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CCS/AWR1642BOOST: About the algorithm content of convertSNRdBToVar

user5916025
Prodigy 230 points
Part Number: AWR1642BOOST

Tool/software: Code Composer Studio

Hi,

I would like to ask about the algorithm formula in convertSNRdBToVar, I have to find the relevant algorithm about CRLB, but there is no way to correspond to the formula on the program, I would like to ask for a more detailed explanation.

Thank you

  • 0
    TI__Guru 69960 points
    Hi,
    Please refer mmw demo user guide for more info.
    All the details about application and algo used is provided in the same doc (doxygen: mmw\docs\doxygen\html\index.html)


    Regards,
    JG
  • 0 in reply to Jitendra Gupta
    Prodigy 230 points
    Hi,
    Excuse me, I didn't make it clear, I am currently researching mmwave_automotive_toolbox_2_4_7, lab0002_short_range_radar project.
    There are some mathematical operations in convertSNRdBToVar. However, there is no description in the file you provided. I hope that there is a more detailed explanation of this content.
    thank you.
  • 0 in reply to user5916025
    TI__Expert 4720 points

    Hi,

    Given an SNR, the minimum variance an unbiased estimator can achieve is given by the 'Cramer Rao Lower bound' (CRLB). So, when we need to convert an SNR measurement to a variance measurement (i.e. what the Kalman filter expects), we use the CRLB (backed off by 3 dB).

    We then scale this variance with the resolution of the particular measurement. Let me know if you have any questions.

    Regards

    Anil

  • 0 in reply to Anil Mani
    Prodigy 230 points
    Hi Anil,
    Can you provide more detailed content, including the reason for the final conversion to a unit, as well as a mathematical formula? It is best to provide the entire CRLB process.
    In addition, not all estimation algorithms can achieve CRLB. We use FFT and use CFAR. Does this ensure that it must satisfy CRLB?
    thank you.
  • 0 in reply to user5916025
    TI__Expert 4720 points

    Hi,

    Regarding the formula, please look at Chapter 3, example 3.14 in the 'The Fundamentals of Statistical Signal Processing: Estimation Theory by Steven M. Kay'.

    Regarding the final conversion to a unit, the variance computed via the CRLB is the frequency variance. Whereas, the actual unit that we are estimating is either range (in meters), or velocity (in meters/sec), and azimuth (in degrees). To convert from a frequency to one of these units we use the associated 'resolution'  (i.e. range resolution, or velocity resolution, or azimuthal resolution). Likewise for the variance. 

    Regarding your question on the suitability of the CRLB, we do the following to mitigate corner-cases.

    1) We double the variance (on account of our algorithm being an FFT).

    2) We do not let the variance be smaller than the resolution.

    Finally, I believe that the FFT is a pretty good algorithm for estimating sinusoidal frequencies (unless the frequencies are closer than bin width).

    Regards

    Anil

  • 0 in reply to Anil Mani
    Prodigy 230 points
    HI Anil,

    Thank you very much for your answer. I can already understand the CRLB part of the principle.
    However, can you explain clearly the suitability of the CRLB?
    Why we double the variance on account of our algorithm being an FFT ?
    Why we do not let the variance be smaller than the resolution?

    thank you
  • 0 in reply to user5916025
    TI__Guru*** 148804 points
    Hi

    We should be able to get back to you early next week

    thank you
    Cesar
  • 0 in reply to Cesar
    TI__Guru*** 148804 points
    Hi,

    I have checked with algorithm developer.

    1) We double the variance because we know that estimate based on FFT is not good
    2) We don't need to have the variance smaller than the resolution because the error will not be smaller than the resolution

    I will close this thread now. If there are new questions please start a new thread

    Thank you
    Cesar