Estimation algorithm for stochastic linear hybrid systems with quadratic guard conditions

The hybrid estimation problem involves computation of both the continuous state and the discrete state estimates of a hybrid system from the measurements. In our earlier work, we have developed an algorithm, called the State-Dependent-Transition Hybrid Estimation (STDHE) algorithm which treats the discrete-state transitions to be dependent on the continuous state and governed by guard conditions in the linear form. This paper presents a hybrid estimation algorithm for the hybrid system whose guard conditions are in the quadratic form. The algorithm finds its applications in many areas such as Air Traffic Control (ATC), unmanned aerial vehicles coordination and control, and robot control. Simulation results show that our algorithm gives high estimation accuracy similar to that given by the Monte Carlo integration-based estimation algorithm while it is much more computationally efficient than the sample-based algorithms.