add body orientation estimation

[adokter]

• For S-band a sine fit on correlation coefficient has been used successfully by Phil Stepanian and Kyle Horton
• For C-band patterns look very different; I've found DBZH, ZDR, and RHOHV all workable quantities, see KNMI scientific report page 148 cont. Main difference is that the fourier component with highest amplitude is not the fundamental but the first overtone (e.g. DBZH, higher reflectivity in side views) or even second overtone (RHOHV, higher correlation coefficient in side views as well as front/tail view)

Proposed approach:

• Earlier vol2bird prototype used a discrete fourier transform to estimate body orientation from DBZH; suggest to switch to simple least-squares fit, to allow data gaps along azimuth
• We can recycle the fitting procedures used for VVP fits, probably easier implementation than using GNU GSL library
• Add a function to libsvdfit.c that essentially describes a sine curve, i.e. a simplification of the vvp function
• make svdfit accept a function as argument, as in legacy vol2bird versions

  
  int (*funcs)(float x[],int Ndx,float afunc[],int Npar)=svd_vvp1func;

float svdfit(float x,int Ndx,float y[],float yfit[],int Npnt, int (funcs)(float x[],int Ndx,float afunc[],int Npar), float apar[],float avar[],int Npar) { //body goes here }

* pass the new sine function to a call of svdfit
* Instead of a simple sine, we may also do a fit of the first, second and third fourier components, i.e. include the sines first overtone. This will bring number of fit parameters to four: i.e. phase, and amplitude of fundamental, first and second overtone. This function may be adequate to fit both C-band and S-band data.

[adokter]

NB: radial functions that have a sum of the fundamental and overtone are nonlinear: fundamental: y_0 = baseline + u_0 sin(phi) + v_0 cos(phi) 1st overtone: y_1 = baseline + u_1 sin(2 phi) + v_1 cos(2 phi) with phi the azimuth

In addition we have the boundary condition that the phases of the two components are equal, i.e. u_1/v_1=u_0/v_0, which for the function y=y_0+y_1 introduces products between fit parameters.

Therefore, easiest to implement a separate fit of either y_0 or y_1 to the radial data

[adokter]

Prototype functionality added by commit a3db9ce8895b85a37f18efac026313b074e73b31

Still to complete:

• [ ] user option to turn on/off body heading fit
• [ ] only have text stdout print body heading info when heading fit turned on
• [ ] user option to select 1st vs 2nd overtone fit
• [ ] fitted baseline values seem too large, just like vertical velocities. check why.
• [ ] add fit results to hdf5 profile