Doppler radars are low cost and light weight sensors that have a potential to find wide applications in building a large team of mobile vehicle platforms. Because of the nonlinearity associated with the measurement from Doppler radars, it is both interesting and challenging to extract meaningful information from the low cost sensors. Building upon the authors' previous work on self localization with a feature-based map with known landmark associations using Doppler radars and an Extended Kalman Filter (EKF), this paper investigates the effects of positioning and the number of landmarks in a feature-based map on the accuracy of the position estimation of a robot. The computations of Cramer-Rao Lower Bound (CRLB) at the terminating sample show that the CRLB has a drastic reduction when the number of landmarks is increased from 1 to 2 while the root mean square errors (RMSE) of EKF indicate a gradual error reduction for the first 4 landmarks. The results presented in this paper will provide an essential guideline on the experiment design for feature-based robot self-localization.