Vibrating Inertial Sensor Calibration for Stiffness Coupling Errors

Resolve Bottlenecks,
Find Innovative Solutions
Generate Solutions

Solution Overview

Problem

Existing MEMS inertial sensors suffer from manufacturing imperfections that lead to errors in angular velocity and orientation measurements due to non-identity of the stiffness matrix and mechanical coupling between vibration axes, which cannot be effectively compensated by existing calibration methods.

Innovation Solution

A calibration method that determines the inverse excitation and detection matrices by applying sinusoidal disturbances through trim commands, directly modifying the stiffness matrix to correct for these imperfections, allowing for precise angular velocity and orientation measurements.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If manufacturing techniques are used to create MEMS sensors, then production cost is reduced, but manufacturing precision deteriorates due to imperfections in stiffness matrix and mechanical coupling

Engineering Contradiction:
Improveproduction costVSAvoidstiffness matrix identity
Core Design Contradiction:
Ease of manufactureVSManufacturing precision

Solution Approach 1:

The calibration method performs preliminary characterization of the stiffness matrix and coupling coefficients before actual measurement operations. By determining these parameters in advance through systematic excitation and detection, the system compensates for manufacturing imperfections and achieves high precision without requiring perfect manufacturing.

Inventive Principle:
Principle #10Preliminary action

2Device complexity

If existing calibration methods are used, then device complexity is maintained, but measurement precision deteriorates due to inability to compensate for manufacturing imperfections

Engineering Contradiction:
Improvecalibration system complexityVSAvoidangular velocity measurement accuracy
Core Design Contradiction:
Device complexityVSMeasurement precision

Solution Approach 1:

The calibration method implements feedback by using detection transducers to measure the actual response of the resonator to known excitation forces. These measurements feed back into the calculation of stiffness matrix elements and coupling coefficients, which are then used to correct subsequent measurements, creating a closed-loop system that continuously compensates for manufacturing variations.

Inventive Principle:
Principle #23Feedback

Solution Approach 2:

The system performs self-calibration by using its own excitation and detection capabilities to characterize its imperfections. The sensor uses its built-in transducers to apply forces, measure responses, and automatically compute correction parameters without requiring external calibration equipment or complex additional components.

Inventive Principle:
Principle #25Self-service

3Measurement precision

If trim commands are applied to modify stiffness matrix, then measurement precision is improved, but device complexity increases due to additional calibration procedures

Engineering Contradiction:
Improveangular orientation accuracyVSAvoidcalibration procedure complexity
Core Design Contradiction:
Measurement precisionVSDevice complexity

Solution Approach 1:

The method changes the parameters of the resonator system by applying trim commands that modify the stiffness matrix elements and coupling coefficients. By systematically varying these parameters through controlled excitation and measuring the responses, the calibration process identifies the actual parameters and uses this information to correct measurements, transforming a complex physical adjustment problem into a calculable parameter optimization task.

Inventive Principle:
Principle #35Parameter changes

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

The method significantly reduces excitation and detection errors, improving the accuracy and reliability of MEMS inertial sensors by pre-compensating excitation forces and correcting detected motion values.

Implementation Method 1

a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y

Methodology Applied
Scientific EffectElectrostatic force: Electrostatics

Implementation Method 2

The detection method involves applying a bias voltage between the fixed and moving combs and observing the resulting charge variations due to capacitance differences between the fixed and moving combs caused by variations in the spacing between their teeth

Methodology Applied
Scientific EffectCapacitance: Capacitance

Implementation Method 3

When the gyroscope rotates around the z-axis, perpendicular to the xy-plane (called the sensitive axis), the combination of the forced vibration with the angular rotation vector generates, through the Coriolis effect, forces that set the moving masses into natural vibration perpendicular to the excitation vibration and the sensitive axis; the amplitude of the natural vibration is proportional to the rotation speed

Methodology Applied
Scientific EffectCoriolis effect: Coriolis Force

Implementation Method 4

They are suspended from fixed anchor points A on the plate by orthotropic suspension springs RS

Methodology Applied
Scientific EffectElasticity: Elasticity

Data Source

PatentEP4185841B1Method for calibrating a vibrating inertial sensor
Publication Date: 2025.11.19 THALES SA
  • EP4185841B1 patent drawingFigure 1
  • EP4185841B1 patent drawingFigure 2
  • EP4185841B1 patent drawingFigure 3

AI summary

Method (100) for calibrating an inertial angular sensor (10) comprising the steps of: A for at least two electrical angles (θj) of the vibration wave: A1 applying, via each of the three trim commands CTi, a sinusoidal stiffness disturbance PSi having a disturbance frequency fi, and for each disturbance applied: A11 determining and storing an estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi, from the excitation commands determined by the drives, B determining from the three estimated excitation forces Fei i=1,2,3 stored in step A11, three matrices 2x2 M'i, a matrix M'i being representative of the gyrometer response to the disturbance PSi, C determining and storing an estimated inverse excitation matrix (formula (A)) and an estimated inverse detection matrix (formula B) from the three matrices M'i determined in step B, an excitation matrix E and a detection matrix D each being representative of the effects of the excitation chain and the effect of the detection chain of the sensor, respectively.