### Abstract

We consider the identification of linear models from quantized output data. We develop a variational approximation of the likelihood function which allows us to find variationally-optimal approximations of the maximum likelihood and maximum-a-posteriori estimates. We show that these estimates are obtained by projecting the mid-point in the quantization interval of each output measurement onto the column space of the input regression matrix. Interpreting the quantized output as a random variable, we derive its moments for generic noise distributions. For the case of Gaussian noise and Gaussian i.i.d. input, we give an analytical characterization of the bias which we use to build a bias-compensation scheme that leads to consistent estimates.

Language | English |
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Journal | IEEE Transactions on Automatic Control |

DOIs | |

State | Accepted/In press - 14 Aug 2019 |

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### Cite this

*IEEE Transactions on Automatic Control*. DOI: 10.1109/TAC.2019.2933134

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*IEEE Transactions on Automatic Control*. DOI: 10.1109/TAC.2019.2933134

**Identification of linear models from quantized data : a midpoint-projection approach.** / Risuleo, Riccardo Sven; Bottegal, Giulio; Hjalmarsson, Hakan.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Identification of linear models from quantized data

T2 - IEEE Transactions on Automatic Control

AU - Risuleo,Riccardo Sven

AU - Bottegal,Giulio

AU - Hjalmarsson,Hakan

PY - 2019/8/14

Y1 - 2019/8/14

N2 - We consider the identification of linear models from quantized output data. We develop a variational approximation of the likelihood function which allows us to find variationally-optimal approximations of the maximum likelihood and maximum-a-posteriori estimates. We show that these estimates are obtained by projecting the mid-point in the quantization interval of each output measurement onto the column space of the input regression matrix. Interpreting the quantized output as a random variable, we derive its moments for generic noise distributions. For the case of Gaussian noise and Gaussian i.i.d. input, we give an analytical characterization of the bias which we use to build a bias-compensation scheme that leads to consistent estimates.

AB - We consider the identification of linear models from quantized output data. We develop a variational approximation of the likelihood function which allows us to find variationally-optimal approximations of the maximum likelihood and maximum-a-posteriori estimates. We show that these estimates are obtained by projecting the mid-point in the quantization interval of each output measurement onto the column space of the input regression matrix. Interpreting the quantized output as a random variable, we derive its moments for generic noise distributions. For the case of Gaussian noise and Gaussian i.i.d. input, we give an analytical characterization of the bias which we use to build a bias-compensation scheme that leads to consistent estimates.

UR - http://www.scopus.com/inward/record.url?scp=85071033756&partnerID=8YFLogxK

U2 - 10.1109/TAC.2019.2933134

DO - 10.1109/TAC.2019.2933134

M3 - Article

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

ER -