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| -rw-r--r-- | 08.-Passive-Radar.md | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/08.-Passive-Radar.md b/08.-Passive-Radar.md index e68255c..f90279b 100644 --- a/08.-Passive-Radar.md +++ b/08.-Passive-Radar.md @@ -84,15 +84,15 @@ If you are using DAB (or other more narrow illuminators), note that this only ha # Range-Doppler Units The range-doppler graph displays bistatic range and bistatic speed. The axes are currently described in CELLS. In order to convert cells to meters or m/s use the following formulas: -$Bistatic Range (meters) = R_b = cell * c/fs$ +$\mathrm{Bistatic Range (meters)} = R_b = cell * \frac{c}{fs}$ Where $c$ is the speed of light, and $fs$ is the sample rate (aka bandwidth), and $cell$ is the x-axis cell. The sample rate by default is set to 2.4 MHz. If you have an illumination signal that is smaller, you should set your sample rate to the closest possible bandwidth that matches that illumination signal. -So for example if we see an object at cell 50 on the x-axis, and we have a sample rate of 2.4 MHz we can calculate $Bistatic Range (meters) = R_b = 50 * 299792458 / 2400000 = 15,614m = 15.6 km$ +So for example if we see an object at cell 50 on the x-axis, and we have a sample rate of 2.4 MHz we can calculate $\mathrm{Bistatic Range (meters)} = R_b = 50 * \frac{299792458}{2400000} = 15614 \mathrm{m} = 15.6 \mathrm{km}$ For converting doppler cells to Hertz the formula is as follows: -$Bistatic Frequency (Hz) = cell * fs / (2*N)$ +$\mathrm{Bistatic Frequency (Hz)} = cell * \frac{fs}{2N}$ Where $fs$ is the sampling frequency as before, $N$ is the sample size of the coherent processing interval (CPI), and $cell$ is the y-axis cell on the graph. @@ -100,13 +100,13 @@ In the passive radar software we provide three configuration files `pr_2ch_2pow2 Example cell 500, sampling rate 2.4 MHz and $N = 2^{22}$ -$Bistatic Frequency (Hz) = f_b = 500 * 2400000 / (2*2^{22}) = 143 Hz$ +$\mathrm{Bistatic Frequency (Hz)} = f_b = 500 * \frac{2400000}{2 \times 2^{22}} = 143 \mathrm{Hz}$ Then to get to speed in m/s we simply multiple the Bistatic Frequency f_b with the wavelength of the illuminator, and multiply by -1. (Positive Doppler decreases the range between you and the target so it has negative speed, it is approaching) So if we were using 560 MHz as our illuminator: -$Bistatic Speed (m/s) = c / f * -f_b = 299792458 / 560000000 * -143 = 76.5m/s = 275 km/h$ +$\mathrm{Bistatic Speed (m.s^{-1})} = -f_b \frac{c}{f} = \frac{299792458}{560000000} \times -143 = 76.5 \mathrm{m.s^{-1}} = 275 \mathrm{km.h^{-1}}$ Note that objects moving along the line connecting the transmitter and receiver will always have 0 Hz Doppler shift, as will objects moving around an ellipse of constant bistatic range. |