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Temperature Drift and Compensation Method of FOG Gyro

Fiber optic gyro (FOG) error modeling enhances precision by compensating for systematic and random noise, primarily using Allan variance analysis, Autoregressive (AR/ARMA) modeling, and thermal calibration . Key error sources include bias drift, scale factor instability, and thermal sensitivity, which are mitigated via Kalman filtering or neural networks to improve inertial navigation accuracy.

Key Components of FOG Error Modeling

Random Error Modeling (Stochastic): Methods include the Autoregressive (AR) model, Allan Variance (AVAR), and Dynamic Allan Variance (DAVAR) for capturing time-varying, stochastic behaviors.
Thermal Error Modeling (Deterministic): Because FOGs are sensitive to temperature, models are built using polynomial fitting or, for higher accuracy, by incorporating the temperature change rate (

$the fraction with numerator d cap T and denominator d t end-fraction$

) and its cross-terms to manage transient thermal effects during startup.
Scale Factor Error Modeling : Data-driven methods are used to model the scale factor's relationship with temperature and input angular rate.

Common Error Models & Methods

AR(2) Model & Kalman Filtering : Preprocessed FOG data is modeled using an autoregressive approach, which, combined with Kalman filtering, significantly reduces random noise (e.g., angle random walk and bias stability).
Thermal Deformation Model (TD-model): Integrates theoretical, physics-based formulas of thermal deformation with experimental data to predict and compensate for temperature-induced phase errors.
Neural Networks (RBF Network) : Radial Basis Function (RBF) neural networks are employed for high-precision, nonlinear compensation of gyro errors across a wide temperature range, significantly reducing mean square error.
Gyroscope Output Optimization : Modeling the angular velocity error (

$cap delta omega$

) rather than the raw output often yields better sensitivity and compensation results.

Common Noise Components (via Allan Variance)

Quantization Noise : High-frequency noise from digital sampling.
Angle Random Walk (ARW): White noise on angular rate.
Bias Instability (BI): Flicker noise, defining long-term stability.
Rate Random Walk (RRW): Random walk of the gyroscope bias.

Implementation Process

Data Acquisition: Collecting static FOG data across varying temperature conditions.
Preprocessing: Removing outliers and compensating for known mechanical, magnetic, or physical offsets.
Model Identification: Determining the order of the AR model using Akaike Information Criterion (AIC).
Filtering & Validation: Applying Kalman filters or machine learning to the data and validating with Allan variance.

Fiber Optic Gyroscope Random Error Modeling Based on Improved ...
Fiber Optic Gyroscope Random Error Modeling Based on Improved Kalman Filtering. ... A modeling method based on time series autoreg...

ACM Digital Library
Modeling Study on Random Error of Fiber Optic Gyro - Scientific.net

Scientific.net
Research on temperature error model of fiber optic gyroscope ...
The polynomial temperature modeling method commonly used in engineering for FOGs is applicable to medium and low-precision FOGs. H...

SPIE Digital Library

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Error Modeling of Fiber Optic Gyroscope Universal Time ...

MDPI

https://www.mdpi.com › ...

MDPI

https://www.mdpi.com › ...

by Z Wang 2024 — In this paper, the errors caused by various physical factors and mechanisms are analyzed in detail, with precession and nutation errors being taken into ... Read more

Fiber Optic Gyroscope Random Error Modeling Based on ...

ACM Digital Library

https://dl.acm.org › doi › abs

ACM Digital Library

https://dl.acm.org › doi › abs

by Y Liu 2022 Cited by 1 — A modeling method based on time series autoregressive model (AR) is proposed to address the problem of the existence of random errors in fiber optic gyroscopes. Read more

Modeling and Prediction of Thermal Deformation Errors in ...

National Institutes of Health (NIH) | (.gov)

https://pmc.ncbi.nlm.nih.gov › articles › PMC10708615

National Institutes of Health (NIH) | (.gov)

https://pmc.ncbi.nlm.nih.gov › articles › PMC10708615

by J Xu 2023 Cited by 3 — For a fiber optic gyroscope , thermal deformation of the fiber coil can introduce additional thermal-induced phase errors, commonly referred ...

Research on modeling and compensation method of fiber ...

IEEE Xplore

http://ieeexplore.ieee.org › document

IEEE Xplore

http://ieeexplore.ieee.org › document

The results of simulation shows that: Kalman filter, which bases on AR (3) model , can effectively eliminate random noise and compensate the FOG' random error . Read more

A laser-driven fiber-optic gyroscope for inertial guidance of ...

Stanford University

https://purl.stanford.edu › ...

Stanford University

https://purl.stanford.edu › ...

In this thesis, we develop a new analytical model that derives the error in an aircraft's position from a gyroscope's known noise and drift, inferred from a ... Read more

Modeling of bias errors in fiber optic gyroscopes with new ...

Harvard University

https://ui.adsabs.harvard.edu › abs › abstract

Harvard University

https://ui.adsabs.harvard.edu › abs › abstract

by C Seidel 2004 Cited by 5 — It allows for the first time to model the FOG signal quantitatively considering temperature dependence, light source parameters and all perturbations and ... Read more

An Optical Signal Processing Model for the Interferometric ...

RAND

https://www.rand.org › pubs › MR482.1.pdf

RAND

https://www.rand.org › pubs › MR482.1.pdf

PDF

by AO Signal 1995 — This report presents a mathematical model for analyzing the optical signal processing employed by closed-loop interferometric fiber op- tic gyroscopes (IFOG) ... Read more

Fiber optic gyro (FOG) scale factor modelling method ...

Google Patents

https://patents.google.com › patent

Google Patents

https://patents.google.com › patent

The present invention relates to a modeling method of optical fiber gyroscope scale factor based on temperature and input angular rate, comprising the ...

Research on temperature error model of fiber optic ...

SPIE Digital Library

https://www.spiedigitallibrary.org › 12.3091364.pdf

SPIE Digital Library

https://www.spiedigitallibrary.org › 12.3091364.pdf

by L Yan 2025 — This paper conducts a study on the temperature error model of. FOG, and establishes a quadratic model of gyro drift in relation to temperature, temperature ... Read more

(PDF) Unified Gyro Error Model

Academia.edu

https://www.academia.edu › Unified_Gyro_Error_Model