Analysis of direction finding error of multi baseline interferometer system

stay 1961 year ,N.Burtnyk,C.W.Mcleish and J.Wolfe Put forward interferometer direction finding technology . Reference resources 《Interferometer direction finder for the h.f. band》 link ：http://www.onacademic.com/detail/journal_1000037038765710_91cd.html

Noun English ：
RF–Radio Frequency
PRI–Pulse Repetition Interval
PW–Pulse Width
de-interleave– Sorting

reference ：
《 A real-time phase correction method for interferometer direction finding system 》（ Electronic world ）

One 、 Direction finding principle of single baseline interferometer

Signal phase difference between two antennas ( Company , radian ) by ：

among ：
D—— The distance between the phase centers of two antennas ( Baseline length ), Company m;
—— The wavelength of the signal , Company m;
—— Signal incidence angle , The unit of ;

Back calculate the incident angle ：

among ：
D—— The distance between the phase centers of two antennas ( Baseline length ), Company m;
—— The wavelength of the signal , Company m;
—— Phase difference between two signals , Unit radian ;

Two 、 error analysis

Make total differentiation of the phase difference formula , give the result as follows ：

among ：

It represents the influence of signal wavelength measurement error on phase difference error . In practical engineering , The accuracy of frequency measurement is higher than 1MHz, After conversion , The influence on the phase difference is 1-2 degree ;

Represents the influence of baseline length error on phase difference error . In practical engineering , The baseline length can be controlled to 0.1mm, After conversion , The influence on the phase difference is 1-2 degree .

therefore , After ignoring the above two errors , The phase difference error is as follows ：

2.1 DF error analysis

1、 The direction finding error increases with the increase of signal wavelength ;
2、 Direction finding error decreases with the increase of baseline length ;
3、 The direction finding error increases with the increase of the incident angle ;
4、 The direction finding error increases with the increase of phase discrimination error .

2.2 Generation of phase discrimination error

1、 The existence of antenna individual differences and mutual coupling effect between antennas ;
2、 The phase of active devices changes with temperature ;
3、AD The effective quantization bits and the signal-to-noise ratio of the link ;

3、 ... and 、 Rayleigh limit （Rayleigh Rseolution Limit）

Rayleigh rule The definition is as follows ： When the center of the diffraction pattern of one point just overlaps the first minimum of the diffraction pattern of another point , According to Rayleigh rule , They can be distinguished .

Minimum resolution angle △θ=1.22λ/D（ The half width is calculated ）

Super resolution algorithm proposed in array signal processing , Such as music Algorithm ,esprit The algorithm has broken through the Rayleigh limit , What is the Rayleigh limit ？

Rayleigh limit comes from Rayleigh criterion in optics , It's about light passing through a small hole , Will produce diffraction phenomenon, forming a bright and dark alley , Also called diffraction ring ;

Rayleigh limit is about resolution , For array signal processing , The resolution of the array mainly depends on the length of the array aperture , The longer the length , The better the resolution , But in practice, the array aperture cannot be infinite , So there is a finite array aperture , That is, a certain array resolution ; The determined array resolution is the Rayleigh limit .

This leads to another problem ： What is resolution ？

Resolution is when two targets are very close , The ability limit to distinguish these two goals ; In other words When the two goals are close , At this time, we can distinguish two goals , A little closer , You can't distinguish between the two goals , Just when you can distinguish two goals , The distance between two targets is their resolution .

Take the discrete Fourier transform as an example ： When the two frequencies of the signal are close enough , Their difference ratio DFT The resolution is still small , You can't see two targets on the spectrum , It is impossible to distinguish two frequency components ; Array signal processing is nothing more than time-domain Fourier transform , It becomes spatial Fourier transform , So it is similar to time domain Fourier transform , Before the super-resolution algorithm was proposed, the Fourier transform algorithm will have Rayleigh limit ;

summary ：

1、 Rayleigh limit is generally related to array aperture , The larger the array aperture , The better the resolution , The Rayleigh limit is inversely related to the array aperture ;

2、 Analogy to FFT（ Its frequency domain resolution is equal to the reciprocal of sampling time , The longer the sampling time is , The better to distinguish ）; Rayleigh limit is related to the method of use , Classical beamforming methods have Rayleigh limits ;
3、 Limited by the actual situation , The array aperture cannot be made infinite , So there is a highest resolution , Rayleigh limit ;