Iterative algorithm for offset and scale estimation for 1d signals superposition with additive and multiplicative noise

Abstract

We describe the algorithm for 1D signal superposition. The superposition is defined by offset and scale. Also the signals contain additive and multiplicative noise. We developed the iterative procedure for superposition of those signals. This procedure includes the separate estimation of offset and scale. The offset is estimated by signals in the Cartesian coordinate system. The scale is estimated by signals in the logarithm coordinate system. The iterative method is approximation to real value of superposition parameters. The parameters of the current iteration depend on the estimation of previous iteration. The error of the parameters estimation from additive gauss noise was by the numerical simulation. The developed algorithm compares with the brute force algorithm (the etalon algorithm). The compassion show that both algorithms are characterized the similar error of the parameters estimation, but developed algorithm is faster.