at any rate

In any event, whatever the case may be; also, at least. For example, At any rate, I promise to be there even if I'm a little late, or It may not pay well, but at any rate it's a job. [Early 1600s] Also see in any case.

The adverb has 2 meanings:

Meaning #1: used to indicate that a statement explains or supports a previous statement; anyhow, they're quiet"; anyway, it's gone"; in any case, there was a brief scuffle"
  Synonyms: anyhow, anyway, in any case, in any event

Meaning #2: if nothing else; (`leastwise' is informal; `leastways' is colloquial)
  Synonyms: at least, leastways, leastwise