Estimation for air combat games with unknown enemy inputs

In a typical application of Kalman filtering, the filter receives the output observation of the system and the control inputs to the system and produces an estimate of the state of the system. In an air combat game, it is unreasonable to assume that direct information about the enemy's inputs are available. Hence, a straightforward application of filtering does not work. In this paper, two different approaches are presented in estimating the states of friendly as well as enemy forces based on the output observation and the friendly control inputs when the enemy inputs are not available. Stochastic simulations are carried out in the context of a game-theoretic feedback controller and compare their performance under noise. The two methods are the Kalman filter and the unknown input-decoupling observer. The Kalman filter treats the enemy inputs as part of the extended state and obtains an estimate of both the state of the two forces and the input of the enemy. Because the filter was originally designed for a linear time-invariant system, an extension of the filter is presented to a nonlinear time-variant system. Unlike the Kalman filter, the input-decoupling observer does not need to estimate the unknown inputs. Rather, the observer is designed to decouple the unknown inputs from the estimate of the state so that the state estimate is insensitive to the enemy inputs.