Defining custom projection for moving all objects on X and Y coordinates

Question

I have a map project wih layers in WGS1984 UTM projection. I also have a bunch of layers without .prj files. When I add it on top of my layers, it's placed with a huge offset on X and Y coordinates but other than that everything is fine, features are not distorted etc. So basically I just need to "move" all the features along X and Y axes and everything will be alright.

Can I define such projection using ArcGIS "Define projection" tool or something else? I need a projection that just adds a linear offset to X and Y coordinates. I know I can fix one layer by using "Spatial Adjustment" tool and it works fine, but my goal is to have a .prj-file that I can use for any such layer.

I'm kinda new to ArcGIS and will give clarifications if needed. Any help would be appreciated, thanks in advance.

Answer 1

It would be much more reliable to try to determine what coordinate system these other layers are using. If in the US, are they in a local State Plane zone? If in Canada, are they in a 3TM system?

Because they have no known coordinate system, you can use ArcMap to try to figure this out. Set the data frame to different possibilities. ArcMap will project the 'known' data to the new system. If you can get them to line up with the 'unknown' layers, you've found the coordinate system.

You can also use this technique to confirm that the layer are simply offset in the x and y directions. Modify the UTM coordinate system through its false easting and false northing values. With tweaking, you can see how well the layers line up.