Issue fitting data to a model

I'm having an issue fitting some data to the model I have attached. The data I have represents the final output of the model (x). I would preferably like to use the fittype function so I can use fitting options. I am trying to estimate A, B, C, and D (although I'm not sure how to deal with x1, x2, and i?). Can anyone help? Im usually OK with fitting data but this particular model has been challenging. Everything I've tried has been very wrong.

Edit: Also I know that k is the independent variable.