On the use of Ljung's results for studying the convergence properties of Hampton's adaptive filter

Recursive stochastic algorithms such as stochastic approximation algorithms introduce problems of convergence in probability. Until now, methods of convergence analysis remained very specific. Recently, Ljung proposed a general method which consists of associating with the stochastic scheme an ordinary differential equation that contains all the information about the asymptotic behavior of the algorithm. These results are used here to study the convergence properties of an adaptive Kalman filter due to Hampton. Some remarks about results obtained by file Ljung approach are introduced and a comparison between these results and the Hampton ones is made.