Diffuse and specular brightness models applied to LEO satellites - Case study: The ONEWEB constellation

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Table 2

DEMC specifications.

	Stochastic random variables			Deterministic random variable	Likelihood of observations
DS Model	p	ζ	σ_demc,ds	µ_demc,ds	Y_obs
	U(0, 1)	U(0, 1)	HN(0, 1²)	DS function	$\begin{matrix} Y_obs \\ m_{s} - μ_{demc, ds} \sim N (0, σ_{demc,ds}^{2}) \end{matrix}$ $Mathematical equation: $\matrix{{{\rm{Y\_obs}}} \cr {{m_s} - {\mu _{{\rm{demc,ds}}}} \sim N(0,\sigma _{{\rm{demc,ds}}}^2)} \cr } $$

DSS Model	β	ζ	σ_demc,dss	µ_demc,dss	Y_obs
	U(0, 1)	U(0, 1)	HN(0, 1²)	DSS function	$\begin{matrix} Y_obs \\ m_{s} - μ_{demc, dss} \sim N (0, σ_{demc, dss}^{2}) \end{matrix}$ $Mathematical equation: $\matrix{{{\rm{Y\_obs}}} \cr {{m_s} - {\mu _{{\rm{demc, dss}}}} \sim N(0,\sigma _{{\rm{demc, dss}}}^2)} \cr } $$

RR Model	k	$H_{(70, 0)}^{1200}$ $Mathematical equation: $H_{(70,0)}^{1200}$$	σ_demc,rr	µ_demc,rr	Y_obs
	U(0, 1)	U(5, 12)	HN(0, 1²)	RR function	$\begin{matrix} Y_obs \\ H^{1200} - μ_{demc,rr} \sim N (0, σ_{demc,rr}^{2}) \end{matrix}$ $Mathematical equation: $\matrix{{{\rm{Y\_obs}}} \cr {{H^{1200}} - {\mu _{{\rm{demc,rr}}}} \sim N(0,\sigma _{{\rm{demc,rr}}}^2)} \cr } $$

Notes. For each model (first column), the prior distributions assumed for the parameters p and ζ, and magnitude noise (σ_demc) (second column), the function being fitted (third column), and the likelihood of the observations (last column). U, N, and HN mean uniform, normal, and half-normal distributions, respectively.

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