Statistical filtering of random measurement errors

In life, we often have to take into account the accuracy of measurements. There is obviously a desire to have the measured value as accurately as possible. This applies to both static and dynamic measurements. Measurements may be made using one or more meters and involve errors that may be systematic or random. The usual approach to obtaining a more accurate value of a measured parameter is the averaging method. This is a simple and quite effective method, especially if the measurements are equally accurate. If there are n measurements, then the averaging method is the addition of n measurements with the same weighting coefficients. The larger n, the more accurate the estimate will be. But with different-precision measurements, the result may not be optimal. To obtain an optimal estimate (estimates with minimal error variance) for multi-precision measurements, the weighting coefficients must take into account their statistical accuracy. Optimal weighting coefficients should ensure a minimum variance of the estimation error. This is the method of statistical filtering of random errors. Statistical filtering of random errors is also applicable for multidimensional problems. For example, its special case is the so-called “Kalman filter”.