Algorithm 1 Distributed Relative-Range Measurement Update
Input:	Range measurement and collaborating node state parametrized with the mean and the covariance: $\{z_k^R,{\widehat{x}}_k^c, cov(x_k^c,x_k^c)\}$
Output:	Local state posterior, $p(x_{k+1}|x_k,z_k^R)$, and cross-covariance, $cov(x_{k+1},x_{k+1}^c)$
1 for each particle $i$
2   Evaluate the conditional distribution, $p(x_k^c|x_k^i)$, Equations (13) and (14)
3   Evaluate the measurement likelihood, $p(z_k^R|x_k^i,x_k^c)$, Equation (7)
4   Evaluate the marginal likelihood: $p(z_k^R|x_k^i)=\int p(z_k^R|x_k^i,x_k^c)p(x_k^c|x_{1:k}^i,z_{1:k-1}^R)d{x}_k^c$
5   Evaluate $p(x_k^{c,i}|x_{1:k}^i,z_{1:k}^R)$, using RBPF formulation [49,50]
6   Evaluate particle weight: ${\tilde{w}}_k^i\propto w_{k-1}^i\times p(z_k^R|x_k^i)$
7   Time update step: $p(x_{k+1}^i|x_k^i,z_k^R)$ and $p(x_{k+1}^{c,i}|x_{1:k}^i,z_{1:k}^R)$
8 end for
9 Normalize the particle weights: $w_k^i={\tilde{w}}_k^i/{\displaystyle \sum }_i{\tilde{w}}_k^i$
10  Evaluate the mean and variance terms, ${\widehat{x}}_{k+1}$ and $cov(x_{k+1},x_{k+1})$, Equations (10) and (11).
11  Update state cross-covariance term: $cov(x_{k+1},x_{k+1}^c)$, Equation (12)
12  return $p(x_{k+1}|x_k,z_k^R)$ and $cov(x_{k+1},x_{k+1}^c)$