Jacobian matrix for covariance transformation from Keplerian to Equinoctial

Orekit usage
1

Hello,
I have to get the Jacobian matrix to transform the covariance matrix of a Keplerian orbit to a covariance matrix in Equinoctial elements.
I saw that there is the possibility to use the method getJacobianWrtCartesian and getJacobianWrtParameters to get the Jacobin from a Cartesian to a Keplerian and vice versa. What about the Equinoctial orbit? Is there any direct way to get the Jacobian matrix starting from / arriving to an Equinoctial orbit?

Thank you!

2

You will have to compose Jacobians.

      KeplerianOrbit   kep           = ...;
      RealMatrix       covarianceKep = ...;

      // convert to Cartesian covariance
      double[][] jk = new double[6][6];
      kep.getJacobianWrtParameters(PositionAngle.MEAN, jk);
      RealMatrix dCdK = MatrixUtils.createRealMatrix(jk);
      RealMatrix covarianceCart = dCdK.multiply(covarianceKep).multiplyTransposed(dCdK);

      // convert to Equinoctial covariance
      double[][] je = new double[6][6];
      EquinoctialOrbit equ = (EquinoctialOrbit) OrbitType.EQUINOCTIAL.convertType(kep);
      equ.getJacobianWrtCartesian(PositionAngle.MEAN, je);
      RealMatrix dEdC = MatrixUtils.createRealMatrix(je);
      RealMatrix covarianceEqu = dEdC.multiply(covarianceCart).multiplyTransposed(dEdC);

Beware that when converting the covariances, the left hand side multiplication calls the multiply method whereas the right hand side multiplication calls the multiplyTransposed method (this avoids creating the intermediate transposed matrix).

Beware also I wrote this skeleton code quickly, you should double check to ensure the transforms are in the correct direction.

3

Thank you Luc!