Proof of expression

Wireless Connectivity Ultra-Wideband
1

Hi,
In dw1000 User Manual in page 227 :

"The resultant time-of-flight estimate, Tprop, in both the three and four message cases may be calculated using the expression:

T𝑝𝑟𝑜𝑝 = (𝑇𝑟𝑜𝑢𝑛𝑑1 × 𝑇𝑟𝑜𝑢𝑛𝑑2 − 𝑇𝑟𝑒𝑝𝑙𝑦1 × 𝑇𝑟𝑒𝑝𝑙𝑦2) /(𝑇𝑟𝑜𝑢𝑛𝑑1 + 𝑇𝑟𝑜𝑢𝑛𝑑2 + 𝑇𝑟𝑒𝑝𝑙𝑦1 +𝑇𝑟𝑒𝑝𝑙𝑦2)"

Where can I find the proof of this expression?

2

I’m not exactly sure where I got this from, but section 1.2 gives the proof.
The-mathematics-of-two-ADSTWR.pdf (437.8 KB)
It looks to be based on this https://mentor.ieee.org/802.15/dcn/16/15-16-0866-00-0008-correction-of-draft-1-annex-d-blurred-equations.doc (warning, .doc file)

1 Like
3

Hi,

This expression was also published by Neirynck et al. here: https://www.researchgate.net/publication/309349921_An_Alternative_Double-Sided_Two-Way_Ranging_Method

They also give the analysis on clock drift error (and compare it to SDS-TWR).