Hybrid systems consist of both continuous state evolutions and discrete state (or mode) transitions. In many hybrid systems, mode transitions are governed by guard conditions that are dependent on the continuous state. These kind of mode transitions can be described by continuous-state-dependent mode transition probabilities. However, most multiple model Kalman filter based algorithms, such as the well-known interacting multiple model (IMM) algorithm, assume constant mode transition probabilities. We propose a hybrid estimation algorithm based on the IMM approach for the stochastic hybrid systems with continuous-state-dependent transitions. We first develop two models to describe the guard conditions for various stochastic hybrid systems. From the models of the guard conditions, we derive the corresponding continuous-state-dependent mode transition probabilities, which are expressed in terms of Gaussian probability density functions (pdfs) or Gaussian cumulative density functions (cdfs). We then propose a hybrid estimation algorithm for the stochastic hybrid systems based on the IMM algorithm. Like the IMM algorithm, our algorithm utilizes Gaussian distributions to represent the continuous state pdfs which are updated analytically at each time step. We also use analytical integration methods to reduce the computational cost of updating the mode probabilities. As a result, the proposed algorithm is computationally efficient and is applicable to high-dimensional problems. The performance of the proposed algorithm is illustrated with two examples in air traffic control tracking applications.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    State Estimation for Stochastic Linear Hybrid Systems with Continuous-State-Dependent Transitions: An IMM Approach


    Contributors:


    Publication date :

    2009-01-01


    Size :

    1883375 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English





    Continuous‐Time Linear State Estimation

    Bar‐Shalom, Yaakov / Li, X.‐Rong / Kirubarajan, Thiagalingam | Wiley | 2002



    Probabilistic Estimation of State-Dependent Hybrid Mode Transitions for Aircraft Arrival Time Prediction AIAA Paper

    Huang, H. / Roy, K. / Tomlin, C. | British Library Conference Proceedings | 2007