A Weighted Least-Squares Approach to Parameter Estimation Problems Based on Binary Measurements

Eric Colinet (1) , Jérôme Juillard (2)

1 DSYS - Département Systèmes
2 E3S - Supélec Sciences des Systèmes

We present a new approach to parameter estimation problems based on binary measurements, motivated by the need to add integrated low-cost self-test features to microfabricated devices. This approach is based on the use of original weighted least-squares criteria: as opposed to other existing methods, it requires no dithering signal and it does not rely on an approximation of the quantizer. In this paper, we focus on a simple choice for the weights and establish some asymptotical properties of the corresponding criterion. To achieve this, the assumption that the quantizer's input is Gaussian and centered is made. In this context, we prove that the proposed criterion is locally convex and that it is possible to use a simple gradient descent to find a consistent estimate of the unknown system parameters, regardless of the presence of measurement noise at the quantizer's input.

Keywords: FIR digital filters; parameter estimation; quantized observations; binary sensors; FIR digital filters.

Domains: Mathematics [math]; Optimization and Control [math.OC]; Engineering Sciences [physics]; Micro and nanotechnologies/Microelectronics; Engineering Sciences [physics]; Signal and Image processing; Computer Science [cs]; Signal and Image Processing

Eric Colinet, Jérôme Juillard. A Weighted Least-Squares Approach to Parameter Estimation Problems Based on Binary Measurements. IEEE Transactions on Automatic Control, 2010, 55 (1), pp.148-152. ⟨hal-00450295⟩