H, G1, G2 photometric phase function extended to low-accuracy data

•A constrained nonlinear least-squares algorithm for the H,G1,G2H,G1,G2 phase function.•New data set of 93 asteroids to reassess the two-parameter version of the relation.•One-parameter version gives a suggestion of the asteroids taxonomic group.•A model selection between the different versions of the photometric phase functions.•An online tool that implements the algorithms.

We introduce a constrained nonlinear least-squares algorithm to be used in estimating the parameters in the H, G1, G2 phase function. As the algorithm works directly in the magnitude space, it will surpass the possible bias problem that may be present in the existing H,G1,G2H,G1,G2 fit procedure when applied to low-accuracy observations with large magnitude variations. With constraints on the photometric phase-curve shape parameters G1 and G2, it guarantees a physically reasonable phase-curve estimate. With a new data set of 93 asteroids, we re-assess the two-parameter version of the H,G1,G2H,G1,G2 function. Finally, we introduce a one-parameter version of the phase function that can give a suggestion of the asteroids taxonomic group based only on its phase curve. A statistical model selection procedure is presented that can automatically select between the different versions of the photometric phase functions. An online tool that implements these algorithms is introduced.