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Service center solved my problems. They replaced motherboard and battery.
Dunno about later, i wasn't having any issues with it.
GPS was erratic, when launching GPS test from diagnostics, it tried very long to launch and then "starting GPS failed".
After motherboard swap, seems it is working fine.
I must add compliment about speedy service - brought phone to Sony oficial service center on 25th, got SMS, that phone is fixed on 27th.
I'm also having GPS problems with my phone which I thought were due to the lollipop upgrade but after downgrading to 4.4.4 found they must be hardware related. See this thread here:
/t5/Xperia-Z3-Compact/no-gps-fix-after-lollipop-update-in-Z3-compact/td-p/967188/page/3
I've just sent back to Sony support for the third time, once they get the phone they are quite quick, had the phone back 7 days later first time and 5 days later second time, however they have not fixed my GPS issue and seem hit and miss with others so wouldn't pin your hopes on getting it back quickly. I've now been without my phone for nearly three weeks 
Hello,
I have a Z3 Compact and I am having issues with GPS since I got it. Basically the phone is unable to find my positions when using only GPS module.
Worst thing is that after taking it to the service technique it works but after applyting updates (recommended by Sony through PC Companion) it stops working and again to the service technique.
I am very dissapointed with it, really. Even when it was working it takes soooooo long to find the position. Compared to my old Samsung Galaxy S III it is really **bleep**ty. Samsung is able to find my position in less than one minute (I have tested it with GPS test app).
Sony guys, is that normal? Does it mean that GPS module is just **bleep**ty and I have to live with that?
Has anybody else had problems like these with the GPS??
Thanks all in advance!
I have a Sony Xperia M2 and all GPS/SatNav apps worked perfectly on KitKat 4.4.4. The instant I installed Lollipop 5.1.1 ALL of them failed. GPS test says it can see 25 satellites. The US have 24 evenly distributed around the world and they guarantee you can see 6 at all times, normally 9 and possibly 12 for a few seconds. Lollipop now sees the Russian GLONASS satellites and they have much the same system though their data formats and frequencies differ slightly. So you should now see 12, normally 18 and exceptionally 24. GPS Test starts looking for satellites and the Signal-to-Noise (SNR) status bars fluctuate as the the signal strength varies. Both systems use Low Earth Orbit (about 26000 miles above the earth) satellites that take 11hours and 56minutes to orbit the earth. The 4 minutes short of 12 hours is to allow for the fact that the earth is rotating and that is how long it takes for a satellite to come back to the same place in the sky.
Once it has found 4 satellites, enough for it to compute a 3D fix, it announces '3D Fix' and the SNR bars freeze. A few seconds later it announces 'No Fix', the SNR bars and the satellites it was using disappear and it starts all over again. It does this ad infinitum.
If, on my phone, I simply put the phone part into Airplane Mode, ie no data connection, it all works again. Clear Airplane Mode and it fails again. You'll like it, but not a lot.
A-GPS is only a shortcut to help the GPS get the correct time, that is satellite time, instead of having to have an atomic clock in the phone, they cost about £20000 and are are quite big. Without A-GPS it works out satellite time from the clock signal sent by the satellites it has found. It needs to know the time on the atomic clock in the satellite so that it can work out how long the message took to arrive at the receiver. By working out the time delay it can work out how far away the satellite is. The signal travel at 186,000 miles a second so the clock has to be accurate to a nanosecond.
If you want to be really clever you can use D-GPS, D for Differential, and this uses a land based GPS transmitter that knows EXACTLY where it is on the earths surface and sends out correction data to GPS receivers to correct the errors due to atmospheric conditions.
The problem is with Lollipop as it all worked beautifully under KitKat.
There is some suggestion that Marshmallow has the same problem.
My phone has been back to Sony TWICE. On both occasions they said the issue had been resolved but it still persists.
On the second occasion the gave me a new M2, but it has the same problem.
If it is any consolation other non-Sony phones have the same issue.
Sony refuse to go back to Kitkat. They also refuse to comment on any non-Sony software.
Android is Google's version of Linux so they are the organ grinder and they should fix it.
Answer:- Buy a proper GPS that is only a GPS or a cheap chinese phone on KitKat and don't upgrade it.
I got one off e-bay for £48, its a 7inch Ph(oneT)ablet and is brilliant.
Two SIM card slots, 16GB memory, SD Slot, Wi-Fi, Bluetooth, compass, accelerometers, what more could you ask for.
I solved this problem by changing in file /etc/system/gps.conf as described in https://code.google.com/p/android/issues/detail?id=81140#c695