How can I avoid requiring global information for performing regression on meter variables?
Your "missing value" formula mentions $v_{i-1}$, and you seem to be suggesting that you'd prefer not to use that. Ok, fair enough. So use an estimate, $\hat{v}_{i-1}$, which is based on weighted regression of $v_{i-1}$ and several preceding values. Give greater weights to more recent values.

You may wish to implement a classifier that labels each reading as "good" or "bogus". Part of that is straightforward, as you already have a "missing" label for some of your samples. The classifier would additionally discard readings that swing implausibly high, or that show physically impossible behavior like having negative derivative.

You don't mention the generative source of bogus readings. If they are due to noise events on the digital channel used for obtaining each reading, then they don't affect the data source and will soon average out. Here is another technique. Suppose you're willing to suffer higher readout latency in exchange for numeric accuracy. Delaying by one sample would let you compute $\hat{v}_{i}$ as median of three values: $v_{i-1}$, $v_{i}$, $v_{i+1}$. Similarly, you could delay by two and find median of five values, or by three with median of seven values.