Optimal asynchronous multi-sensor registration in 3 dimensions

The success of multi-sensor data fusion requires an important step called sensor registration, which involves estimating sensor biases from sensors' asynchronous measurements. There are two difficulties in the bias estimation problem: one is the unknown target states which serve as the nuisance variables in the estimation problem, the other is the highly nonlinear coordinate transformation between sensors' local and common coordinate frames. In this work, we focus on the 3-dimensional scenario and propose a new nonlinear least squares (LS) formulation which avoids estimating target states. The proposed LS formulation eliminates the target states by exploiting the nearly-constant velocity property of the target motion. To address the intrinsic nonlinearity, we propose a block coordinate descent (BCD) scheme for solving the formulation which alternately updates various bias estimates. Specifically, semidefinite relaxation technique is introduced to handle the nonlinearity brought by angle biases. Furthermore, two BCD algorithms with different block picking rules are proposed. Finally, the effectiveness and the efficiency of the proposed BCD algorithms are demonstrated in the numerical simulation section.