Novel Results on Mode Estimation in Jump Systems

In a previous work a ν-modes estimator for a class of jump systems was developed using conditionally-linear (CL) filtering. Several additional results are provided in this work. A closed-form solution for the two-modes time-invariant deterministic case is obtained. Upper and lower bounds of the solution are found and a stability analysis is carried in the whole feasibility domain. A closed-form expression for a potential function is obtained in the three-modes case. In the ν-modes deterministic case, new stability regions are characterized, which lie in the interior of the feasibility domain. This shows that most of the modes are de-facto non-observable in the time-invariant deterministic case. A method that overcomes the convergence to the inner equilibrium points is introduced based on switching in the estimator’s parameters. The performances of the CL filter applied to noisy measurements in the time-varying case are analyzed via extensive numerical simulations. Non-dimensional driving parameters are defined such as a signal-to-noise ratio, a relative frequency of the estimator’s switching, and the false alarm or miss detection threshold. An application to gyro failure detection is presented. A central outcome of this study is the understanding that there is an optimum for the number of the estimator’s switches required for convergence, and that the presence of noises alleviates the need for switching.