The received signal strength (RSS) is a common source of information used for estimating the distance between two wireless nodes, whether these nodes are stationary or mobile. Minimum mean squared error distance estimation methods that use the RSS require prior knowledge of both the variance of the noise and, in the case of mobile sensors, the dynamics of the nodes’ mobility. In mobile applications, where low computational complexity is important, pseudo-optimal estimations are preferred, as they do not require such information. In this case, the maximum likelihood estimator (MLE) is often used. In this paper, we propose an efficient pseudo-optimal log-power based distance estimation method using RSS under lognormal shadowing, that improves the MLE. It does not require a priori knowledge either of the movement dynamics or of the variance of the noise. The method is based on adaptively minimizing the variance of the prediction error, using a random walk model with correlated increments. It is analytically demonstrated that the distance estimation error variance of the proposed method improves the MLE in both the static and mobile cases. We use a simulated velocity model example to compare its performance with other algorithms in this group, such as the linear mean square filter and the Gauss–Newton search.