Microprocessor Implementation of a Time Variant Floating Mean Counting Algorithm Page: 2 of 25
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WSRC-MS-98-00787
1. Introduction
Rate estimation of nuclear pulses emitted from nuclear detectors has been well documented in
papers written as early as 1965 [1] to as recently as 1990 [2]. It is well known that pulses emitted
from a nuclear detector can vary with time [2] and an accurate estimate of the count rate must be
based on a sufficient number of pulse counts within a sample period as well as the recent history
of pulse counts acquired in previous sample windows to accurately estimate the current rate.
This paper will review the attributes of three popular counting methods and show the
implementation of one of these methods, the floating mean algorithm, on an embedded controller
system. The software discussion will look at how to apply the chosen algorithm on two popular
platforms: the Motorola 68HC11 and the Intel 805X series embedded controllers.
2. Mathematical Algorithms
2.1 Quasi-exponential algorithm
The quasi-exponential algorithm is a digital adaptation of the traditional analog RC type rate
meter [2]. The RC type rate meter was based on a detector output charge being applied to the
capacitor and then dissipating off the capacitor in a time period (T) determined by the resistor
value employed. The resultant output is a most recent value weighted mathematical expression
in which a residual "history" of previous pulses is summed with the most recent value.
Mathematically, the output (rate) can be expressed as:
n n-i
(1) Rn =a/T E (1-a) N1
i=1
where a is effectively the weighting factor applied to each measurement (analogous to the time
constant of an RC circuit), T is the sample interval for a single measurement, Ni is the number of
pulses in the ith measurement, n is the total number of measurement sets being considered, and
Rn is the resultant rate. For sufficiently small values of a, it can be shown that the expression can
be reduced to a recursive algorithm in which the current rate is a weighted function of the
previous rate and the current measurement [2].
2.2 Floating mean algorithm
The floating mean algorithm does not lend itself well to analog implementation. The algorithm
predicts the current rate as an equally weighted mean of the last m measurements.
Mathematically, the floating mean may be expressed as:
n
(2) Rn = 1/(mT) ENi
i=q
where R~ is the current rate estimate, m is the number of measurements included in the mean, T
is the time interval for a single measurement, Ni is the number of pulses measured in the ith
measurement, n is the total number of measurements acquired (thus the nth measurement is the
most recent measurement), and q is equal to 1 when n < m and q is equal to n-m+1 when m>n
[2].
For the purposes of microprocessor implementation, the pulses may be stored in a circular buffer
with the m + 1 sample discarded as new measurements are acquired.
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Huffman, R. K. Microprocessor Implementation of a Time Variant Floating Mean Counting Algorithm, article, November 25, 1998; Aiken, South Carolina. (https://digital.library.unt.edu/ark:/67531/metadc686772/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.