Estimating Global Relative Position and Orientation With Local Relative Position Measurements

Estimating the global relative position and orientation of agents is a critical task for navigation in GNSS-denied environments. This paper proposes a simple yet efficient and robust method to solve this problem in 2D space using only sparse local relative position measurements. First, we derive a complex linear model to characterize the relationship of position, orientation, and measurements of all agents. Then, for the estimation problem, we establish a broadly applicable uniqueness condition that is robust against measurement noise. Further, we develop a nonlinear least-squares method based on variable separation. and its distributed version to solve the estimation problem with guaranteed local convergence. Simulations verify that the uniqueness condition can be easily checked under noise, and both methods can accurately estimate the global relative position and orientation of agents after several iterations.