Algorithm 1. Computational workflow of the proposed ARTSS

Input: Forward ESKF parameters: ${\widehat{x}}_{f,k|k-1}$, $P_{f,k|k-1}$, $P_{f,k}$, $H_k$, $R_k$, ${\Phi }_{k+1|k}$, and raw measurement $z_k$ Output: Smoothed states ${\widehat{x}}_{s,k}$ 1: For $k=N-1$ down to $0$ do 2:  Compute standard innovation and its covariance using Equations (17) and (18) 3:  Calculate element-wise standardized innovation ${\tilde{v}}_{k,i}$ using Equation (19) 4:  Construct diagonal equivalent weight matrix $B_k$ using Equation (20) with $c=1.345$ 5:  Reconstruct robust forward gain ${\overline{K}}_k$, state ${\overline{x}}_{f,k}$, and covariance ${\overline{P}}_{f,k}$ via Equations (21)–(23) 6:  Modulate smoothing gain $K_{s,k}$ via Equation (24) 7:  Update smoothed state ${\widehat{x}}_{s,k}$ via Equation (25) 8:  Apply 360-degree cross-period correction specifically to the heading angle error component (${\varphi }_U$) within the state vector ${\widehat{x}}_{s,k}$ to prevent angle wrap-around divergence:      If ${\varphi }_U>{180}^{°}$, then ${\varphi }_U={\varphi }_U-{360}^{°}$      If ${\varphi }_U<-{180}^{°}$, then ${\varphi }_U={\varphi }_U+{360}^{°}$ 9:  Update smoothed error covariance $P_{s,k}$ via Equation (26) 10: End For