many visual localization methods [@meer1991robust][@hartley2003multiple]. The advantage of RANSAC is the simplicity for implementation, and the effectiveness in many scenarios with moderate percentage of outliers. However, RANSAC cannot tolerate extreme percentage of outliers, say 90%. In addition, it cannot guarantee the deterministic global optimality due to the probabilistic convergence.

![The projected map points on the map image (left column) and the detected image key points on the query image (right column), with inlier correspondences in red and outliers in blue. The initial correspondences found by feature descriptor matching (top), and the consensus set correspondences searched by RANSAC (middle) and proposed consensus maximization algorithm (bottom). []{data-label="fig.overview"}](overview){width="50.00000%"}

In contrast to RANSAC, another solution to consensus maximization is global optimization based methods. It gives globally optimal solution without relying on an initial value [@brown2015globally][@campbell2017globally], while it cannot perform in real-time due to the considerable computation time. Most existing global optimization methods aim at general pose estimation problems. They employ branch-and-bound (BnB) as the basic framework to reduce the search space [@olsson2008branch], or mixed integer programming for further acceleration [@li2009consensus][@chin2016guaranteed]. But the computational cost is still unsatisfactory as the pose space $SE(3)$ is coupled. Even inertial measurement is provided, it cannot be easily substituted 