Algorithm 3 Recursive clock parameter estimator

1:Previous time records:  $\{x_N,y_N\}=\{C_1\left(t_N\right),C_2\left(t_N\right)\}$ Previous sum parameter:  $\mathrm{\Phi }$ Input:  $\{x_{N+1},y_{N+1}\}=\{C_1\left(t_{N+1}\right),C_2\left(t_{N+1}\right)\}$ Output:  ${\hat{\tau }}_{12}$, ${\hat{\alpha }}_{12}$ Parameters:  $\lambda$ 2: Update the sum parameter $\mathrm{\Phi }\leftarrow \lambda \mathrm{\Phi }+\frac{{(x_{N+1}-x_N)}^2}{y_{N+1}-y_N}$ 3: Update the clock skew ${\hat{\alpha }}_{12}\leftarrow {\hat{\alpha }}_{12}+\frac{x_{N+1}-x_N}{\mathrm{\Phi }}\left(1-{\hat{\alpha }}_{12}\frac{x_{N+1}-x_N}{y_{N+1}-y_N}\right)$ 4: Calculate the time-offset ${\hat{\tau }}_{12}\leftarrow y_{N+1}-{\hat{\alpha }}_{12}{x}_{N+1}$ 5: Save the time records $\{x_N,y_N\}\leftarrow \{x_{N+1},y_{N+1}\}$ 6:return${\hat{\alpha }}_{12}$ and ${\hat{\tau }}_{12}$