The convergence of an instrumental-variable-like recursion

The convergence of a modified form of the IV (instrumental-variable) recursion (actually a case of the integral adaptation algorithm of Landau) for the parameters of a scalar transfer function time series model is considered. It is known that this algorithm requires at least a positive real condition for its convergence. Here it is shown that the recursion converges without being monitored. In any case, the result is disappointing because the positive real condition depends on the transfer function characteristic function.