I need to estimate the coordinate of a source, denoted as $x \in \mathbb R^3$. To do this, I deploy one reference node and $n$ other nodes. The coordinates of the reference node $a_0 \in \mathbb R^3$ and the other nodes $a_i \in \mathbb R^3, i=1,\ldots,n$ are known. And I have the following range difference measurement model: $$ d_i=\|a_i-x\|-\|a_0-x\|+r_i,i=1,\ldots,n, $$ where $d_i$ is the range difference measurement and $r_i$ is the i.i.d. gaussian noise whose mean is $0$ and variance is $\sigma^2$.
Suppose I have an unbiased estimator $\hat x=\phi(a_0,a_1,\ldots,a_n,d_1,\ldots,d_n)$, I want to know how to calculate the Cramer-Rao lower bound of this estimator, i.e., the lower bound of the variance $E(\|\hat x-x\|^2)$ of the unbiased estimator.
Thanks!