Q2. What is the way to solve the localization problem?
When full-position measurements are available, the localization problem becomes linear and can thus be solved by using linear optimization methods [10–12].
Q3. What is the value of the block-trace of a matrix?
The block-trace of a matrix defined by blocks P = [Pij ] with i, j ∈ {1, . . . , n} is the sum of its diagonal blocks, blkTr(P ) = ∑ni=1 Piitrace of the block-trace of a matrix A is equal to its trace, Tr(blkTr(A)) = Tr(A).
Q4. What is the interest of the presented algorithm?
The interest of the presented algorithm is that the states are estimated relative to the centroid, instead of relative to an anchor.
Q5. What is the simplest way to estimate the state of a block?
The anchor-based estimation is carried out with the Jacobi algorithm and the authors give theoretical and experimental proofs of convergence for general block diagonal covariance matrices.
Q6. What is the important factor in the estimation of the results?
Its placement influences the accuracy of the final results, and the estimation errors at the agents are usually analyzed as a function of their distances to the anchor [18].
Q7. What is the Jacobi method for solving a relative noise?
the authors would like their algorithm to be applicable to a wider case of relative noises, in particular to independent noises, with not necessarily diagonal or equal covariance matrices.
Q8. How many agents are used as anchors?
The authors study the performance of the presented algorithm in a planar multiagent localization scenario (Fig. 1) with n = 20 agents (circles) that get noisy measurements (crosses and ellipses) of the position of agents which are closer than 4 meters.
Q9. how does the Jacobi method compute a solution for xaVa?
The Jacobi method [19] iteratively computes a solution for x̂aVa = D −1N x̂aVa + D −1η, by initializing a variable x̂aVa(t) ∈ R(n−1)p with an arbitrary value x̂aVa(0), and updating it at each step t with the following rule,x̂aVa(t+ 1) = D −1N x̂aVa(t) +D −1η.