Don't see why it wouldn't be legal. Typicaly there is no expectation of privacy if you are in a public place. Your photo and video are fair game so long as not used ofor commercial purpose. BUT, before I would do this yu may want to consult with your attorney. You may think the video supports your case. Someone else may see something in iyt that hurts you.
There may also be problems with this in different jurisdictions. For example I know in Canada, Google is going around snapping street level shots for Google Maps. The Canadian right to privacy groups and various government departments are looking to determine if this is even legal.