A Learning-Based Approach for Bias Elimination in Low-Cost Gyroscopes Daniel Engelsman

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A Learning-Based Approach for Bias Elimination in

Low-Cost Gyroscopes

Daniel Engelsman

The Hatter Department of Marine Technologies

University of Haifa

Haifa, Israel

dengelsm@campus.haifa.ac.il

Itzik Klein, Senior Member, IEEE

The Hatter Department of Marine Technologies

University of Haifa

Haifa, Israel

kitzik@univ.haifa.ac.il

Abstract—Modern sensors play a pivotal role in many operat-

ing platforms, as they manage to track the platform dynamics at

a relatively low manufacturing costs. Their widespread use can

be found starting from autonomous vehicles, through tactical

platforms, and ending with household appliances in daily use.

Upon leaving the factory, the calibrated sensor starts accumulat-

ing different error sources which slowly wear out its precision

and reliability. To that end, periodic calibration is needed, to

restore intrinsic parameters and realign its readings with the

ground truth. While extensive analytic methods exist in the

literature, little is proposed using data-driven techniques and

their unprecedented approximation capabilities. In this study,

we show how bias elimination in low-cost gyroscopes can be

performed in considerably shorter operative time, using a unique

convolutional neural network structure. The strict constraints of

traditional methods are replaced by a learning-based regression

which spares the time-consuming averaging time, exhibiting

efﬁcient sifting of background noise from the actual bias.

Index Terms—Inertial Measurement Units, Gyroscopes, Cali-

bration, State Estimation, Deep Learning

I. INTRODUCTION

Inertial sensors are subjected to a wide range of measure-

ment errors which obscure the meaningful signal and degrade

their reliability. Uncalibrated sensors are characterized by out-

putting wrongful measurements, a phenomenon that worsens

when these quantities are integrated, to obtain the navigation

solution. These deviations can be corrected by low-pass ﬁlters

or state estimation algorithms (e.g. Kalman ﬁlters), however

knowledge of initial errors is required apriori, to prevent its

projection on other state variables. Noise reduction can be

obtained by averaging measurements from multiple IMUs,

and similarly, bias can be mitigated by subtracting opposite

polarities of an IMU pair, mounted on the same axis. However,

often this redundancy is not achievable or just not affordable,

thus calibration is inevitable, especially when platforms are

exclusively dependent on the sensor performance.

Calibration refers to the task of determining the relationship

between measurand outputs and their corresponding refer-

ences, which serve as ground-truth (GT) [1]. Following the

calculation procedure, the sensor intrinsic parameters can be

readjusted to minimize unwanted error sources, thus improving

its performance. Model-based approaches offer an in-depth

analysis of the error origins using different statistics and

signal processing tools [2], [3]. Given a new measurement,

the errors are identiﬁed and compensated, depending on how

well they align with the model. In ideal noise-free condi-

tions, a single time step is all that is required to determine

the null bias, by simply differencing the output from zero.

However realistically, minimum error is largely affected by

the averaging time period, as noise suppression exhibits a slow

error decay. This approach faces another obstacle when sterile

conditions cannot be met, as in real-time scenarios, when

platform is subjected to disruptions, giving rise to misesti-

mated parameters. Recently, data-driven approaches showed

superior performance over model-based methods in several

navigation related tasks [4]. For example, an end-to-end deep-

learning framework was shown to improve velocity estimation

of an autonomous underwater vehicle [5]. In pedestrian dead

reckoning, learning approaches outperform model-based ap-

proaches, offering better position accuracy [6], [7], and mode

classiﬁcation performance [8]. Recently, data-driven method

was driven for denoising of accelerometer readings [9].

Therefore, to solve the calibration problem, this paper

introduces a data-driven method, capable of estimating GT

biases using supervised learning approach. By doing so, we

show that: (i) non-linear estimators, i.e. convolutional neural

networks (CNN), can outperform linear model-based calibra-

tion (ii) the well-trained model can reduce averaging times

by one order of magnitude (iii) learnable parameters enhance

model robustness to non-stationary disturbances.

The rest of the paper is organized as follows: Section II

elaborates on the gyroscope error model, Section III describes

our strategy and the proposed solution, Section IV presents

analysis and results and Section V gives conclusions.

II. GYROSCOPE ERROR MODEL

Sensor errors are generally classiﬁed into two categories:

stochastic and deterministic sources. The ﬁrst type is unmod-

elable due to unknown origin, changes randomly between time

steps but overall variance remains constant when remeasured.

The second type is modelable, constant between time steps

but may vary when remeasured [10]. The linear relationship

between the gyro outputs ˜ωb

ib and the true angular rates ωb

ib,

contains both errors, and is commonly modeled as

˜ωb

ib =M ωb

ib +bg+wg(1)

arXiv:2210.04568v1 [eess.SP] 10 Oct 2022

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ALearning-BasedApproachforBiasEliminationinLow-CostGyroscopesDanielEngelsmanTheHatterDepartmentofMarineTechnologiesUniversityofHaifaHaifa,Israeldengelsm@campus.haifa.ac.ilItzikKlein,SeniorMember,IEEETheHatterDepartmentofMarineTechnologiesUniversityofHaifaHaifa,Israelkitzik@univ.haifa.ac.ilAbstractM...

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A Learning-Based Approach for Bias Elimination in Low-Cost Gyroscopes Daniel Engelsman

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