Thanks for another informative post, Martin. Here's what I found on Rogers-and-Satchell: It is designed to be 'drift-independent'. I'm not sure what the advantage of that is. The n-day volatility_RS is (volatility_RS)^2 = (1/n)*SUM_from_i=1_to_i=n[ ln[Hi/Oi]*ln[Hi/Ci] + ln[Li/Oi]*ln[Li/Ci] ] This is apparently designed to measure the deviation from the trendline between Oi and Ci for every day from i=1 to n. It is an all-intra-day (no interday) measure.
You want to use the log definition, because a key assumption of Black-Scholes is that price is lognormal, that is, price returns as measured by ln[CLOSEtoday/CLOSEyesterday] have a normalized Gaussian probability distribution.