We consider the problem of tracking moving algal bloom fronts using an unmanned surface vehicle (USV) equipped with a sensor that measures the concentration of chlorophyll a. Chlorophyll a is a green pigment found in plants, and its concentration is an indicator of phytoplankton abundance. Our algal bloom front tracking mission consists of three stages: deployment, data collection, and front tracking. At the deployment stage, a satellite collects an image of the sea from which the location of the front, the reference value for the concentration at this front and, consequently, the appropriate initial position for the USV are determined. At the data collection stage, the USV collects data points to estimate the local algal gradient as it crosses the front. Finally, at the front tracking stage, an adaptive algorithm based on recursive least squares fitting using recent past sensor measures is executed. We evaluate the performance of the algorithm and its sensitivity to measurement noise through MATLAB simulations. We also present an implementation of the algorithm on the DUNE onboard software platform for marine robots and validate it using simulations with satellite model forecasts from Baltic sea data.