Optimal 3-D Landmark Placement for Vehicle Localization Using Heterogeneous Sensors

Optimal placement of sensors or landmarks for the localization of an autonomous guided vehicle (AGV) based on range measurements is considered. The optimization relies on the Fisher information matrix (FIM). A closed-form expression of the FIM determinant is obtained for 2-D and 3-D spaces, considering heterogeneous sensors and distance-dependent ranging errors. Analytical bounds on the FIM determinant are derived, and several optimal landmark placement expressions for specific scenarios using two groups of landmarks are given. A minimax formulation for the optimal landmark placement is proposed and iteratively solved using exponential smoothing. There are several key features integrated into the proposed approach. These include 1) averaging of the cost function over elementary regions of the AGV search space to include the effect of the whole search space, 2) using a projected gradient search to stay within the boundaries of the landmark search space, and 3) searching on a convex space for placing the landmarks. Convergence issues of the proposed algorithm are discussed. Numerical results demonstrate that the proposed optimal landmark placement enables accurate AGV localization over significantly large volume or area of the search space compared with the case when landmarks are randomly placed.