Genetics problem, test-crossed
The 15:1 phenotypic ratio resulting from the self cross suggests duplicate dominant genes without cumulative effect.
In other words, two genes with complete dominance and dominant alleles producing the same phenotype, but independently, meaning that dominance at one locus ~ dominance at the other locus ~ dominance at both loci as far as phenotype is concerned.  

So, in the self cross:
AaBb x AaBb =>
9 A_B_  double dominance = dominance
3 A_bb dominance from A
3 aaB_ dominance from B
1 aabb recessive
So that's where you get your 15:1 dominant:recessive phenotypic ratio.  

Now, with a testcross, you were on the right track:
AaBb x aabb =>
1 AaBb
1 Aabb
1 aaBb
1 aabb
So, comparing this to the selfing results above, you'd get 3 dominant : 1 recessive for your phenotypic ratio.