Distributed Optimal Estimation from Relative Measurements for Localization and Time Synchronization

Abstract

Abstract.We consider the problem of estimating vector-valued variables from noisy "relative" measurements. The measurement model can be expressed in terms of a graph, whose nodes correspond to the variables being estimated and the edges to noisy measurements of the difference between the two variables. This type of measurement model appears in several sensor network problems, such as sensor localization and time synchronization. We consider the optimal estimate for the unknown variables obtained by applying the classical Best Linear Unbiased Estimator, which achieves the minimum variance among all linear unbiased estimators.We propose a new algorithm to compute the optimal estimate in an iterative manner, the Overlapping Subgraph Estimator algorithm. The algorithm is distributed, asynchronous, robust to temporary communication failures, and is guaranteed to converges to the optimal estimate even with temporary communication failures. Simulations for a realistic example show that the algorithm can reduce energy consumption by a factor of two compared to previous algorithms, while achieving the same accuracy.

Estimation From Relative Measurements: Electrical Analogy and Large Graphs

“…The problem of interest is to estimate the node variables from all the available measurements. This estimation problem is relevant to several sensor and multi-agent network applications, such as localization with noisy distance and angle measurement [1][2][3], time-synchronization [2,4,5] and motioncoordination [6]; see [6,7] for an overview. The estimation problem we study is an instance of a general class of parameter estimation problems in sensor networks called selfcalibration [3,8].…”

“…On the positive side, this simplifies the construction of estimation algorithms in large-scale networks because it justifies considering a relatively small subset of measurements. Distributed algorithms to estimate the node variables from relative measurements have been examined in [2,7] in which nodes with embedded processing and communication capability estimates their variables by local computation and communication. Although the algorithms in [2,7] were developed for finite graphs, in a large graph these algorithms may take a long time to provide accurate estimates, since the information about all the available measurements are fused iteratively to determine the estimates.…”

“…Distributed algorithms to estimate the node variables from relative measurements have been examined in [2,7] in which nodes with embedded processing and communication capability estimates their variables by local computation and communication. Although the algorithms in [2,7] were developed for finite graphs, in a large graph these algorithms may take a long time to provide accurate estimates, since the information about all the available measurements are fused iteratively to determine the estimates. The results of this paper suggest that it may be possible to devise algorithms such that they obtain estimates quite fast, while sacrificing little accuracy.…”

Multi-agent localization from noisy relative pose measurements

“…Recalling that P z θ is a diagonal matrix, then each variablê θ i (t) asymptotically converges to the i-th entry [θ] i of the vectorθ in (3) [14], [16] that would be computed by a centralized system.…”

“…By operating with AP −1 δ δ and AP −1 δ A T , it can be seen that (11) is the i − th row of (16). The system (16) converges toθ, and equivalently each θ i (t) in (11) converges to [θ] i for i ∈ {2, .…”