Is recursive least square to estimate coefficients of ARMA(p,q) is equivalent to newton's method of finding coefficients using this -
$$C_{m+1}=C_m+(X^TV_mX)^{-1}X^T(Y-P_m)$$
EDIT:
I've used that equation in logistic regression to find coefficients. How to determine coefficients of ARMA(1,1) using following dataset -
$$ \begin{matrix} Period & Value \\ 1 & 15 \\ 2 & 12\\ 3 & 19 \\ 4 & 21 \\ 5 & 17\\ \end{matrix} $$
Here I've found a MATLAB function which uses Recursive Kalman Filter to estimate coefficients and here the process has been explained. It outputs $ar$ and $ma$ coefficients only and they are very different from those produced by R.
For a given 100 observations, it outputs - $$ar: 0.9616\,\,\,\,ma: -179.4289\,\,\,\,\sigma: 0.0012 \,\,\,\, LL: -160.2952$$
with the same R (setting include.mean = FALSE) produced - $$ar: 0.9590\,\,\,\,ma: 1.0000\,\,\,\,\sigma^2: 0.01309\,\,\,\, LL: 70.66$$