Estimation problems with bounded, uniformly distributed noise arise natural
ly in reconstruction problems from over complete linear expansions with sub
tractive dithered quantization. We present a simple recursive algorithm far
such bounded-noise estimation problems. The mean-square error (MSE) of the
algorithm is "almost" O(1/n(2)), where n is the number of samples. This ra
te is faster than the O(1/n) MSE obtained by standard recursive least squar
es estimation and is optimal to within a constant factor.