The secondary combustion radiation of rocket plume can be significantly reduced by using potassium flame agent, which leads to unprecedented improvement of missile invisibility. With the advantage of spatial heterodyne spectroscopy on weak spectrum signal detailed detection, potassium signal detection experiment in missile plume spectrum was performed by a near infrared spectrum instrument. Alcohol burner flame was used to simulate the missile plume, while the outside sky was regarded as background. Two of the modern spectral estimation methods, Autoregressive AR algorithm and MUSIC algorithm, were used to extract the potassium signal. Both algorithms can suppress noise, extract potassium signal and narrow the width of its characteristic peaks. For AR algorithm, the characteristic peak of 766.49 nm reduce 21% respectively, and noise reduce 42%. While for MUSIC algorithm, those characteristic peak reduce 50% and noise reduce 47%. The results illustrate that MUSIC algorithm has a better performance, and the application that using spatial heterodyne technology to identify the jet aircraft such as missiles is feasible.