class HKalIFilt: public TObject

 Checks for potential issues when site with index iSite is filtered.

 Filter a site using the conventional formulation of the Kalman filter
 equations.

 C_k = (I - K_k * H_k) * C^{k-1}_k
 K_k = C^{k-1}_k * H^T_k * (V_k + H_k * C^{k-1}_k * H^T_k)^-1

 These are simpler equations compared to the Joseph or Swerling
 forumations. Only one inversion of a matrix with the dimension of the
 measurement vector is neccessary. However, the updated covariance
 matrix may not be positive definite due to numerical computing problems.

 This filter method uses the Joseph stabilized update of the covariance
 matrix.

 K_k = C^k-1_k * H^T * (V_k + H_k * C^k-1_k * H_k^T)^-1
 C^k = (I - K_k * H) * C^k-1_k * (I - K_k * H)^T + K_k * V_k * K_k^T

 This method is numerically more stable than the conventional or
 Swerling formulations of the Kalman equations.
 It guarantees that the updated covariance matrix is positive definite
 if the covariance from the prediction step and the measurement noise
 covariance are also positive definite.

 Implements the sequential Kalman filter..
 May only be used if:
 the measurement noise matrix is diagonal or it is constant
 and the projection function is h(a) = H * a.

 The advantage of this method is that is avoids matrix inversions.

 Swerling calculation of covariance matrix for filtered state and the
 Kalman gain matrix.

 C_k = [ (C^k-1_k)^-1 + H^T_k * (V_k)^-1 * H_k ]^-1
 K_k = C_k * H^T_k * (V_k)^-1

 This form requires two inversions of matrices with the dimension of the
 state vector and one inversion of a matrix with the dimension of the
 measurement vector. It can be more efficient if the dimension of the
 state vector is small.

 Update of the covariance matrix and state vector for the filter step
 using the U-D filter. A UD decomposition of the covariance matrix
 is used and only the U and D matrices are propagated.

 This method increases the numerical precision of the Kalman filter.
 It cannot be used together with the annealing filter.

 Literature:
 Optimal State Estimation: Kalman, H infinity and Nonlinear Approaches
 Chapter 6.4: U-D filtering
 Dan Simon

 Kalman Filtering: Theory and Practice using MATLAB, 3rd edition
 Chapter 6.5: Square Root and UD Filters
 Mohinder S. Grewal, Angus P. Andrews

 G. J. Bierman, Factorization Methods for Discrete Sequential Estimation,
 Academic Press, New York 1977

 Propagate the covariance matrix between measurement sites.
 Must not be called before propagateTrack().
 When applying the UD filter use propagateCovUD() function instead.

 iFromSite:  index of measurement site to start propagation from.
 iToSite:    index of measurement site to propagate to (will be modified).

 Update of the covariance matrix' U and D factors after the prediction
 step.

 iFromSite:  index of measurement site to start propagation from.
 iToSite:    index of measurement site to propagate to (will be modified).

 Only the matrix upper triangular U with the elements of D on its
 diagonal are stored in the site.

 Literature:
 Kalman Filtering: Theory and Practice using MATLAB, 3rd edition
 Chapter 6.5: Square Root and UD Filters
 Mohinder S. Grewal, Angus P. Andrews
 and
 Catherine L. Thornton, Triangular covariance factorizations for Kalman filtering,
 Ph.D. thesis, University of California at Los Angeles, 1976

 Propagates the track between measurement sites.

 iFromSite:  index of measurement site to start propagation from.
 iToSite:    index of measurement site to propagate to (will be modified).

 Update chi^2 after having filtered site number iSite.

 Reset data members to fit a new track.

 Input:
 hits:        the array with the measurement hits. Elements must be of
              class HKalMdcHit.
 iniStateVec: initial track state that the filter will use.
 iniCovMat:   initial covariance matrix that the filter will use.
 pId:         Geant particle id.
 momGeant:    Geant momentum that will be written in the output tree.
              Ignore if this is not simulation data.

 Implements the projection function h(a) that calculates a measurement
 vector from a track state.

 Output:
 projMeasVec: The calculated measurement vector.
 Input:
 site:      Pointer to current site of the track.
 stateType: Which state (predicted, filtered, smoothed) to project on a
            measurement vector.
 sys:       Coordinate system to use (sector or virtual layer coordinates)

 Covariance matrices must be positive definite, i.e. symmetric and
 all its eigenvalues are real and positive. Returns true if this
 is the case.

 Exclude a site from the measurement. Requires that prediction, filtering and smoothing
 has been done before. If smoothing has been disabled it will be done in this function.
 iSite: index in sites array of the site to exclude

 Run the filter step in Kalman filter for a site.
 Must be called after the prediction step.
 Different Kalman filter equations are used as set by setFilterMethod().
 iSite: index of site to filter

 Runs the Kalman filter over a set of measurement hits.
 Returns false if the Kalman filter encountered problems during
 track fitting or the chi^2 is too high.

 Input:
 hits:        the array with the measurement hits. Elements must be of
              class HKalMdcHit.
 iniStateVec: initial track state that the filter will use.
 iniCovMat:   initial covariance matrix that the filter will use.
 pId:         Geant particle id.
 momGeant:    Geant momentum that will be written in the output tree.
              Ignore if this is not simulation data.

 Propagates the track to the next measurement site and update
 covariance matrices.

 iFromSite:  index of measurement site to start propagation from.
 iToSite:    index of measurement site to propagate to.

 Do the prediction and filter steps of the Kalman filter by propagating
 the track between the measurement sites iFromSite and toSite.

 iFromSite: index of track site to start propagation from
 toSite:   index of track site to propagate to.

 Implements the smoother by Rauch, Tung and Striebel for the Kalman filter.
 Requires that the prediction and filter steps for all measurement
 sites have been executed before.

 Sort the competitors in each site by weight.

 Propagates the track from the last fitted MDC position till track intersection
 with META plane (is defined by META-hit and normal vector to rod's plane.
 Should only be called after having filtered all sites.

 Input:
 metaHit:
 metaNormVec:

 Transform all sites using the Kalman system's rotation matrix.

 Transform all sites using the inverse rotation matrix stored in the
 Kalman system. This will transform the sites back to sector coordinates
 after a call of transformFromSectorToTrack() and if the rotation matrix
 has not been modified in the meantime.

 Replace sites of the Kalman system with new hits.
 hits: array with new measurement hits. Must be of class HKalMdcHit.

 Returns the measurement error of site.

 Input:
 site: measurement site.

 Returns the measurement vector of measurement site.

 Input:
 site: measurement site.

 Returns number degrees of freedom, i.e. number of experimental points
 minus number of parameters that are estimated.

 Print or suppress error messages.

 Print or suppress warning messages.

 Set options for the Kalman filter.
 kalRotateOptions: Tilt coordinate system.
 There are (approximately) three options:
 1. kNoRot:
    Don't tilt the coordinate system.
 2. kVarRot:
    Tilt the coordinate system so that the z-axis will always
    point in the initial track direction. Assuming track curvature
    is not large this ensures that the track state parameters
    tx = tan(p_x / p_z) and ty = tan(p_y / p_z) remain small.
    Angles close to 90° would result in large values for tx and ty
    due to the tangens and poor results for the Kalman filter.

 Set the rotation matrix.
 rotXangle: rotation angle around x axis in radians.
 rotYangle: rotation angle around y axis in radians.