Assume a target at a distance R and has a radial velocity component of Vr. The roundtrip
distance to target is 2R. This is equivalent to 2R/λ wavelengths or (2R/λ)2π = 4πR/λ
radians. If the phase of the transmitted signal is φo, then the phase of the received signal
Alternatively, let the transmitted frequency be ft. The received signal can be represented
as sin(2 ( )) rec t R A = K πf t − t. The round-trip time tR is equal to 2R/c. With a radial
velocity of Vr the round-trip time is changing as R = R0 – Vrt. Thus, the received signal is
Thus, the received frequency changes by a factor 2ftVr/c = 2Vr/λ., which is the same as
before. The Nyquist criterion says that fmax = PRF/2, combining this with Equation (1),
This is the maximum unambiguous velocity. Higher velocities cause velocity folding or
This summarizes the Doppler dilemma: a large Rmax implies a small Vmax and vice versa
Doppler process recognizing and dealing with range and velocity aliases
- On examining horizontal and vertical shapes of object. For example range-aliased incoming objects become skinny close-by objects. Incoming objects suspicious 3m – 150m wide, 130m – 6.2 km height.
- Then we examine reflectivity in conjunction with other factors,
- Changed PRF–real echoes will not change position, but aliases will. This is not always an option.
- Velocity folding causes a change in sign, which is relatively easy to spot if the Folding is within a larger region.
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