Estimation Problems in Hybrid Systems
Estimation Problems in Hybrid Systems
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In this article, the problem of estimating the state of a discretized hyperbolic scalar partial differential equation is studied. The discretization of the Lighthill-Whitham-Richards equation with a triangular flux function using the Godunov scheme is shown to lead to a hybrid linear system or Switched Linear Systems (SLS) with a number of modes exponential in the size of the discretized model. Some geometric properties of the partition of the space into polyhedra (in which a mode is active) are exploited to find heuristics to reduce the number of modes to a representative set. This motivates a new approach inspired from a well established technique for hybrid system estimation, namely the interactive multiple model (IMM). qThe performance of this new variant of the IMM is compared to the extended Kalman filter and the ensemble Kalman filter using the Mobile Millennium data set.