A quantized order estimator

This paper considers the order estimation problem of stochastic autoregressive exogenous input (ARX) systems using quantized data. Based on the least squares algorithm and inspired by the control systems information criterion (CIC), a new kind of criterion and a new system order estimation algorithm are proposed for ARX systems with quantized data. When the upper bounds of the system orders are known and the persistent excitation condition is satisfied, the system order estimates given by this algorithm are shown to be consistent for a small quantization step. Furthermore, a concrete method is given for choosing quantization parameters to ensure that the system order estimates are consistent. A numerical example is given to demonstrate the effectiveness of the theoretical results of the paper.