After some time, it appeared that the previous detection criteria based on a predetermined threshold gave an abnormal false alarm rate (too many humans were declared as potential intruders) when applied to some specific populations, (ethnic groups living in some particular areas characterized by altitude, temperature, etc.).
More extensive studies showed that the human population heartbeat mean value m varies between groups and obeys a Gaussian distribution whose mean value is m0 = 74.3 and standard deviation is sm = 7. The standard deviation of the heartbeat of all these groups is identical with s = 7. This is the combination of all the group statistics which gives the human general distribution whose mean value is m0 = 74.3 and standard deviation is s0 = 10 (s0 = (sm2+s2)0.5 = 10). It is described in graph 1 In this condition a specific threshold has to be determined for each group in order to achieve a "Constant False Alarm Rate" (CFAR) whatever the population.
It was decided that this "local threshold" has to be applied to each group of ten individuals belonging to the same tribe or family living in the same area (to be sure of the group homogeneity).
The process was to compare every individual of a group i to a threshold based of an estimation of the group characteristic mi , assuming that every group obeys a Gaussian distribution.
In a first step it was decided to exclude the individual being tested from the mean value estimation in order not to distort this estimation if this individual is an intruder. That means that a threshold was calculated specifically for each individual from estimation made on the characteristic of the nine other individuals of the same group.
For a "standard" human group (m0 = 74.3, s0 = 9.9) what is the threshold TCFAR to be applied to achieve the probability of false alarm of 1% when CFAR processing is used (if no averaging is implemented).?
What is the resulting probability of detection of an intruder whose characteristics are m = 115, s = 15 (Radman general population)
What is the false alarm probability for a human group i whose true characteristic are mi= 85 and si = 7 with the standard criterion (if no averaging is implemented).
What is the "local threshold" Ti to be applied to guarantee the false alarm probability of 1% and what is the probability of detection for a Radman mixed in that group with CFAR processing.
Same questions for a group j characterized by mJ = 70 and sj = 7
If you click on the graph above, you will be taken to a large graphic representation of the normal curve. Click the "Back" button on your browser to return to this page. The detailed graph is large enough that you will be able to read accurately the number of standard deviations for low probability of false alarm, although you will have to scroll. Another option is to use the inverse normal distribution function on a spreadsheet.