Why is the Allan Deviation (ADEV) so useful in today’s technical world? In a nutshell, with this development we have much more accurate and precise timing systems like the marvel of GPS. During my life, timing accuracy has improved a billion fold, and ADEV has been the metric to characterize and quantify these amazing improvements. Because of these improvements time determination moved from astronomical to atomic in 1967, and this metric was and still is the main measurement technique optimally combining the readings of atomic clocks to generate the smoothest time-scale and the most accurate.
Allan Deviation Birth and Usefulness
Today (12 May 2022), I Googled “Allan deviation,” and got 135 million hits. ADEV is the square root of the Allan variance, and its usefulness is ever-expanding. WHY?
I hope to give you a feel for why in this blog article. I wrote my master’s thesis in 1965, which gave birth to the Allan variance, by asking the question, “What happens to the classical variance and standard deviation in the presence of different kinds of noise and as a function of different measurement parameters?”
From this investigation, we learned that noise has a spectrum of colors and that for some kinds of noise, like flicker-noise frequency modulation, the classical variance has no well-defined mean value, and its magnitude increases without limit. Yet, flicker-noise is ubiquitous in nature. So, we learned that the classical variance and standard deviation, in general, are not good measures. It is like taking a black and white picture of a rainbow. You only get intensity and no color. Yet, noise has a large spectrum of colors.
The Allan variance can be shown to be the optimum estimate of the change in rate in an ideal atomic clock in a variance sense, as a function of the sampling time. It was used to assure the atomic clocks needed for GPS had sufficient accuracy and timing stability to meet the needs of this high accuracy navigation system. As the sampling time is varied, ADEV gives a picture of the changes in an atomic clock’s rate– displaying the different colors of noise.
Changes are Like Repentance
Like in life, changes are like repentance. As we exercise faith in Jesus, we change our behavior to be closer to His teachings. In metrology, we desire to know the signal in the presence of noise. ADEV allows us to characterize the different kinds of noise so we can better understand and utilize the signal we are looking for in the midst of the noise. And, there is always noise.
In life, we are trying better to know Jesus’s true teachings in the midst of Satan’s noise and distractions, so that we can change our behavior to be consistent with His perfect life. This takes us toward the abundant life that He promises. “I am come that they might have life, and that they might have it more abundantly.” (John 10:10)
Signal to Noise (S/N) is fundamental in all of metrology. Similarly, knowing truth from error is fundamental in life. This is like sorting out God’s word in the midst of Satan’s noise. We have His sure promise that as we treasure up His word we will not be deceived. (Joseph Smith Matthew 24:30, JS Mark 13:26, and JS-M 37 in the Pearl of Great Price) So, as we feast upon His word in His holy scriptures (2 Nephi 31:20-21) and in personal revelations from Him, our signal to noise (S/N) will get better and better, and then we are on the path for the ultimate blessing and promise of a fullness of joy.
I have learned the extremely important lesson in my physics career that including God in my work makes all the difference. I believe He has blessed me greatly because I have focused my work on how to best serve Him and His precious sons and daughters. I believe He helped me with my master’s thesis, and in accountable other occasions. I know He is there continually for all of us if we will but come unto Him. (Matt. 11:28-30).
Improvement in ADEV
There was an imperfection in ADEV that we lived with for sixteen years. Then again with help from the Lord and wonderful colleagues, I was able to develop the Modified Allan variance (MVAR), which then gave us more full color of the different noise processes we see in atomic clocks, in nature, in measurement systems, and due to environmental perturbations.
After the development of MVAR and seeing its usefulness, a few years later, the telecom community came to me and asked for help to characterize the noise in telecom networks. Out of that effort came the “Time variance” measure (TVAR), which is a derivative of MVAR. I believe the Lord inspired that effort as well. The square roots of these three measures, AVAR, MVAR, and TVAR are ADEV, MDEV, and TDEV, respectively, and all three became IEEE (Institute of Electrical and Electronics Engineers) standards in 1988.
