Notes.md

• 1. Code
  • 1.1. run_dense3D_magfield
    • 1.1.1. pipeline
    • 1.1.2. dynModel
    • 1.1.3. domain_cartesian_dx
    • 1.1.4. particleFilter
      • 1.1.4.1. ai
      • 1.1.4.2. xl
      • 1.1.4.3. particle
      • 1.1.4.4. how to use GP to predict
      • 1.1.4.5. sequential process
• 2. Q&A
  • 2.1. why does dynModel contain noise when predicting state?
  • 2.2. SS = dy* P(:,:,i)*dy' + R;
• 3. Issue
• 4. Todo
  • 4.1. compare smoother with filter
  • 4.2. try to understand the dynModel: does it contain anything related to angular velocity?
  • 4.3. 3.3

1. Code

1.1. run_dense3D_magfield

1.1.1. pipeline

1.1.2. dynModel

    dynModel = @(xn,dx,dt,Q) [xn(1:2) + [cos(xn(3)), -sin(xn(3)) ; ...
                sin(xn(3)), cos(xn(3))]' * dx(1:2)' ; xn(3) + dx(3) + sqrt(Q) * randn]; 

1.1.3. domain_cartesian_dx

[eigenval,~,eigenfun_dx,NN] = domain_cartesian_dx(nBasisFunctions,d,LL);

domain_cartesian_dx - Laplace operator eigendecomposition in a hypercube

  eigenval = @(n) sum((pi*bsxfun(@rdivide,n,2*L)).^2,2);

1.1.4. particleFilter

1.1.4.1. ai

a means ancester

1.1.4.2. xl

xl = xl(:,ai);

1.1.4.3. particle

xn_traj = zeros(nNonLin, N_P, N_T); % Collection of all trajectories

1.1.4.4. how to use GP to predict

1.1.4.5. sequential process

2. Q&A

2.1. why does dynModel contain noise when predicting state?

At first I did not think it is good to use dynModel for propogate the state of particles, since it add some noise to the state, being so strange. However, now I accept that since the noise addition is how the pf gets its covariance or uncertainty.

2.2. SS = dy* P(:,:,i)*dy' + R;

dy is the derivative of measurement with respect to the map. The map containes 515 coefficients, including linear kernel and RBF kernel.

3. Issue

4. Todo

4.1. compare smoother with filter

4.2. try to understand the dynModel: does it contain anything related to angular velocity?

4.3. 3.3