In high-speed optical fiber communications, chromatic dispersion (CD) estimation is essential for the monitoring and compensation of CD-induced impairments. Compared with coherent detection, in short-reach optical communication systems, intensity modulation/direct detection (IM/DD) is more widely used, and the existing dispersion estimation techniques usually require training signals or a large amount of data for curve fitting or machine learning. However, these methods cannot provide in-service estimation. This paper presents a novel technique for in-service CD estimation in IM/DD short-reach optical communication systems based on our derived analytical model. With the analytical model, the in-service CD estimation is realized via the direct power spectrum analysis of the received signal. Unlike previous studies that only work with single-frequency sinusoidal signals, the practical random data with the rectangular type of base waveform is considered in our model. Therefore, our method can be applied to the dispersion estimation of various pulse amplitude modulation (PAM) based systems. Our proposed training free in-service CD estimation method is verified and investigated, where results show that better than 0.5% accuracy in dispersion estimation can be achieved in optical communication systems with up to 40 GBaud data rate and 100 km transmission distance.