Efficient and Guaranteed Planar Pose Graph optimization Using the Complex Number Representation In this paper, we present CPLSync, a certifiably correct algorithm to solve planar pose graph optimization (PGO) using the complex number representation. We formulate planar PGO as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to complex semidefinite programming (SDP). Furthermore, we simplify the corresponding semidefinite programming to Riemannian staircase optimization (RSO) on complex oblique manifolds that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through comparisons with existing methods as well as applications on planar PGO in simultaneous localization and mapping (SLAM), which indicates that the proposed algorithm is capable of solving planar PGO certifiably, and is more efficient in numerical computation and more robust to measurement noises than existing stateoftheart methods. The C code for CPLSync is available at https:github.comfantaoshaCPLSync.

On the Tunable Sparse Graph Solver for Pose Graph Optimization in Visual SLAM Problems We report a tunable sparse optimization solver that can trade a slight decrease in accuracy for significant speed improvement in pose graph optimization in visual simultaneous localization and mapping (vSLAM). The solver is designed for devices with significant computation and power constraints such as mobile phones or tablets. Two approaches have been combined in our design. The first is a graph pruning strategy by exploiting objective function structure to reduce the optimization problem size which further sparsifies the optimization problem. The second step is to accelerate each optimization iteration in solving increments for the gradientbased search in GaussNewton type optimization solver. We apply a modified Cholesky factorization and reuse the decomposition result from last iteration by using Cholesky updatedowndate to accelerate the computation. We have implemented our solver and tested it with open source data. The experimental results show that our solver can be twice as fast as the counterpart while maintaining a loss of less than 5% in accuracy.