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The estimation of position coordinates of a navigating ship is one of the navigational subprocesses. The methods used in this process are either deterministic (the case of a minimum number of navigational parameters measurements) or probabilistic (in cases where we have access to information redundancy). Naturally, due to the accuracy and reliability of the calculated coordinates, probabilistic methods should be primarily used. The article presents the use of the method of least squares and Kalman filtering in algorithms in integrated navigation for the estimation of position coordinates, taking into account ship movement parameters.
This paper describes the research concerning precise short-time GPS solutions conducted in the Centre of Applied Geomatics, Military University of Technology, Warsaw, Poland. The data from ASG-EUPOS software and EPN (EUREF Permanent Network) standards and models. In this study, the adapted 3-hour observation window is shifted every hour for obtaining hourly geocentric coordinates in ITRF2005 reference frame. The adjusted network consisted of over 130 stations from Poland and the neighbouring countries, the period covered observations collected from June 2008 through June 2010. These two years of observations allowed for examining short-period oscillations which were found to be closely related to the tidal (dynamic) frequencies. The analysis of the residua from the IERS2003 tidal model was performed using the least squares method with the Eterna software. It confirmed the existence of significant (several millimetres) oscillations in the frequencies corresponding to S1, K1 and K2. The paper describes the idea of data processing and analysis, presents the results of vertical (the Up component) oscillations in main tidal frequency bands, and also includes discussion of possible explanation of the existence of short-period oscillations in the GPS precise solutions and the possibility of propagation of short-period oscillations into long-period spurious changes in the daily (standard) GPS solutions.
A concept of the vector space of imperceptible observation errors in linear Gauss-Markov models with uncorrelated observations, initially proposed in the earlier work of the author, is presented together with some improvements and new developments. The gross errors falling into that vector space pass absolutely undetected through all possible statistical tests set in the least squares estimation and unnoticeably distort the resulting values of one or more of the model parameters. The relationship is established between the concept of imperceptible gross errors and the concept, proposed by other authors, of the gross errors which can be detected but not identified due to specific properties of a network's structure. The theory is illustrated with a simple numerical example.
Pojęcie wektorowej przestrzeni niedostrzegalnych błędów obserwacyjnych w modelach liniowych Gaussa-Markowa z obserwacjami nieskorelowanymi, zaproponowane we wcześniejszej pracy autora, przedstawione jest z pewnymi udoskonaleniami i nowymi dokonaniami w tym obszarze. Błędy grube trafiające do tej przestrzeni są zupełnie niewykrywalne w jakichkolwiek możliwych testach statystycznych wykonywanych w procesie estymacji metodą najmniejszych kwadratów i niezauważenie zniekształcają wynikowe wartości jednego bądź więcej parametrów modelu. Pokazana jest zależność między pojęciem błędów grubych niedostrzegalnych a proponowanym przez innych autorów pojęciem błędów grubych wykrywalnych ale nieidentyfikowalnych na skutek specyficznych własności struktury sieci. Teoria ilustrowana jest prostym przykładem liczbowym.
This paper deals with the idea of estimation of the substrate consumption rate at each point of the tube of the classical distributed parameter bioreactor and its application to the monitoring of this system. It is shown how to approximate the profile of this parameter on the basis of the orthogonal collocation method and the recursive least-squares procedure with adjustable forgetting factor. Then, it is suggested how to apply this profile for monitoring of the bioreactor work (calculation of the current mass flux of the substrate being reacted in the reactor tube and of the total mass of the substrate reacted in the bioreactor tube during its activity). The idea presented in this paper ivas validated by means of the computer simulation and the results proving its very good performance complete the paper.
Content available remote Least-squares estimation for a long-horizon performance index
Estimation of a parametric, discrete-time model for a SISO dynamic plant, derived for minimisation of a performance index determined as a sum of squared prediction errors within some time horizon is considered. A formula for a Long-Horizon Least-Squares (LHLS) off-line solution as well as a theorem for an LHLS recursive on-line scheme are derived. The LHLS scheme reveals some features of Least-Squares (LS) estimation and Instrumental-Variable (IV) estimation. An algorithm for the on-line LHLS scheme is presented and compared with LS and IV estimation schemes for a linear, second-order system. The fast convergence of the derived LHLS on-line scheme is demonstrated in the case of detecting changes in parameters of a non-stationary system.
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