Non-reciprocal time dilation Is this report describing Absolute Lorentz Transformation legitimate or pseudoscience? The reporting sounds like the kinds of things I see in newbie's questions on the twin paradox, or crackpot theories trumpeted on certain discussion forums.
Also, this quote

If you look at the GPS satellites, the satellite time is slowing down, but according to the GPS satellites, our time is not slowing down—which would occur if it were reciprocal. Instead, our time is going faster relative to the satellites, and we know that because of constant communication with the satellites.

makes me ponder, what is the orthodox interpretation for this? 
 A: The author falls into a trap filled with the bodies of those who don't really understand relativity. The article starts by saying:

In contrast, Einstein's theory of special relativity describes reciprocal time dilation between two moving objects, such that both moving objects' times appear to be slowed down relative to each other.

This refers to the notorious twin paradox. If I and my twin are moving at constant speed in a straight line then I will observe my twin's clock to be running slow but my twin will observe my clock to be running slow. The argument of the article is that if this is true, then how come both we on the ground and the GPS satellite agree that the GPS satellite clock is running faster than clocks on the Earth's surface. Shouldn't symmetry require that the GPS satellite observes Earth clocks to be running slow while on Earth we abserve the GPS clocks to be running slow. There appears to be a contradiction.
The reason there is no contradiction is that the author has made two errors.
Firstly the satellites are not moving in a straight line at constant velocity, they are moving in a circle centred on the Earth. I calculate the time dilation for this geometry in my answer to Is gravitational time dilation different from other forms of time dilation? and also Can a ultracentrifuge be used to test general relativity?. With this geometry, as with all geometries where acceleration is involved, the time dilation is not symmetric. Both the stationary and rotating observer will agree on whose clock is running slow and whose clock is running fast. This is of course also the resolution to the twin paradox because the twin's motion is accelerated.
The other error is that in any case the time dilation is dominated by GR effects. Gravitational effects speed up the GPS clock relative to the Earth's surface by about 45 µs/day while special relativistic effects slow it by only about 7 µs/day. So the GPS clock difference of about 38 µs/day is dominated by GR, and in GR time dilation is also asymmetric.
So the whole article is founded upon a false premise, or more precisely a true premise that is used where it's inapplicable.
A: The relativistic effect of slowing down of time are higher than the speeding up effect due to Gravitational effects in orbits which are far away from earth's centre. We understand that astronauts on space staion actually were found to age less by 0.005 seconds. However, for GPS satellites, their orbits could be closer to earth and hence the time speeding up effect due to Gravitation could be more pronounced than the slowing down effect due to relative velocity. Hence GPS satellites may be showing a NET NET faster time than observers on earth. 
A: Time dilation is not reciprocal.
https://www.youtube.com/watch?time_continue=18&v=P16EOmtGnG0&feature=emb_logo
The clock hypothesis of special relativity (SR) uses the term clock synchronization, but it is an asynchronous method that depends on the speed of light.
