nag_tsa_multi_kalman_sqrt_invar (g13ebc) Example Program Results

Example 1

The square root of the state covariance matrix is

 -1.7223   0.0000   0.0000   0.0000 
 -2.1073   0.5467   0.0000   0.0000 
 -1.7649   0.1412  -0.1710   0.0000 
 -1.8291   0.2058  -0.1497   0.7760 

The matrix AK (the product of the Kalman gain
matrix with the state transition matrix) is

 -0.2135   1.6649 
 -0.2345   2.1442 
 -0.2147   1.7069 
 -0.1345   1.4777 

Example 2

Covariance matrix PE from nag_tsa_multi_kalman_sqrt_var (g13eac) is
 
  1.6761   1.4744   1.2519   1.6852 
  1.4744   1.3646   1.1367   1.4651 
  1.2519   1.1367   1.0668   1.3445 
  1.6852   1.4651   1.3445   2.2045 

Covariance matrix PF from nag_tsa_multi_kalman_sqrt_invar (g13ebc) is
 
  5.0635  -1.5512   0.0231   1.1756 
 -1.5512   0.8503  -0.0492  -0.3631 
  0.0231  -0.0492   0.0648  -0.0217 
  1.1756  -0.3631  -0.0217   0.3336 

Matrix U' * PF * U is 
 
  1.6761   1.4744   1.2519   1.6852 
  1.4744   1.3646   1.1367   1.4651 
  1.2519   1.1367   1.0668   1.3445 
  1.6852   1.4651   1.3445   2.2045 

The matrix KE from nag_tsa_multi_kalman_sqrt_var (g13eac) is
 
  0.3699   0.9447 
  0.3526   0.8199 
  0.2783   0.5375 
  0.1588   0.6704 

The matrix KF from nag_tsa_multi_kalman_sqrt_invar (g13ebc) is
 
 -0.5857  -1.4263 
 -0.0280   0.2239 
  0.0170   0.1200 
 -0.1405  -0.4519 

U' * KF is
 
  0.3699   0.9447 
  0.3526   0.8199 
  0.2783   0.5375 
  0.1588   0.6704