Can somebody please provide an intuitive answer or reference for the following questions?

Q1: Dependence of estimation performance on number of data points -- I could not find any information whether the estimation performance of Adaptive filters such as Least Mean Square (LMS), Constant Modulus Algorithm (CMA) and Kalman Filters depend on the number of data points or not. Is there any information whether the mean square error between the actual and estimated parameters reduces with the increase in the number of data points or not?

Q2: Dependence of convergence on number of data points -- For instance, information such as if convergence of these adaptive filters (or in general) depends on the number of data points i.e., if these require a large number of data points to have good estimation performance.

• Number of data points means signal length, or do you mean filter length (number of tap weights) ? Aug 21, 2017 at 19:10
• I mean signal length Aug 21, 2017 at 19:12

For both LMS, RLS and Kalman filters, convergence primarily depends on the number of data points being processed; i.e., number of iterations. However this convergence rate is different for different filter types, reflecting their complexity and/or sophistication. The simple LMS filter has the slowest rate of convergence (roughly 10 to 20 times the filter tap weight length) whereas the RLS and Kalman filters display a convergence rate of roughly $2$ times the filter length (Haykin_Adaptive Filter Theory) for WSS inputs.