Approximate Distributed Kalman Filtering for Cooperative Multi-agent Localization

Abstract

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

Optimal Estimation on the Graph Cycle Space

“…The update law (12) can be rewritten (15) where is the graph's weighted cycle degree matrix is the graph's weighted cycle adjacency matrix and is the vector of cycle discrepancy. Similarly, when the tension estimates are stacked into a single vector the update law corresponding to (13) can be expressed as (16) To represent the flagging process in a similar manner, we define the directed adjacency matrix of graph as if otherwise.…”

Distributed collaborative 3D pose estimation of robots from heterogeneous relative measurements: an optimization on manifold approach

“…When robots' absolute orientations are known, the problem of cooperative localization through pose graph optimization becomes a linear estimation problem (Sanderson, 1998;Barooah et al, 2010). The problem we consider, is however, non linear since orientations are not known.…”

Distributed Kalman Filtering

“…Other DKF applications can be seen in [335], [336], [338], [339] . [38], [39], [40], [41], [42], [43], [44], [105], [106], [109], [114], [119], [156], [179], [191], [197], [213], [214], [215], [216], [221], [233], [237] , [238] and [242]. [204] • Only the estimates at each Kalman update over-head are exchanged [205] • Analyzes the number of messages to exchange between successive updates in DKF [206] • Global Optimality of DKF fusion exactly equal to the corresponding centralized optimal Kalman filtering fusion [276] • A parallel and distributed state estimation structure developed from an hierarchical estimation structure [297] • A computational procedure to transform an hierarchical Kalman filter into a partially decentralized estimation structure [298] • Optimal DKF based on a-priori determination of measurements [300] 2.3.…”