This paper proposes a practical framework for measuring the external force applied to a construction manipulator (front load vector) by using a hydraulic sensor. Such a force measurement system requires high accuracy and robustness considering the uncertainty in the construction machinery field, but it inevitably includes measurement errors owing to difficult-to-reduce modeling errors. Our framework thus adopts a relative accuracy improvement strategy without correcting the models for the practicality. It comprises (i) quantifying the internal error range (IER) by using the sum of the maximal measurement errors of static and dynamic friction forces, which change in postural and kinematic conditions, (ii) calculating the error force vector by using IER to select cylinders (sensors) that have less error, and (iii) outputting the front load vector using the cylinders whose error force vector is minimum. Experiments were conducted using an instrumented hydraulic arm. The results indicate that our framework can enhance the relative accuracy of external force measurement independently of various postural and kinematic conditions.