  The least mean squares (LMS) filter is often derived via the Wiener filter
solution. For a system identification scenario, such a derivation makes it hard
to incorporate prior information on the system's impulse response. We present
an alternative way based on the maximum a posteriori solution, which allows
developing a Knowledge-Aided Kaczmarz algorithm. Based on this Knowledge-Aided
Kaczmarz we formulate a Knowledge-Aided LMS filter. Both algorithms allow
incorporating the prior mean and covariance matrix on the parameter to be
estimated. The algorithms use this prior information in addition to the
measurement information in the gradient for the iterative update of their
estimates. We analyze the convergence of the algorithms and show simulation
results on their performance. As expected, reliable prior information allows
improving the performance of the algorithms for low signal-to-noise (SNR)
scenarios. The results show that the presented algorithms can nearly achieve
the optimal maximum a posteriori (MAP) performance.
