This work presents a methodology for real-time estimation of wildland fire growth, utilizing afire growth model based on a set of partial differential equations for prediction, and harnessing concepts of space-time Kalman filtering and Proper Orthogonal Decomposition techniques towards low dimensional estimation of potentially large spatio-temporal states. The estimation framework is discussed in its criticality towards potential applications such as forest fire surveillance with unmanned systems equipped with onboard sensor suites. The effectiveness of the estimation process is evaluated numerically over fire growth data simulated using a well-established fire growth model described by coupled partial differential equations. The methodology is shown to be fairly accurate in estimating spatio-temporal process states through noise-ridden measurements for real-time deploy ability.
This work presents a methodology for real-time estimation of wildland fire growth, utilizing a fire growth model based on a set of partial differential equations for prediction, and harnessing concepts of space-time Kalman filtering and Proper Orthogonal Decomposition techniques towards low dimensional estimation of potentially large spatio-temporal states. The estimation framework is discussed in its criticality towards potential applications such as forest fire surveillance with unmanned systems equipped with onboard sensor suites. The effectiveness of the estimation process is evaluated numerically over fire growth data simulated using a well-established fire growth model described by coupled partial differential equations. The methodology is shown to be fairly accurate in estimating spatio-temporal process states through noise-ridden measurements for real-time deployability.
The problem of assigning a group of Unmanned Aerial Vehicles (UAVs) to perform spatially distributed tasks often requires that the tasks will be performed as quickly as possible. This problem can be defined as the Min–Max Multiple Depots Vehicle Routing Problem (MMMDVRP), which is a benchmark combinatorial optimization problem. In this problem, UAVs are assigned to service tasks so that each task is serviced once and the goal is to minimize the longest tour performed by any UAV in its motion from its initial location (depot) to the tasks and back to the depot. This problem arises in many time-critical applications, e.g. mobile targets assigned to UAVs in a military context, wildfire fighting, and disaster relief efforts in civilian applications. In this work, we formulate the problem using Mixed Integer Linear Programming (MILP) and Binary Programming and show the scalability limitation of these formulations. To improve scalability, we propose a hierarchical market-based solution (MBS). Simulation results demonstrate the ability of the MBS to solve large scale problems and obtain better costs compared with other known heuristic solution.