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Stochastic Sensor Calibration

This project develops statistical methods and software for modeling the stochastic error structure of inertial sensors, GNSS receivers, and related navigation devices. The central goal is to move beyond ad hoc calibration rules by using wavelet-based representations of sensor noise, robust estimation, and principled model selection to identify error processes that can be used reliably in downstream navigation filters.

Much of this work is built around the generalized method of wavelet moments and its multivariate and multi-signal extensions. These methods use the scale-wise behavior of sensor errors to estimate latent stochastic models efficiently, even when several error sources are superposed or when the data contain outliers. The resulting tools are designed for practical calibration settings: low-cost MEMS IMUs, repeated calibration runs, redundant gyroscope configurations, vibration-contaminated measurements, and online calibration platforms.

The project also studies the limits of commonly used approaches. In particular, work on Allan variance-based regression clarifies when classical engineering procedures can be statistically inconsistent, while the later wavelet-based frameworks provide computationally efficient alternatives for automatic model identification, calibration, and uncertainty-aware signal reconstruction.

Selected related publications include:

  • Automatic Identification and Calibration of Stochastic Parameters in Inertial Sensors
  • An Algorithm for Automatic Inertial Sensors Calibration
  • Theoretical Limitations of Allan Variance-based Regression for Time Series Model Estimation
  • Wavelet-Based Improvements for Inertial Sensor Error Modeling
  • A Computationally Efficient Framework for Automatic Inertial Sensor Calibration
  • A Multisignal Wavelet Variance-Based Framework for Inertial Sensor Stochastic Error Modeling
  • Multivariate Signal Modeling With Applications to Inertial Sensor Calibration
  • Multi-Signal Approaches for Repeated Sampling Schemes in Inertial Sensor Calibration
  • Accounting for Vibration Noise in Stochastic Measurement Errors of Inertial Sensors
Robust Statistics Signal Processing Applied Statistics
Roberto Molinari
Assistant Professor in Statistics

My research interests include robust statistics, signal processing, model selection and differential privacy.

Publications

IEEE Transactions on Signal Processing, 72, 2117–2129
This publication contributes to work in signal processing, with a focus reflected in its title: Accounting for Vibration Noise in Stochastic Measurement Errors of Inertial Sensors.
Project

arXiv preprint arXiv:2303.18167
This publication contributes to work in signal processing, with a focus reflected in its title: Accounting for Vibration Noise in Stochastic Measurement Errors.
Project

Sensor calibration is usually performed only on one error signal although calibration sessions often collect repeated samples. This work formally puts forward and studies adequate solutions to consider all replicates to improve predictive accuracy.
Project Link to paper

IEEE Transactions on Instrumentation and Measurement
This work compares current moment-matching techniques used to calibrate inertial sensors and identifies the optimal technique from a theoretical (and applied) perspective
Project Link to paper

IEEE Transactions on Signal Processing
Low-cost inertial sensors are increasingly being used jointly in order to improve their navigation performance and this work provides a computationally feasible solution to solve these complex problems
Project Link to paper

IEEE Transactions on Instrumentation and Measurement
This work combines the information from multiple signals to improve the estimation of stochastic model estimation for sensor calibration
Project

IEEE Aerospace and Electronic Systems Magazine, 33, (8), 30–36
This publication contributes to work in signal processing, with a focus reflected in its title: Use of a New Online Calibration Platform With Applications to Inertial Sensors.
Project

2018 IEEE/ION Position, Location and Navigation Symposium (PLANS), 534–540
This publication contributes to work in applied statistics, signal processing, with a focus reflected in its title: A Two-Step Computationally Efficient Procedure for IMU Classification and Calibration.
Project

2018 IEEE/ION Position, Location and Navigation Symposium (PLANS), 1342–1350
This publication contributes to work in signal processing, with a focus reflected in its title: An Optimal Virtual Inertial Sensor Framework Using Wavelet Cross Covariance.
Project

2018 IEEE/ION Position, Location and Navigation Symposium (PLANS), 108–117
This publication contributes to work in signal processing, with a focus reflected in its title: Improved Stochastic Modelling of Low-Cost GNSS Receivers Positioning Errors.
Project

IEEE Sensors Journal
This paper introduces a robust, user-friendly R-based software platform using the generalized method of wavelet moments for efficient and statistically sound calibration of stochastic errors in inertial sensors, even with outlier-affected data
Project Link to paper

Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), 3028–3038
This publication contributes to work in signal processing, with a focus reflected in its title: A Computational Multivariate-Based Technique for Inertial Sensor Calibration.
Project

Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), 3053–3060
This publication contributes to work in signal processing, with a focus reflected in its title: An Automatic Calibration Approach for the Stochastic Parameters of Inertial Sensors.
Project

This work generalizes the theoretical form of Allan variance to include nonstationary processes, enabling more accurate interpretation and noise pattern detection in both stationary and nonstationary cases
Project Link to paper

2017 IEEE International Workshop on Metrology for AeroSpace (MetroAeroSpace), 364–368
This publication contributes to work in signal processing, with a focus reflected in its title: An Overview of a New Sensor Calibration Platform.
Project

IEEE Transactions on Instrumentation and Measurement
This paper enhances the Generalized Method of Wavelet Moments (GMWM) for parametric estimation of stochastic error signals by incorporating model moments, improving its statistical efficiency and finite sample performance to rival maximum likelihood estimation, with demonstrated benefits in inertial sensor calibration
Project Link to paper

IEEE Sensors Journal
This work discusses issues with maximum likelihood identification of inertial sensor noise model parameters
Project Link to paper

IEEE Signal Processing Letters
This work formally proves the statistical inconsistency of Allan variance-based parameter estimation for latent models, highlighting its limitations, especially in inertial sensor calibration, and contrasting it with a statistically sound alternative
Project Link to paper

2015 International Association of Institutes of Navigation World Congress (IAIN), 1–4
This publication contributes to work in applied statistics, signal processing, model selection, with a focus reflected in its title: An Inertial Sensor Calibration Platform to Estimate and Select Error Models.
Project

Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015), 1998–2002
This publication contributes to work in applied statistics, signal processing, with a focus reflected in its title: A Computationally Efficient Platform for Inertial Sensor Calibration.
Project

Proceedings of the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2015), 2003–2006
This publication contributes to work in applied statistics, signal processing, model selection, with a focus reflected in its title: Automatic and Computationally Efficient Method for Model Selection in Inertial Sensor Calibration.
Project

Navigation: Journal of The Institute of Navigation
An algorithm based on the Generalized Method of Wavelet Moments (GMWM) is presented for identifying the nature and parameters of stochastic processes in time series, enabling automatic model selection and ranking, with applications demonstrated for low-cost MEMS IMUs
Project Link to paper

2014 IEEE/ION Position, Location and Navigation Symposium - PLANS 2014, 1227–1231
This publication contributes to work in signal processing, with a focus reflected in its title: Study of MEMS-Based Inertial Sensors Operating in Dynamic Conditions.
Project

Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), 1092–1097
This publication contributes to work in applied statistics, signal processing, with a focus reflected in its title: An Algorithm for Automatic Inertial Sensors Calibration.
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