It is known that detecting a high-speed and accelerating target is affected by the range migration and Doppler frequency migration in the linear frequency modulation pulse compression radar. In order to solve this problem

the model of received signal is established and the characteristics of the received signal are analyzed firstly. Then a target detection algorithm based on the scaling processing and the fractional Fourier transform is proposed. With the proposed algorithm

the range migration is compensated via using the scaling processing

and the Doppler frequency migration is compensated by using the fractional Fourier transform. Therefore it is able to improve the detection performance of a high-speed and accelerating target.