Set theoretic estimation through triangular noise distribution

Abstract

In most digital signal processing applications, we need to estimate an object from the observations of a physical system which is noise corrupted. In this paper, we propose a general set theoretic estimation by using a preassumed noise distribution. Although noise is usually unbounded and nonuniformly distributed, we propose using the triangular distribution to approximate the unknown noise distribution. With this approximation, we can construct the local feasible solution sets from the solution space and more local feasible sets can also yield a smaller global feasibility set and more reliable estimates. Besides we can obtain a single estimate from the global feasibility set by using the assumed distribution. Simulation shows that our scheme cannot only provide a solution set as set theoretic estimation does but also a correct estimate as recursive least-square (RLS) does. The mismatch effects between the assumed triangular and actual noise distribution are also studied and are not severe. It is shown that our algorithm converges much faster than the conventional RLS estimation even under the distribution mismatch.