Unable to understand how the paper simplifies the covariance matrix - Kalman filter The paper Convergence Analysis of the Unscented Kalman Filter for Filtering Noisy Chaotic Signals

presents the convergence analysis of Unscented Kalman Filter

download
http://www.eie.polyu.edu.hk/~cktse/pdf-paper/ISCAS07-Feng1.pdf . The Measurement update equations from Eq16 -- Eq19 are clear to me but I don't understand how Eq(20) is derived which is $P_n = K_nR_n$ where $P_n$ is the covariance of the filtering error and $R_n$ is the covariance matrix of the measurement noise. Can somebody please show the steps how Eq(20) is reached ? I tried something like this starting from Eq(18) but I am stuck --

$$ P_n = P_n^- - K_n P_{y_n y_n}K_n^T,$$
$$ = P_{y_n y_n} - R_n - K_n P_{y_n y_n}K_n^T  $$ (substituting Eq 19)
$$ = P_{x_ny_n} - K_n P_{y_n y_n}K_n^T   $$
In order to derive equation (20) you can use the following steps:


From substitution of  equation (16) into equation (18)


$$  P_n = P_{n|n-1} - K_nP^t_{x_ny_n}$$


Now plugging right side equation of (19) into the last equation


$$  P_n = P_{n|n-1} - K_n(P_{y_ny_n} - R_n)=$$
$$ =P_{n|n-1} - K_nP_{y_ny_n} + K_nR_n $$


Now Pluging (16) again we know that
$$ K_nP_{y_ny_n} = P_{x_ny_n}$$
putting this back we get 


$$ P_n=P_{n|n-1} - P_{x_ny_n} + K_nR_n $$


Using left side equation of (19) we get the desired result
$$P_n = K_nR_n$$