Intermediate Reports | |
| IR1 | A brief derivative how I plan to use Urkowitz' approximation for ED outputs to estimate the compound CIR. Might be interesting to read through, since it is a brief document. The part with superimposed noise might not be correct, however. |
| IR2 | An analysis about how to choose integration and sampling periods. Illustrates the costs for not fulfilling the Nyquist theoreme. Also includes a few plots where one can see the effects graphically. Also gives a new (intuitive) insight in Urkowitz' approximation if 2WT_i=1. |
| IR3 | In this report I analyzed if and how the start time w.r.t. the leading edge influences the outcome of the integration, especially in terms of ranging error. As we know from literature, uncertainty between start instant and leading edge leads to this famous minimum MAE of T_s/4. It turns out that if we are using sinc-functions to approximate our signal, this uncertainty can be halved. Furthermore, it I doubt that the uncertainty is uniformly distributed, I tend to say that it is rather Gaussian. This document analyzes the uncertainty for different integration and sampling periods w.r.t. approximation error and ranging error (MES and LE). A close look is given at T_i=T_s=2 ns, which might be of vital interest for ranging. |
| IR4 | In this document I gave a closer look at the noise statistics after correlation and averaging, where I am bound to say that it is nothing but a mere appendix to Thomas' previous paper submitted to ICU. For averaging, I calculated the actual distribution of noise samples, whereas for correlation I only calculated first and second order moments. I analyzed both zero-mean and perfect autocorrelation codes, but I must admit that I made this investigation for ideal lowpass-filtered noise only. However, what may be emphasized in this document opposing to Thomas' paper is the fact that due to averaging/integrating/correlating the variance of the noise actually reduces (that is, the standard deviation increases less than the mean value, if no averaging was performed). |
| IR5 | A first try with TPS for ranging only, using direct, parallel, sinc and sliding algos. - UPDATED! |
| IR6 | It is well known that by integrating over Ti, the minimum MAE is Ti/4 if the leading edge is estimated to be at the center of the integration interval. However, it is not so well known how to model this uncertainty -- I tried to explain my approach and compared it to a few others. |
| IR7 | In this report I had a closer look at the sliding algorithm; I tried several integration times, resulting in several resolutions and compared them among each other. The results were rather surprising, getting that with 3 ns integration we get a resolution of 1 ns, but still with subnanosecond ranging errors. However, I am not too sure if I modelled the uncertainty for this particular method sufficiently, so the results have to be considered preliminary. |
| IR8 | This report takes a detailed look at the parallel structure and compares its performance for k=0, k=1 and the IEEE CM1 and CM2. Furthermore, I proved that the parallel structure is identical to the direct structure with a two-tap moving average filter and based on that proof I designed an equalizer to recover the samples prior to MA filtering. Equalization outperforms the parallel structure for all channel models and for both Ti=4 and Ti=8 ns. I also did linear approximation to refine the results, but this was not a good choice as the results show. |
| IR9 | A report similar to IR8: Here I take a closer look at the sliding algorithm and proof its equivalency to a direct algorithm followed by an M-tap MA filter. Based on that proof, I designed equalizers to recover the high-res PDP estimation. Performance of the equalized and the original sliding algorithm is evaluated for K=1 and K=0, for both ranging and channel estimation. Lots of questions are still unanswered, but it's a start. This IR makes IR7 OBSOLETE! |
| IR10 | A report describing the uncertainties due to finite rate sampling of the ED output. Tries to do it on a theoretical basis, but does not manage to get beyond a few obvious results... |
| IR11 | Still to come...should then describe the optimum thresholds for various algorithms. |
| IR12 | Interpolation algorithms. Sinc and LS interpolation, together with prior equalization (thanks to C. Vogel) is evaluated for both ranging and channel estimation. At least, there is a bit of theoretical framework as well. |
| IR13 | Sliding Algo revisited: Now I try channel estimation with CVX (toolbox), and it seems to work well. THIS IS A FIRST VERSION, THERE WILL BE AN UPDATE! |