Algorithm 1. PC-MAPF-GM for scalar gravity matching navigation

Input: scalar gravity observations $z_{1:k}$, INS-predicted positions ${\widehat{p}}_{\mathrm{INS},k}$, INS displacement increments $\Delta s_k$, INS covariance $P_{\mathrm{INS},k}$, multi-scale gravity anomaly maps $M^{(1)},M^{(2)},\dots ,M^{(S)}$, particle number $N$, sequence length $L$. Output: corrected position estimate ${\widehat{p}}_k$.