Abstract: ‍ ‍By employing a frequency increment across the array antenna， Frequency Diverse Array-Multiple Input Multiple Output （FDA-MIMO） radar is able to produce a range-direction dependent response， which is different from conventional phased array radar that can only generate direction dependent beampattern. This unique feature brings about additional degree of freedom in range dimension. However， sampling error also brings about the problem of steering vector mismatch. Moreover， the presence of angle error will further exacerbate the mismatch of guidance vectors， greatly affecting the detection probability of the detector. In addition， excessive target speed can also have an impact on the target detection of FDA-MIMO radar. The impact of target velocity is manifested in two aspects： firstly， it can lead to range migration and Doppler frequency migration of radar echo signals， which can cause diffusion of the echo signal in both the range and Doppler dimensions， reducing the accumulated gain of the radar， and thus affecting the detection performance of the moving targets； secondly， it can cause phase changes in the radar echo signal， which can affect the parameter estimation accuracy for the targets； thirdly， the Doppler frequency expansion caused by frequency increment may occur， which further affects radar detection performance. The objective of this paper is to deal with the above issues. This article focuses on the problem of target detection in moving target in Gaussian noise background. In order to address the range migration and Doppler spread caused by target motion， a new algorithm is proposed in this paper， which is based on a modified Keystone transform. The echo signal model of the FDA-MIMO radar for moving target is derived first. On this basis， in moving target detection， the range migration and Doppler expansion caused by the frequency increment of FDA-MIMO radar is analyzed. To solve this problem， we develop a modified Keystone transform algorithm， where the frequency offset across the transmit array is taken into consideration. This method is not going to need a parameter searching process， which reduces the system computational complexity and improves the efficiency for real-time signal processing. After the problems of range migration and Doppler frequency expansion are solved， the array mismatch still exists. In addition， in order to improve the target detection performance under array mismatch conditions， this paper derives an adaptive detector under range and angle mismatch. The idea of signal subspace is introduced into this problem， where we can separate the target signal and array mismatches in different subspace. On this basis this paper proposes a subspace construction method for FDA-MIMO radar under range and angle mismatch conditions. Furthermore， we resort to the GLRT （Generalized Likelihood Ratio Test） criterion， and derive an adaptive detector for FDA-MIMO radar under range and angle mismatch conditions. The simulation results show that in the background of Gaussian white noise， the proposed algorithm can correct range migration and Doppler spread effects caused by target velocity， and its detection performance is superior to traditional GLRT methods under array range angle mismatch conditions. In addition， the performance of the Keystone spatial processing detector proposed in this article is similar to that of the Keystone all spatial processing detector， but with lower computational complexity.