Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A generalized state space representation of a dynamical system with random modes is presented. The new formulation includes a term, in the dynamics equation, which depends on the most recent state's linear minimum mean squared error (LMMSE) estimate. This can be used to model the behavior of a feedback control system featuring a state estimator. The measurement equation is allod to depend on the previous LMMSE estimate of the state, which can be used to represent the fact that measurements are obtained from a validation window centered at the predicted measurement and not from the entire surveillance region. The matrices comprising the system's mode constitute an independent stochastic process. The proposed formulation generalizes several problems considered in the past, and allows a unified modeling of new ones. The LMMSE optimal filter is derived for the considered problem. The approach is demonstrated in the context of target tracking in clutter and is shown to yield performance that is competitive to that of several popular nonlinear methods.
['Daniel Sigalov', 'Tomer Michaeli', 'Yaakov Oshman']
I am writing a research paper on a idea Linear Optimal Estimation in Feedback Hybrid Systems with Application to Tracking in Clutter
[{"from": "human", "value": "I am writing a research paper on a idea Linear Optimal Estimation in Feedback Hybrid Systems with Application to Tracking in Clutter"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A generalized state space representation of a dynamical system with random modes is presented. The new formulation includes a term, in the dynamics equation, which depends on the most recent state's linear minimum mean squared error (LMMSE) estimate. This can be used to model the behavior of a feedback control system featuring a state estimator. The measurement equation is allod to depend on the previous LMMSE estimate of the state, which can be used to represent the fact that measurements are obtained from a validation window centered at the predicted measurement and not from the entire surveillance region. The matrices comprising the system's mode constitute an independent stochastic process. The proposed formulation generalizes several problems considered in the past, and allows a unified modeling of new ones. The LMMSE optimal filter is derived for the considered problem. The approach is demonstrated in the context of target tracking in clutter and is shown to yield performance that is competitive to that of several popular nonlinear methods."}]