ADEV has great use in the time and frequency community, MDEV in the navigation community, and TDEV in the telecom community. However, because these natural noise processes persist across all of metrology, the number of uses continues to grow.
Unusual uses of ADEV and Allan variance
While I am pleased with the increased use of these measures, I have also been surprised with the large range of applications—everything from the precision of alcohol detection in drunks, to heart-rate monitoring, to ocean tides, to carbon-dioxide emission level variations, to rainfall variations, and the list goes amazingly on.
I recently learned that the Allan variance was used to examine data from the James Webb Space Telescope.
I subscribe to academia.edu, which shows who is using any of my publications. Since I subscribed over a year ago, I have about two thousand papers that mention my publications. For me, I view it a greater opportunity let the world know of God’s love; it is not for self aggrandizement. “Pride goes before the fall”
Why Such A Blog Article?
My main goal in writing this blog article is to help people deal with the noise in life and to know of God’s infinite love for them (John 3:16). Satan has an uncountable number of noise distractions and distortions to take us away from the truth. I know Christ is the way, the truth, and the life (John 14:6) and we have His remarkable promise, “Ye shall know the truth, and the truth shall make you free.” And “If the Son, therefore, shall make you free, ye shall be free indeed.” (John 8:32, 36) Because of Satan’s noise, we are admonished in addition to treasuring up His word to, “Pray always, that you may come off conqueror; yea, that you may conquer Satan, and that you may escape the hands of the servants of Satan that do uphold his work.” (D&C 10:5)
Gratitude fills my heart for my uncountable blessings, as I have learned over the years to do things His way, rather than my way. He will not force nor ever violate our agency (free choice), which is fundamental to His perfect plan of happiness. I know that as we ask, seek, and knock, we will receive, find, and have opened to us (Matt. 7:7-8) the best way to fulfill our life’s missions that will be the greatest blessing to us and to all whom we are privileged to serve. Let us be grateful as well for the challenges in life; from them we grow as we ask Him what lessons we are to learn from these experiences in our lives. The bottom-line is to trust in Him.
For more Technical Details
For those who have some math, engineering, or physics skills there is a six-minute video where I explain in simple terms the message of my master’s thesis to Dr. Elizabeth Donley, which gave birth to ADEV, as she conducts the IEEE ORAL HISTORY of my life. The IEEE ORAL HISTORY is also available on my book’s website with two other fun and short video clips, in laymen’s terms, on how we were invited to go to Israel and how time is optimally generated from an ensemble of atomic clocks. I also have on my book’s website an explanation in laymen’s terms of the Allan variance.
When Dr. Donley came to our home 5-6 November 2018, I shared with her a fairly comprehensive tutorial–including her questions and comments that has been put up on the IEEE/UFFC website: Educational Resources | IEEE UFFC (ieee-uffc.org). Even for someone without a technical background, there are some fun insights and perspectives shared, and I was able to share my testimony–to let the people of the world know that God loves them.
Little Did We Know What the Future Would Bring
Back in 1965, no one had a clue where this work would go, but the Lord knew, and now—in a troubled world—I have the opportunity to share a happier path for life and for the life beyond for all who desire to know the TRUTH—during my 86th trip around the sun while focusing and following the Son (Jesus the Christ)! As the Savior said to the Father, “…not as I will, but as thou wilt.” (Matt. 26:39) So, let it be with us and make the world be a much better place.
For those who desire, the fun part is that the Lord has led me to share using the scientific method the validity of His scriptures and the validation of the infinite atonement of our Lord and Savior. (See links below).
May the Lord bless you and yours, I pray. May your heart be continually filled with gratitude and learn from the lessons of life by having a wonderful S/N–signal to noise, as you follow the Spirit and ignore Satan’s distractions.
David W. Allan
P.S. PLEASE TAKE NOTE
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