This paper is concerned with the parameter estimation of deterministic autoregressive moving average (DARMA) systems with quantization data. The estimation algorithms adopted here are the least squares (LS) and the forgetting factor LS, and the signal quantizer is of uniform, that is, with uniform quantization error. The authors analyse the properties of the LS and the forgetting factor LS, and establish the boundedness of the estimation errors and a relationship of the estimation errors with the size of quantization error, which implies that the smaller the quantization error is, the smaller the estimation error is. A numerical example is given to demonstrate theorems. Keywords Discrete-time linear time-invariant systems, parameter estimation, quantized output.
Summary
This paper considers the estimates of parameters of stochastic autoregressive exogenous input (ARX) systems with quantized data. The quantized error caused by quantized data brings difficulties to the parameter estimation of ARX systems. Therefore, I start with the boundedness of quantized error and design the size of quantized error thanks to good properties of the least squares. Then the influences of the noise of the system itself and the bounded noise caused by quantized error on the parameter estimation error are analyzed, respectively. The inputs of the system are designed to make the system satisfy the persistent excitation condition, so as to ensure the boundedness of the parameter estimation error. A numerical example is given to demonstrate the theorem.
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