1 Single-target speed measurement principle
1. Fourier transform :
FFT transform converts the time domain signal into the frequency domain;
The sine wave in the time domain produces a peak in the frequency domain. Typically, signals in the frequency domain are complex (i.e. each value is a phasor with amplitude and phase).
Sinusoidal signals with the same frequency and different initial phases undergo FFT transformation and generate peaks at the same abscissa position (equal frequency), but the phases of the peak signals are different, and the phase of the peak is equal to the initial phase of the sine wave.
2. Intermediate frequency signal:
The initial phase Φ0 of the intermediate frequency signal IF is the phase difference between the TX signal and the RX signal at the time point corresponding to the starting point of the IF signal:
Therefore, for an object at position d with the radar , the IF signal will be A sine wave,
Asin(2πf_0 t + ϕ_0)
where f_0= S＊2d/c
Φ_0= 4πd/λ
When the object is stationary, the frequency difference and phase difference between the transmitting signal and the receiving signal are as follows:
When the object is moving, the transmitting signal remains unchanged, and the receiving signal is delayed by Δτ, and the phase changes are as follows:
When the object moves, the transmit signal remains unchanged, and the received signal undergoes a delay of Δτ. The phase changes are as follows:
3. Principle of speed estimation:
FMCW radar emission interval is Two Chirps of Tc, each reflected Chirp pulse is processed by Range-FFT. Corresponding to the Range-FFT of each Chirp, peaks with different phases will appear at the same position. This phase difference is related to the displacement of the moving object.
Since Δϕ=4πΔd/λ where Δd=v＊T_c can be derived, v=λ＊Δϕ/(4π＊T_c )
2 Speed measurement of multiple targets
If multiple moving objects with different speeds are at the same distance from the radar when measuring, the bichirp speed measurement method will not work. Since the objects are at the same distance from the radar, the generated IF signal frequency Will be the same, passing the distance FFT will produce a single peak that represents the combined signal of objects at the same distance. To measure speed, more than two Chirp signals must be emitted.
To estimate the speed of multiple objects at the same distance, it is necessary to emit a set of N equally spaced chirp pulses, called "frames". For two objects that are equidistant and have different speeds, in the same frame, extract each phase at the peak after passing Range FFT, and do Doppler FFT, which will produce two different peaks, and their corresponding abscissas are the phases of each object. Difference. The velocities of two objects at the same distance and different speeds are v1 and v2 respectively, as shown in the figure below:
3 Velocity resolution
According to the discrete Fourier transform theory, the two discrete frequencies ω1 and ω2 can only be resolved when Δω 2π/N. The
formula is derived as follows:
Therefore, the speed resolution depends on the frame time, that is:
v_res=λ/(2T_f )
4 The maximum speed measurement of radar
Since the speed measurement is based on phase difference, there will be speed ambiguity, and it is non-ambiguous only when Δϕ π.
The maximum speed can be derived from the speed calculation formula v=λ＊Δϕ/(4π＊T_c):
v_max=λ/(4T_c)
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