Updating a widget every second with an AlarmManager and IntentService

Question

I have googled a lot and tried so many variations but I just can't get my code working. I have a widget that NEEDS to be updated every second but only when the screen is unlocked.

The widget itself should do 2 things:

1. set an onClickListener to send the user to my MainActivity
2. edit a textbox every second

Since the intervall is really small with one second I thought I have to use an AlarmManger together with an IntentService for the update. Elapsed_Realtime should be right since I don't want to wake up the phone when locked. So this is how my

AppWidgetProvider.onUpdate(Context context, AppWidgetManager appWidgetManager, int[] appWidgetIds)

looks like:

    @Override
public void onUpdate(Context context, AppWidgetManager appWidgetManager, int[] appWidgetIds) {

    final AlarmManager alarmManager = (AlarmManager) context.getSystemService(Context.ALARM_SERVICE);
    final Intent intent = new Intent(context, UpdateService.class);
    final PendingIntent pendingIntent = PendingIntent.getService(context, 0, intent, 0);

    alarmManager.cancel(pendingIntent);
    alarmManager.setRepeating(AlarmManager.ELAPSED_REALTIME, SystemClock.elapsedRealtime(),1000, pendingIntent);
}

Do I really need a loop over the widget-IDs here?

This is how my UpdateService looks like:

public class UpdateService extends IntentService {

    public static int testInt = 0;

    public UpdateService() {
        super("stuff UpdateService");
    }

    @Override
    protected void onHandleIntent(Intent intent) {

        RemoteViews remoteViews = new RemoteViews(this.getPackageName(), R.layout.my_widget);

        //stuff
        remoteViews.setTextViewText(R.id.textView,String.format("%02d",variableThatChangesEverySecond));
        // more stuff

//set onClickListener
        final Intent openApp = new Intent(this, MainActivity.class);
        final PendingIntent pendingAppIntent = PendingIntent.getActivity(this, 0, openApp, 0);
        remoteViews.setOnClickPendingIntent(R.id.myRelativeLayout, pendingAppIntent);

        ComponentName thisWidget = new ComponentName(this,myWidget.class);
        AppWidgetManager appWidgetManager = AppWidgetManager.getInstance(this);

//log a testInt to see how often my widget gets updates
        testInt = testInt + 1;
        System.out.println(testInt);

        appWidgetManager.updateAppWidget(thisWidget, remoteViews);
    }
}

Although I set my intervall 1000ms = 1s my widget updates not exact and only like once in one or two minutes. Here is the logcat to see the updateIntervalls:

06-08 19:21:10.444  19376-19749/mypackage.myapp I/System.out﹕ 1
06-08 19:22:42.900  19376-19798/mypackage.myapp I/System.out﹕ 2
06-08 19:23:02.449  19376-19807/mypackage.myapp I/System.out﹕ 3
06-08 19:24:43.035  19376-19860/mypackage.myapp I/System.out﹕ 4
06-08 19:25:43.087  19376-19876/mypackage.myapp I/System.out﹕ 5
06-08 19:26:43.149  19376-19905/mypackage.myapp I/System.out﹕ 6
06-08 19:27:43.214  19376-19936/mypackage.myapp I/System.out﹕ 7
06-08 19:28:43.282  19376-19960/mypackage.myapp I/System.out﹕ 8
06-08 19:29:43.290  19376-19986/mypackage.myapp I/System.out﹕ 9
06-08 19:30:43.355  19376-20051/mypackage.myapp I/System.out﹕ 10
06-08 19:31:43.419  19376-20096/mypackage.myapp I/System.out﹕ 11

Where is my mistake? Thank you so much, you are my last hope...