Basic theory of accelerometer, gyroscope and magnetometer. Newton’s law of Classical Mech. Inertial and non inertial reference system: centrifugal, Coriolis and Euler forces. IMU hardware description. Static IMU’s Noise evaluation: mean and std deviation in all axis w.r.t. data sheet. Drift effect in MATLAB. Sit-to-stand experiment with 2 IMUs: development of an algorithm able to estimate the duration of stand-up, sit-down and variation of the bending angles.

1. Biomedical Transducers a.a.
2011/12
Inertial Sensors
Daniele Antonioli
Luca Faggianelli
Jian Han
Mekki Mtimet
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2. Outline
 Introduction to Inertial Sensors;
 Static Evaluation of the Noise;
 Sit to Stand Task Evaluation;
 Conclusions.
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3. Inertia and Inertial Frame
• Inertial Frame of Reference: is a frame in a
state of constant, rectilinear motion with
respect to one another: an accelerometer at
rest in one would detect zero acceleration;
• Newton’s First Law of Inertia: an observer in a
inertial frame of reference observes a body:
inertia is the natural tendency of that body to
remain immobile or in motion with constant
speed along a straight line;
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4. Inertia and Inertial Frame
• Newton’s Second Law: A force will accelerate
a body, in the direction of the force at a rate
inversely proportional to the mass of the
body;
• Mass is the linear quantification of inertia;
• The laws of Classical Mechanics
(Biomechanics included) are valid and
maintain the same form in all inertial
reference systems.
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5. What is a sensor?
• Instrument capable to transduce a physical
quantity to a measurable electric signal;
• Accuracy vs Precision;
• Inertial sensor: functioning principle based on
inertial phenomena.
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6. Inertial Sensors
• Accelerometers: sense linear acceleration
[m/s^2] along a specific axis;
• Gyroscopes: sense angular velocity axis,
measured in [rad/s];
• Magnetometer: sense the strength of a
magnetic field, measured in [mGauss].
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7. Inertial Sensor Benefits and
Applications
• Low cost;
• Small size, Portable;
• Ultra Low-power systems;
• Wireless.
• Ambulatory monitoring;
• Unsupervised monitoring;
• Fall & Gait;
• Activity detection.
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8. 2.STATIC CALIBRATION
EXPERIMENT
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9. 2.1 Brief Hardware Description
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10. 2.2 Static Noise Evaluation
2.2.1 Description
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11. INERTIAL MEASUREMENT UNITS
XSENS SENSOR(with cables) OPAL SENSOR(wireless)
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12. 2.2.2 Evaluate and characterize the
noise in terms of mean and standard
deviation of the ouputs
• Mean() function
• Std() function
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13. The results for XSENS IMU are as follows:
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14. The results for OPAL IMU are as follows:
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15. 2.3 Evaluate the drift effect
• Detrend() function
• Polyfit() function, y=mx+b
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16. The results for XSENS IMU are as follows:
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17. The results for OPAL IMU are as follows:
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18. 2.4 What are the main difference
between the noises on each sensor?
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19. Ay vs Ay1
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20. From these plots we can conclude that:
• The Xsens IMU, has overall better
performance with respect to the Opal
IMU;
• The Xsens trend of noise drift is almost
parallel to the time axis and the signals
have lower offsets with respect to the
Opal signals.
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21. 2.5 Does the standard deviation of the noise
correspond to that reported in the data sheet?
• Xsens: As we can see in the tables above, the data reported in the
datasheet and our measured ones, differ from a factor of ±.001; So we
obtain very good measurements in terms of accuracy and precision;
• Opal: In this case we have to convert the data from [μg/»Hz] to [m/s2]
for the linear acceleration Noise and from [°/s/»Hz] to [rad/s] for the
angular velocity, using the bandwidth data B = 50[Hz]. Also in this case
we obtain good measurement in terms of accuracy and precision.
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22. 3. Sit to Stand
• Opal IMU1 placed on the Thigh, in lateral
position;
• Opal IMU2 placed on the Trunk, at L5 height;
• 4 trials with 5 repetitions at different speed;
• f_{sample} = 128[Hz];
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23. Sit to Stand
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24. Extracted Signals
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25. Digital Filtering
2
sample
cut
n
f
f
W
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Normalized CutOff Frequency
Because of Noisy signals: Lowpass Filtering needed
[b,a] = butter(order,Wn,type): extract the coefficients;
filtfilt(b,a,input): No Phase Shift, forward + backward
filtering.

26. Algorithm
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Results
LPF
Pulses
Detection
Edges
Detection
Integration
Validation
Good/Bad
Knee
Angles
Timings
Acc(x,y)
Gyro(z)

27. Results: Plots
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Thigh Accelerometer x and y
axis Thigh Gyroscope z axis

28. Results: Table
StS Time mean
[s]
TtS Time mean
[s]
StS Angle
mean [°]
TtS Angle
mean [°]
Trial 1 1.7984 1.4375 94.7484° - 90.1806°
Trial 2 1.391 1.1719 96.3518° - 92.9096°
Trial 3 1.4672 1.3531 75.5568° - 71-7260°
Trial 4 .9906 .09562 71.6656° - 69.1158°
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4 Trials 5 Repetitions StS = Sit to Stand Task TtS = Time to Sit Task

29. Sit to Stand Conclusions
+ Results achievable with only 1 IMU (on the
thigh)
+ Robust algorithm
• Kalman fusion filter to improve the algorithm
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