Point file to raster

I have a point file of trees in my study area, which includes the attributes of each tree. Each tree also has a crown radius associated with it. I need to summarize the attributes of these points into a 5-meter raster file. The 5-meter raster file placement is defined by a 5-meter fishnet.

I would like a suggestion as to which method is the most statistically robust.

One method I thought might work is:

For a given 5 X 5 meter cell, take the area of each crown that occupies a cell and multiply it by the attribute of interest. Do this for each crown and sum these values and divide by the total area of crown occupying the given cell.

i.e. Let the shape i be have the value of some attribute of the Tree … say Crown bulk density, (CBDi ) Then the value of the grid cell X = sum(CBDi * Ai) / sum (Ai) where Ai is the area of each crown within the cell.

I don't know how to perform this method in ArcGIS though.

Another simple method:

1. Do a point to raster and calculate the mean value and snap the raster to the defined raster.
2. Choose either bilinear or nearest neighbor for the resampling method in the environment settings.

If you have access to ArcGIS for Desktop, you can use:

Documentation: Point to Raster (Conversion)
http://resources.arcgis.com/en/help/main/10.1/index.html#//00120000002z000000

followed by some map algebra:

Example: Performing map algebra on a raster
https://www.e-education.psu.edu/geog485/node/116

If you don't have access to arcgis:

Example: Point to raster using GDAL
http://fuzzytolerance.info/blog/gdal-to-the-rescue/

Question which may help:
http://gis.stackexchange.com/questions/2809/what-raster-based-gis-systems-really-work

If you have a polygon dataset that is your grid then you could use the spatial join geoprocessing tool but make sure you have 'one to many' set. This will give you a grid where the attributes of each intersecting point is attached to a grid cell. It would then be a matter of using the summary statistics tool.