The width of the trunk suggests robusta. It does not rule out filifera. Here is a narrow-stemmed filifera, the California fan palm, in habitat in the desert of Baja California.
And here is a group of plants from that same population, which lies at the extreme southern end of the plant's range.
This site is discussed in this publication, if you really want to see the gory details.
The stem on robusta tends to be narrower but it also tends to be somewhat tapered (twice as wide at the bottom as it is at the top?). I'm not really seeing that in the original photo but maybe it's the case.
As I said before I don't think the differences between the two plants (which you can generally boil down to one being bigger in trunk and crown) are all that important unless you're concerned about size. We have filiferas and hybrids of hybrids sprouting as volunteers everywhere around here... the birds transport seeds far and wide from plants in cultivation.
Some friends of ours used to haunt the canyons where the Washingtonias and Braheas grow together, so we got a taste of what they look like outside of human cultivation. Eagle eyes will discern a couple of Braheas in that landscape shot as well, they are the silver blue palms.