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

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 technical note, 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.