Parameter estimation of systems subject to random state changes

Parameter estimation for a linear regression model subject to abrupt random state changes is formulated as an optimization problem. An identification algorithm comprising state regime classification and parameter identification is developed. The samples of the system are first partitioned into different groups called clusters, corresponding to different states. The standard linear-least-square method is then used to identify the parameters. The cluster control is a matrix of predetermined rank and can be computed by the singular-value-decomposition algorithm. Two iterative algorithms that ensure the decrease of the objective function are then proposed. An example is given to show the effectiveness of the method