Unbiasedness of simultaneous independent measurement

Abstract

We manage to get the true parameter value out of biased data without any zero calibration, a result which has not been reported to our knowledge. In order to obtain the true value of a given physical quantity out of biased noises, a general model and an algorithm based on simultaneous independent measurements are demonstrated. A decision function is constructed using variable measuring vectors. A nonlinear estimator is provided using linear combinations of differential statistics of initial observations. Repeated gyroscope experiments targeting the Earth's local rotation velocity are implemented to validate the algorithm and the estimator. Experimental results show that the true rotation velocity is obtained even if initial observations are either positively or negatively biased. Therefore, it is possible to get the true value of a physical quantity using simultaneous multi-dimensional measurements, no matter whether systematic biases exist or not. This reveals a phenomenon that physical observations, even though obscured by time-varying biases and noises, have an intrinsic true-value feature which has not been made use of in current theories and applications.