If we consider the position corresponding to each temperature sample as time point, then we actually get a sequence of temperature sample. To deal with the noise in the sequence of signal, the typical method is to design a filter.
So, in the forth algorithm, we design one digital filter to filt out the noise in data, and get a smooth curve. Similar to the algorithm of Polynomial Fitting, we can get the point of maximum gradient directly from that curve, and then move one sensor to there. When the senso get new data, the data will be put into the original data set, and a new curve can be generated and new maximum gradient point can be found. If the new point is almost the same as the previous one, the algorithm terminated; If it is quite different from the previous one, a sensor will be moved to that place to collect new data. This procedure will iterate until we always get the same point.
Following is the output of the Filting algorithm and the temperature distribution gotten by densely sampling the temperature alone the strand. As the Polynomial Fitting, Filting is faster than Back Track Binary Search.