  Long-time coherent integration (LTCI) is one of the most important techniques
to improve radar detection performance of weak targets. However, for the
targets moving with constant Cartesian velocities (CCV), the existing LTCI
methods based on polynomial motion models suffer from limited integration time
and coverage of target speed due to model mismatch. Here, a novel generalized
Radon Fourier transform method for CCV targets is presented, based on the
accurate range evolving model, which is a square root of a polynomial with
terms up to the second order with target speed as the factor. The accurate
model instead of approximate polynomial models used in the proposed method
enables effective energy integration on characteristic invariant with feasible
computational complexity. The target samplings are collected and the phase
fluctuation among pulses is compensated according to the accurate range model.
The high order range migration and complex Doppler frequency migration caused
by the highly nonlinear signal are eliminated simultaneously. Integration
results demonstrate that the proposed method can not only achieve effective
coherent integration of CCV targets regardless of target speed and coherent
processing interval, but also provide additional observation and resolution in
speed domain.
