I've tried to update but then I got this error

Here's the error information in that box:

W:GPG error: http://extras.ubuntu.com precise Release: 
The following signatures were invalid: BADSIG 16126D3A3E5C1192 Ubuntu Extras Archive Automatic Signing Key <[email protected]>, 
W:Failed to fetch http://ppa.launchpad.net/unity-team/hud/ubuntu/dists/precise/main/source/Sources  404  Not Found,
W:Failed to fetch http://ppa.launchpad.net/unity-team/hud/ubuntu/dists/precise/main/binary-i386/Packages  404  Not Found, 
E:Some index files failed to download. They have been ignored, or old ones used instead.

And my Internet connection is working fine.

After trying

$ sudo apt-get install ppa-purge 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
ppa-purge is already the newest version.
The following packages were automatically installed and are no longer required:
  language-pack-zh-hans language-pack-kde-en language-pack-kde-zh-hans
  language-pack-kde-en-base kde-l10n-engb kde-l10n-zhcn
  language-pack-zh-hans-base firefox-locale-zh-hans
  language-pack-kde-zh-hans-base
Use 'apt-get autoremove' to remove them.
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

$ sudo ppa-purge ppa:unity-team/hud
Updating packages lists
W: GPG error: http://extras.ubuntu.com precise Release: The following signatures were invalid: BADSIG 16126D3A3E5C1192 Ubuntu Extras Archive Automatic Signing Key <[email protected]>
W: Failed to fetch http://ppa.launchpad.net/unity-team/hud/ubuntu/dists/precise/main/source/Sources  404  Not Found    
W: Failed to fetch http://ppa.launchpad.net/unity-team/hud/ubuntu/dists/precise/main/binary-i386/Packages  404  Not Found
E: Some index files failed to download. They have been ignored, or old ones used instead.
Warning:  apt-get update failed for some reason
PPA to be removed: unity-team hud
Warning:  Could not find package list for PPA: unity-team hud

I've tried

$ sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 16126D3A3E5C1192 
Executing: gpg --ignore-time-conflict --no-options --no-default-keyring --secret-keyring /tmp/tmp.v6Ucus0B10 --trustdb-name /etc/apt/trustdb.gpg --keyring /etc/apt/trusted.gpg --primary-keyring /etc/apt/trusted.gpg --recv-keys --keyserver keyserver.ubuntu.com 16126D3A3E5C1192
gpg: requesting key 3E5C1192 from hkp server keyserver.ubuntu.com
gpg: key 3E5C1192: "Ubuntu Extras Archive Automatic Signing Key <[email protected]>" not changed
gpg: Total number processed: 1
gpg:              unchanged: 1

And then started the same procedure but of no use.