Estimation of measurement results with poor information using the dynamic bootstrap grey method

• DGBM can realize multi-sensor data fusion and parameter estimation successfully.
• DGBM has advantage for small sample and probability distribution unknown problems.
• Measurement results estimation accuracy based on DGBM is higher than other methods.

Because of time, cost or safety restrictions, multi-sensor measurement results are commonly of poor information characterized by small data samples and an unknown data distribution. A dynamic bootstrap grey method is proposed to handle such problems considering that traditional statistical methods cannot. For small data samples, the proposed method has a lower relative estimation error of the measurement results compared to the grey bootstrap method and the Monte Carlo method. It is also superior to the Bessel method for large data samples. Based on two sets of experimental data, the estimation reliability of the dynamic bootstrap grey method is above 95% with a confidence level of 99.7% while providing a very low relative error of the estimated expected measured value and estimated measurement uncertainty. The presented results show that the dynamic bootstrap grey method can estimate the measurement results successfully without requiring data distribution information or a large sample size.