Determination of the phase difference between two sinusoidal signals with noise components using samples of these signals is of interest in many measurement systems. The samples of signals are processed by one of many algorithms, such as 7PSF, UQDE and MSAL, to determine the phase difference. The phase difference result must be accompanied with estimation of the measurement uncertainty. The following issues are covered in this paper: the MSAL algorithm background, the ways of treating the bias influence on the phase difference result, comparison of results obtained by applying MSAL and the other mentioned algorithms to the same real signal samples, and evaluation of the uncertainty of the phase difference.

We present an alternative method to detect and measure the concentration changes in liquid solutions. The method uses Digital Holographic Interferometry (DHI) and is based on measuring refractive index variations. The first hologram is recorded when a wavefront from light comes across an ordinary cylindrical glass container filled with a liquid solution. The second hologram is recorded after slight changing the liquid’s concentration. Differences in phase obtained from the correlation of the first hologram with the second one provide information about the refractive index variation, which is directly related to the changes in physical properties related to the concentration. The method can be used − with high sensitivity, accuracy, and speed − either to detect adulterations or to measure a slight change of concentration in the order of 0.001 moles which is equivalent to a difference of 0.003 g of sodium chloride in solutions. The method also enables to measure and calculate the phase difference among each pixel of two samples. This makes it possible to generate a global measurement of the phase difference of the entire sensed region.

The paper presents new differencing algorithms for post-processing GPS data, using double or triple carrier phase differences and multiple baseline sessions. The characteristic feature of the new algorithms is, that they use full sets of Schreiber's type observation differences with theoretically proved diagonal weight matrices. The proposed estimation models are equivalent to the least squares estimation applied to the original system of un-differenced observation equations. The theoretical ground of the algorithms are the theorems on the properties of differencing equations of Schreiber's type. The theorems become practically useful mainly in case of functional models with triple-differences. In a classical approach, this task was simplified for the sake of necessity of inverting non diagonal covariance matrix, usually of a large dimension. Diagonal weight matrix is also obtained in case of multiple point observation session where correlation of the GPS vectors forces in practice the use of the simplified stochastic models. The proposed method eliminates also the problem of selection of a reference satellite. It is very important especially in case of long observation sessions. The algorithms are applied in professional software for GPS relative positioning.