the official OpenPGP public signing key stored in your GPG keyring, in order to check the ISO new image (it MUST BE identical to the official one published by the Tails project). To obtain this public key: download it then invoke gpg --import tails-signing.key. If you don't know anything about all this and don't want to explore then the present document is not for you, therefore upgrade Tails using the standard procedure. If you don't know and want to explore you may first install Tails from Debian or Ubuntu using the command line and GnuPG (then be prepared to benefit from this document).
Process (bird's view)
This section describes the process. The "Usage" section, below, contains detailed instructions.
You will:
download a VCDIFF patchfile, created by me (using the 'xdelta3' software), which describes the differences between the old version of the Tails image (you already have) and the new one. For example a file named 'tails-amd64-6.15.1.iso_to_6.16.xdelta3' enables you to patch the Tails AMD 6.15.1 ISO image into a 6.16 version. It is useless if you don't already have the file named 'tails-amd64-6.15.1.iso'.
invoke 'xdelta' which will apply the patch, creating the new ISO file
check this new ISO image
use it to boot Tails
Usage
stop Tails (because during this process you will modify the ISO image it uses!)
on a command line (the directory containing your Tails ISO image file must be the current directory), invoke the 6 following commands:
export Tails_PREVIOUS_VERSION=6.15.1 # replace '6.15.1' by the version number of the image file you already have
export Tails_VERSION=6.16 # replace '6.16' by the version number of the newest version
wget --no-clobber http://makarevitch.com/Tails/upd_xdelta/tails-amd64-${Tails_PREVIOUS_VERSION}.iso_to_${Tails_VERSION}.xdelta3 # download the pertinent patchfile. If the file doesn't exist then there is no available patch for you, sorry.
wget --no-clobber https://tails.net/torrents/files/tails-amd64-${Tails_VERSION}.iso.sig # download the official GPG seal
xdelta3 -d -stails-amd64-${Tails_PREVIOUS_VERSION}.iso tails-amd64-${Tails_PREVIOUS_VERSION}.iso_to_${Tails_VERSION}.xdelta3 tails-amd64-${Tails_VERSION}.iso # apply the patchfile
gpg --verify tails-amd64-${Tails_VERSION}.iso.sig # check the new image file
If it does NOT produce a gpg: Good signature from "Tails developers (offline long-term identity key)" message then something failed (it never happened to me nor to numerous friends) and DO NOT USE the new image.