We consider the frequency estimation of periodic signals using noisy time-of-arrival (TOA) information with missing (sparse) data contaminated with outliers. We tackle the problem from a mathematical optimization standpoint, formulating it as a linear regression with an unknown increasing integer independent variable and outliers. Assuming an upper bound on the variance of the noise, we derive an online, parallelizable, near-CRLB optimization-based algorithm amortized to a linear complexity. We demonstrate the outstanding robustness of our algorithm to noise and outliers by testing it against diverse randomly generated signals. Our algorithm handles outliers by design and yields precise estimations even with up to 20% of contaminated data.