As a life long dog owner myself we know that it is in the nature of dogs to protect their territory and those in it by barking. It is half the reason we get a dog in the first place.
As to what happens next, the neighbours next course of action would be to complain to the environmental health department of the local council.
They will either simply write a letter asking you to keep the dogs quiet if they are being lazy or they will monitor the noise level from the neighbours house.
A high level of persistent noise is required such as a party with loud music and the windows open.
It is unlikely that your dogs will reach the required level.
As such there is little you either need to do or can do, they have to prove the case against you , you do not have to prove your dogs are innocent.
You might wish to consider whether there are some simple steps you can take such as block their view from the window.
I hope this helps, if there are any further points please reply I will be happy to respond.