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

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

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

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

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

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

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

Demos

Bristol 91st ESGI Mountain Biking Tracking

Real time processing

a a