Conditional Mean Prediction of Unknown Values in a Lag Embedding

I wish to implement the algorithm from the paper: Singular Spectrum Analysis With Conditional Predictions for Real-Time State Estimation and Forecasting in R. I'm having trouble with Step 2 of the algorithm:

So say I have the following extended lag-embedded matrix X̃ of size M x N (4 x 20):

   1.0135518 -0.7113242 -0.3906069  1.5652030  0.0439317 -1.165609  1.0701692  1.0825379 -1.2239744 -0.0321446  1.1815997 -1.4969448 -0.7455299  1.0973884 -0.2188716 -1.0719573  0.9922009  0.4374216 -1.6880219 0.2609807
  -0.7113242 -0.3906069  1.5652030  0.0439317 -1.1656093  1.070169  1.0825379 -1.2239744 -0.0321446  1.1815997 -1.4969448 -0.7455299  1.0973884 -0.2188716 -1.0719573  0.9922009  0.4374216 -1.6880219  0.2609807        NA
  -0.3906069  1.5652030  0.0439317 -1.1656093  1.0701692  1.082538 -1.2239744 -0.0321446  1.1815997 -1.4969448 -0.7455299  1.0973884 -0.2188716 -1.0719573  0.9922009  0.4374216 -1.6880219  0.2609807         NA        NA
   1.5652030  0.0439317 -1.1656093  1.0701692  1.0825379 -1.223974 -0.0321446  1.1815997 -1.4969448 -0.7455299  1.0973884 -0.2188716 -1.0719573  0.9922009  0.4374216 -1.6880219  0.2609807         NA         NA        NA

NB: D here is 1.

How would I code the above Step 2 in R to estimate the NAs?