (L^-1₃₁)(R_ECI11) + (L^-1₃₂)(R_ECI21) + (L^-1₃₃)(R_ECI31)
M₃₂ = (L^-1₃₁)(R_ECI12) + (L^-1₃₂)(R_ECI22) + (L^-1₃₃)(R_ECI32)
M₃₃ = (L^-1₃₁)(R_ECI13) + (L^-1₃₂)(R_ECI23) + (L^-1₃₃)(R_ECI33)

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