This paper presents and compares two different least squares (LS) approaches to identify the dynamic forces acting on a structure from acceleration measurements. An overview of different papers dealing with such inverse problems is realized in the introduction. An original technique based on weighting LS is suggested to improve the classical method in the case of complex structures showing heterogeneous stiffnesses. This technique is applied to an experiment realized on an engine cylinder block. A second LS technique, known as total LS (TLS), is presented and adapted to the indirect force measurement problem by the means of the principal component analysis (PCA). Both Weighted LS and Weighted TLS approaches are compared in a theoretical way and in the frame of the experiment on the engine cylinder block.