Sound speed is of great importance for high velocity impact phenomena because it is a fundamental parameter to deduce the shear moduli, strengths and phase transitions of materials at high pressure. It has attracted much attention because of significant challenges to experiment and simulation. In practice, with the development of laser interferometer measurement system, one can obtain velocity-time histories of windowed-surfaces or free surfaces with high resolution in shock or ramp compression and unload experiments. This development provides a possible way to infer the sound speed from these velocity profiles. The key problem is to build valid analysis technique to extract the sound speed. Commonly used Lagrangian analysis methods include backward integration method, incremental impedance matching method, transfer function method and backward characteristic analysis method. However, all of these methods hardly infer the right results from the nonsymmetric impact and release experiment with only one depth of material due to the complex impedance mismatch among a flyer, sample and window. Some decreasing impedance mismatch techniques have been developed for the experiments including reverse impact or using a high strength flyer, but these techniques will limit the pressure range or need a newly designed gun with large caliber. In fact, the traditional backward characteristic analysis method only considers the sample/window interaction while bending of the incoming characteristics due to impedance difference between the flyer and sample is always ignored, which causes a distortion to the loading condition of samples. Thus in this work, we add forward characteristics to describe rarefaction wave reflection at the flyer/sample interface. Then a reasonable loading-releasing in-situ velocity profile of the interface can be derived from this improvement. We use the improved/tradition characteristics and incremental impedance matching method to analyze a synthetic nonsymmetric impact experiment in which the flyer, sample and window are of Al, Cu and LiF, respectively. Synthetic analyses suggest that the modified characteristic method can give more accurate results including sound speed-particle velocity and release path at high pressure. Compared with other methods, the new characteristic method just needs to know the release path of flyer and window that can be calibrated by well-developed technique, moreover, this method also does not need to know the form of equation of state and constitutive model of the sample. Calculation of this method is not complex and the iterative approach usually achieves convergence in less than 10 steps. All of these features will facilitate using this method to infer sound speed from the velocity profile of nonsymmetric impact experiments.