Timeline for Direct Correlation (DC) Time Delay Estimation: Variance Keeps Decreasing for Increasing SNR?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 26, 2018 at 14:45 | vote | accept | LDPC | ||
| Oct 15, 2017 at 16:34 | history | edited | Olli Niemitalo | CC BY-SA 3.0 | deleted 82 characters in body |
| Oct 10, 2017 at 13:01 | history | edited | Olli Niemitalo | CC BY-SA 3.0 | added 29 characters in body |
| Oct 9, 2017 at 15:09 | history | edited | Olli Niemitalo | CC BY-SA 3.0 | added 183 characters in body |
| Oct 8, 2017 at 13:29 | comment | added | Olli Niemitalo | Hmm one idea, in my Fig. 2 you do get error at $d = 0,\, d = 0.25,$ and $d = 0.5$. So if they did the same bias elimination, these are actually about worst possible values for $d$. | |
| Oct 8, 2017 at 12:14 | comment | added | Olli Niemitalo | I don't get it either, would have to properly read the article maybe... | |
| Oct 8, 2017 at 11:36 | comment | added | LDPC | Yes. That's exactly my issue with the paper. According to the description of the figure I posted, they claim $d = 0$, $d = 0.25$ and $d = 0.5$, for each of the plots. For the case of no delay, I don't understand how the correlation keeps decreasing. Either way, in my simulation I get decreasing values of variance for whichever delay I try. | |
| Oct 8, 2017 at 11:08 | history | edited | Olli Niemitalo | CC BY-SA 3.0 | added 218 characters in body |
| Oct 8, 2017 at 10:50 | comment | added | Olli Niemitalo | Like you say, with $d=0$ and no noise, even crude interpolation will be perfect. I consider $d$ a uniform random variable. Non-zero variance implies that something is random! | |
| Oct 8, 2017 at 10:40 | comment | added | LDPC | Also, sorry for any sillyness. For d=0, I still don't understand how the variance reaches a limit, at least conceptually. In the paper, they obtain the result for no delay as well. The parabola around which you fit should be perfectly symmetric in the case of zero delay and infinite SNR (from my understaning), and as such I don't understand how the parabolic fitting messes with my results | |
| Oct 8, 2017 at 10:40 | history | edited | Olli Niemitalo | CC BY-SA 3.0 | added 4 characters in body |
| Oct 8, 2017 at 10:39 | comment | added | Olli Niemitalo | I did not read the article properly, but perhaps then it's not just one parabolic interpolation, but multiple. If the errors from those are independent and there is averaging of zero bias interpolation results going on, then the average will have less error. | |
| Oct 8, 2017 at 10:34 | comment | added | LDPC | Thank you so much for the detailed and insightful answer. From my understanding, then, you get a fixed bias due to the sub-optimal method of interpolation. My question, in that case, lies with why the Least Squares estimator keeps decreasing in variance according to the paper, since they use the exact same interpolation method. | |
| Oct 8, 2017 at 10:21 | history | answered | Olli Niemitalo | CC BY-SA 3.0 |