In this work a new algorithm is derived for the onboard calibration of three-axis strapdown magnetometers. The proposed calibration method is written inthe sensor frame, and compensates for the combined effect of all linear time-invariant distortions, namely soft iron, hard iron, sensor nonorthogonality, and bias, among others. A maximum likelihood estimator (MLE) is formulated to iteratively find the optimal calibration parameters that best fit to the onboard sensor readings, without requiring external attitude references. It is shown that the proposed calibration technique is equivalent to the estimation of arotation, scaling and translation transformation, and that the sensor alignment matrix is given by the solution of the orthogonal Procrustes problem. Good initial conditions for the iterative algorithm are obtained by a suboptimal batch least squares computation. Simulation and experimental results with low-cost sensors data are presented and discussed, supporting the application of the algorithm to autonomous vehicles and other robotic platforms.