This paper addresses the problem of estimating the states of a group of agents from noisy measurements of pairwise differences between agents' states. The agents can be viewed as nodes in a graph and the relative measurements between agents as the graph's edges. We propose a new distributed algorithm that exploits the existence of cycles in the graph to compute the best linear state estimates. For large graphs, the new algorithm significantly reduces the total number of message exchanges that are needed to obtain an optimal estimate. We show that the new algorithm is guaranteed to converge for planar graphs and provide explicit formulas for its converge rate for regular lattices.

Target tracking typically refers to the problem of determining the position of a mobile agent based on a stream of noisy measurements. Here, we are interested in the problem of estimating the trajectory of a mobile agent based on noisy measurements collected by a team of autonomous vehicles-a problem that is relevant to applications such as surveillance, disaster relief, and scientific exploration. Even small mobile agents typically have access to a multitude of sensing modalities capable of providing position information. When available, GPS provides information about the position of the agent carrying the GPS antenna in a earth-fixed coordinate system. Inertial Measurement Units (IMUs) or/and vision sensors (Borenstein et al., 1997; Nistér et al., 2004; Olson et al., 2003) can provide measurements of the relative position of an agent across time. However, since these measurements are noisy, their integration over time typically leads to high rates of error growth (Olson et al., 2003; Makadia & Daniilidis, 2005; Oskiper et al., 2007). Several sensors are also capable of providing measurements regarding relative positions between agents. These include vision-based sensors such as cameras and light detection and ranging sensors (LIDARs), or RF sensors using angle of arrival (AoA) and time difference of arrival (TDoA) measurements. The problem of fusing measurements regarding relative positions between mobile agents for estimating their locations is commonly known as cooperative localization in the robotics literature (Kurazume et al., 1994; Rekleitis et al., 2002; Mourikis & Roumeliotis, 2006). The use of a group of mobile agents to track a mobile target can result in low estimation errors, even

We address the problem of estimating the state of a multi-agent system based on measurements corrupted by impulsive noise and whose dynamics are subject to impulsive disturbances. The qualifier "impulsive" refers to the fact that noise and disturbances are relatively small most of the time, but occasionally take large values. Noise and disturbances are modeled as mixtures of Gaussian and a Laplacian processes, leading to a maximum likelihood estimator that can be computed by solving a convex sum-of-norms optimization that can be solved online very efficiently. The approach has been validated both in simulation using synthetic data and in real hardware using a team of Unmanned Air Vehicles (UAVs) equipped with an onboard video cameras, inertial sensors, and GPS to cooperatively geolocate and track a ground-moving target agent.

This paper addresses the problem of estimating the states of a group of agents from noisy measurements of pairwise differences between agents' states. The agents can be viewed as nodes in a graph and the relative measurements between agents as the graph's edges. We propose a new distributed algorithm that exploits the existence of cycles in the graph to compute the best linear state estimates. For large graphs, the new algorithm significantly reduces the total number of message exchanges that are needed to obtain an optimal estimate. We show that the new algorithm is guaranteed to converge for planar graphs and provide explicit formulas for its convergence rate for regular lattices.