Vert Systems: Mountain Biking Tracking Simon Fowler Jonathan Black, - - PowerPoint PPT Presentation

vert systems mountain biking tracking simon fowler
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Vert Systems: Mountain Biking Tracking Simon Fowler Jonathan Black, - - PowerPoint PPT Presentation

Vert Systems: Mountain Biking Tracking Simon Fowler Jonathan Black, Jacqueline Christmas, Mikhail Krastanov, Jakub Nowotarski, Jan Sieber, Robert Szalai, Jakub Tomczyk, Ellen Webborn Bristol 91st ESGI Mountain Biking Tracking Problem Outline


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Vert Systems: Mountain Biking Tracking Simon Fowler

Jonathan Black, Jacqueline Christmas, Mikhail Krastanov, Jakub Nowotarski, Jan Sieber, Robert Szalai, Jakub Tomczyk, Ellen Webborn

Bristol 91st ESGI Mountain Biking Tracking

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Problem Outline

Sensor located on the helmet of the rider contains GPS : p(t) ∈ R3 (1Hz) Accelerometer : ˆ a(t) ∈ R3 (100Hz) Gyroscope : ˆ Ω(t) ∈ R3x3 (100Hz) Magnetometer : ˆ m(t) ∈ R3 (100Hz) Aim: Obtain trajectory of rider at higher accuracy and time resolution than the GPS data.

Bristol 91st ESGI Mountain Biking Tracking

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Wavelet smoothing

Analysed data including pre-processing raw data using wavelet transform.

200 400 600 800 1000 −30 −20 −10 10 20 Raw signal (acceleration) 200 400 600 800 1000 −30 −20 −10 10 20 200 400 600 800 1000 −30 −20 −10 10 20 S4 S3 200 400 600 800 1000 −30 −20 −10 10 20 S5

Figure: Example of wavelet smoother performed on linear acceleration of the sensor with respect to x axis.

Bristol 91st ESGI Mountain Biking Tracking

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Determining orientation matrix

To evolve the rotation matrix we use the gyroscope data ˙ R(t) = ˆ Ω(t)R(t) to evolve in discrete time steps we use Rn+1 = exp

  • ˆ

Ωnhn

  • Rn

The angular velocity matrix is defined as ˆ Ω =   ˆ ω3 −ˆ ω2 −ˆ ω3 ˆ ω1 ˆ ω2 −ˆ ω1   , where ˆ ω1, ˆ ω2, ˆ ω3 are the gyroscope measurements.

Bristol 91st ESGI Mountain Biking Tracking

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Model

˙ X(t) = V(t), ˙ V(t) = R(t) · ˆ a(t) + gravity, ˙ R(t) = ˆ Ω(t) · R(t), R(t) · ˆ m(t) = magnetic north, X(t) = p(t), R(t)TR(t) = I Where Ω is the matrix of gyro measurements, and R is the rotation matrix between the two frames.

Bristol 91st ESGI Mountain Biking Tracking

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Method-Least squares

Two approaches were considered - the first solves the model’s equations using least squares. The system is large

  • ver-determined

nearly linear solved iteratively with Gauss-Newton iteration considers a segment of trajectory at once

Bristol 91st ESGI Mountain Biking Tracking

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SLIDE 7

Method-Kalman Filter

The second method solves the dynamical system with hidden states xn and observations yn. xn = Θxn−1 + en, yn = Wxn + ǫn

xn-1 xn

yn

where xn =         pn vn vn−1 Rn Rn−1 gravity         , yn =     pn ˆ an ˆ gn ˆ mn     Θ updates location assuming constant velocity between time-steps. W is the transformation from states to observations.

Bristol 91st ESGI Mountain Biking Tracking

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Demos

Bristol 91st ESGI Mountain Biking Tracking

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Real time processing

a a