Without realizing what you are doing, or without realizing what is happening. This is the everyday, useful member of the family — far more common in real English than the adjective 'unknowing'. You put it with a verb: 'She unknowingly deleted the file', 'He had unknowingly been talking to the CEO all evening', 'Passengers unknowingly carried the virus home'.

Its real job is to remove blame. When you say someone did something unknowingly, you are saying: yes, they did it, and no, it was not their fault — they did not have the information. That is why you meet it constantly in news reports, court language, safety notices, and apologies. 'Customers unknowingly paid the higher rate' tells you exactly who to be angry with, and it is not the customers.

It is neutral in tone and works in both speech and writing, though in casual speech people often prefer 'without knowing it' or 'by accident'. Note that those two are not the same: 'by accident' or 'accidentally' says the result was not what you intended; 'unknowingly' says you did not even know the action was happening or what it meant. You can knock over a glass accidentally — you can't really knock it over unknowingly, because you felt it. But you can unknowingly insult someone, because the insult was invisible to you.

Position is flexible: before the main verb ('she unknowingly signed'), after the object ('she signed the form unknowingly'), or after the auxiliary ('had unknowingly signed'). All three sound natural.