Gamma MSP: Reference Manual

doppler_2d

ANSI-C programs: doppler_2d.c

NAME
doppler_2d- Calculate Doppler centroid as a function of slant range and azimuth position  using  line to line  cross-correlation measurements of SAR raw data (IQ ADC format:).

SYNOPSIS
doppler_2d <SAR_par> <PROC_par> <signal_data> <dop2d> [loff] [blsz] [nbl] [a2_flg][b0_flg] [b1_flg][c0_flg] [ambig_flag] [namb]

EXAMPLES
doppler_2d RSAT_5011.par p5011.slc.par 5011.raw 5011.dop2d 0 2048 

Analyze the data set 5011.raw using a blocksize of 2048 echoes, starting from the line offset given in the processing parameter file. Default Doppler centroid parameters are estimated from the raw data.

DESCRIPTION
The correlation algorithm used in Doppler averages the complex correlatation between adjacent echoes for each range bin. (see MSP documentation for doppler). The resultant estimates of the Doppler centroid are  wrapped modulo the pulse repetition frequency. Doppler ambiguity is equivalent to a shift of the Doppler centroid by the pulse repetition frequency (Hz). For the 1-D case, where the Doppler centroid is a function of range  alone, the unwrapping is performed by looking at the difference in Doppler centroid for adjacent range bins and adding  or subtracting a multiple of the PRF such that the difference is less than PRF/2.  Sensors such as Radarsat-1 that are not yaw steered can exhibit doppler variations of 20 Hz/sec along-track. The Doppler centroid model must then be extended to include this along-track variation if multiple raw data frames are to be processed. This extended  parametric model for fd is a function both of slant-range r relative to center swath and the along-track time t relative to the center of the raw data set.

fd(r, t) = a0 + b0*t + c0*t**2 + (a1 + b1*t)r + a2*r**2                     (1)

The range used in equation 1 is relative to the center of the raw data swath.  The time argument t is relative to the center time of the entire raw data set.
The programs doppler and doppler_real estimate parameters parameters a0, a1, and a2 only.

For the 2d implemnation that includes the along-track variation in Doppler centroid we apply the line-to line correlation algorithm for a set of along-track blocks . This yeilds the ambiguous centroid on  a 2-D array of points as a function of relative slant range and time.  This array  of measurements is unwrapped in 2-D by comparision with a parameterized set of Doppler model functions and the model with the least error is used to unwrap the centroid estimates. The unwrapped Doppler centroid estimates are  then used to determine the 2-D model parameters a0, a1, a2, b0 and b1 and the c0 by performing a  least-squares fit.

The global Doppler ambiguity can either be set to a given number, or from the  unambiguous Doppler centroid estimated by dop_ambig (recommmend).  The user can also optionally select which of the parameters a1, b0, b1, and c0 are fit.  Below is the typical output from running doppler_2d on an ERS2 raw data set:

$ doppler_2d raw/ERS2_ESA.par raw/p19990915_test.slc.par raw/19990915.fix 19990915.dop_2d
*** 2-D Doppler centroid estimation for IQ SAR data ***
*** Copyright 2006, Gamma Remote Sensing, v1.8 20-Nov-2006 clw ***

SAR sensor description: ERS2 C-BAND radar 5.3 GHZ 15.55 MHz BW
scene title: 19990915 ERS2_ESA.par orbit:23027 frame:2907

image start time sec:    66323.5830     center time:   66331.9172
radar wavelength (m):    0.05656461
ADC mode, f_samp, chirp offset freq. (Hz): IQ  1.89625e+07
pulse repetition frequency (Hz):        1679.878455
range to first sample (m.):              829147.393
number of range samples:                 5616
range sample spacing (m.):                 7.904890
offset to first echo (lines):       0
number of lines to process:     28002
block size (lines):              4096
number of blocks:                   6
fit parameter flags  a2: 0  b0: 1  b1: 1 c0: 0
order of Doppler polynomial fit:  6
single byte values, (2 values/sample in IQ mode), #samples/echo:   5616

number of sample points in DC bias sum:   22173104
I channel offset:  15.506937
Q channel offset:  15.514473

block:    1   starting echo:      0  block center time:      -7.1154
block:    2   starting echo:   4096  block center time:      -4.6771
block:    3   starting echo:   8192  block center time:      -2.2389
block:    4   starting echo:  12288  block center time:       0.1994
block:    5   starting echo:  16384  block center time:       2.6377
block:    6   starting echo:  20480  block center time:       5.0760

search increment for fd0:      6.250e-02
search increment for dfd0/dt:  1.250e-03
search increment for dfd0/dr:  5.631e-06

chisqm:  5.560e-02 c1m:  0.000e+00  c2m:  -0.00125  c3m:   0.00000
number of valid points: 31776

Doppler Ambiguity Resolver (DAR) centroid (center swath) (Hz):       0.000  ambiguity number:  0

estimated Doppler polynomial coeff.:       24.639 -8.734e-04  0.000e+00 -1.356e+00  1.797e-05  0.000e+00
Doppler standard deviation (measured - model):     16.152 Hz

writing updated MSP processing parameter file: raw/p19990915_test.slc.par

The output file has 4 columns:
1. range sample number
2. estimated doppler centroid
3. polynomial fit of the doppler centroid
4. difference of the measured value with respect to the fit

To get a set of plots of doppler centroid in Hertz versus slant range sample number withone plot for each block:

echo "plot 'raw/19990915.dop_2d' u 1:2 with lines lc 3 lw .5, 'raw/19990915.dop_2d' u 1:3 with lines lc 1 lw .5"  |gnuplot

An example plot is shown below:

OPTIONS
The auto-focus program af may also be used to resolve the global Doppler ambiguity.

SEE ALSO
Users Guide, typedef_MSP.h, MSP Processing Parameter File, doppler, doppler_real, af, dop_ambig, azsp_IQ