Peter C. Niedfeldt and Randal W. Beard, Convergence and Complexity Analysis of Recursive-RANSAC: A New Multiple Target Tracking Algorithm, in IEEE Transactions on Automatic Control , vol.61, no.2, pp.456-461, Feb. 2016, DOI: 10.1109/TAC.2015.2437518.
The random sample consensus (RANSAC) algorithm was developed as a regression algorithm that robustly estimates the parameters of a single signal in clutter by forming many simple hypotheses and computing how many measurements support that hypothesis. In essence, RANSAC estimates the data association problem of a single target in clutter by identifying the hypothesis with the most supporting measurements. The newly developed recursive-RANSAC (R-RANSAC) algorithm extends the traditional RANSAC algorithm to track multiple targets recursively by storing a set of hypotheses between time steps. In this technical note we show that R-RANSAC converges to the minimum mean-squared solution for well-spaced targets. We also show that the worst-case computational complexity of R-RANSAC is quadratic in the number of new measurements and stored models.