When traveling in the park, especially if you're an individual or an independent group, it's best to register with the park office and let them know your intentions. There is no "rescue" service of any kind in Mongolia, but at least they'll know where to begin looking for you if you do go missing or get hurt. Locals are very kind and helpful, but if you do get seriously injured, it will basically be up to your own initiative and strength to get you out of there. Good seasonal clothing, first aid kit, backcountry equipment for the activity your planning and a little knowledge of the area are essential. A good map.
When traveling alone anywhere, it's always a good thing to play it safe. There is potential to run into a few rogues along your route. It is a wild place and far from anywhere. That's what's appealing. Hopefully as a traveler you already have the experience to read situations as they arise when coming across certain individuals. When camping for the night, it's a good idea to ask a local herder to camp near their ger yurt for extra safety. If that's not possible, be discreet in choosing where to set up the tent.
fees/permits
Park permit is required to enter the ATB National Park. Buy an ATB National Park permit from ATB National Park Administation office in Ulgii center. Park permit costs 3000 tugrik Approx. $2.4 . If you are going into the park, which is next to the border with Russia and China, you will also need a border permit obtained from the border guards office in Ulgii center. Not having one can potentially get you arrested. Your tour company will take care of this for you, or you can ask at the national park information office for someone to help arrange this for you if traveling independently.
Independent travellers in the park will find that park rangers and border guards will stop and ask for permits and fine you accordingly if you don't have them.