A Practical Filter for Systems With Unknown Parameters

1973 ◽  
Vol 95 (4) ◽  
pp. 396-401 ◽  
Author(s):  
T. Soeda ◽  
T. Yoshimura
Keyword(s):  
Dynamic Systems ◽  
Digital Simulation ◽  
A Priori ◽  
A Priori Information ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
Time Dynamic ◽  
Filter Performance ◽  
Modeling Errors ◽  
Priori Information

This paper deals with the problem of a practical filter for discrete-time, dynamic systems with unknown parameters whose variation cannot be estimated in advance. The modeling errors caused by unknown parameters clearly degrade the filter performance and sometimes lead to divergence of estimation errors. Divergence is said to occur when the calculated covariance of estimation errors becomes very small comparing with the actual covariance. A practical filter that modifies the calculated covariance is developed as a technique for controlling the divergence. This is done by testing whether or not the actual residual at each stage is likely to have come from the calculated distribution, and the calculated covariance is modified when the test is rejected. The numerical results of digital simulation indicate that divergence of estimation errors is observed when the a priori information for dynamic systems is in error and that the divergence is prevented by the proposed filter.

Profile-based Maximum Penalised Likelihood Trajectory Estimation from Space-borne LOS Measurements

2016 ◽  
Vol 66 (3) ◽  
pp. 278 ◽  
Author(s):  
Taihe Yi ◽  
Zhen Shen ◽  
Zhengming Wang ◽  
Bing Liu ◽  
Dongyun Yi
Keyword(s):  
A Priori ◽  
A Priori Information ◽  
Missile Defense ◽  
Unknown Parameters ◽  
Trajectory Estimation ◽  
Bayesian Paradigm ◽  
Phase Profile ◽  
Passive Sensors ◽  
Penalised Likelihood ◽  
Priori Information

Estimating the boost-phase trajectory of a ballistic missile using line of sight measurements from space-borne passive sensors is an important issue in missile defense. A well-known difficulty of this issue is the poor-observability of the target motion. A profile-based maximum penalised likelihood estimator is presented, which is expected to work in poor-observability scenarios. Firstly, a more adaptable boost-phase profile is proposed by introducing unknown parameters. Then, the estimator is given based on the Bayesian paradigm. After that, a special penalty for box constraint is constructed based on a mixed distribution. Numerical results for some typical scenarios and sensitivity with respect to a priori information are reported to show that the proposed estimator is promising.

NEW METHOD FOR SPLITTING PRODUCTION AND INJECTION IN JOINT WELLS USING MODIFIED CRM MODEL

2021 ◽  
Vol 7 (3) ◽  
pp. 106-122
Author(s):  
Alexander D. BECKMAN
Keyword(s):  
Functional Dependence ◽  
A Priori ◽  
Material Balance ◽  
Geological Structure ◽  
Balance Model ◽  
A Priori Information ◽  
Production Rates ◽  
Unknown Parameters ◽  
Injection Wells ◽  
Priori Information

Operating several oil-bearing facilities with a single grid of wells, the problem of dividing oil and liquid production rates by facilities is urgent. Known engineering techniques based on reservoir transmissibility coefficients and effective oil-saturated thickness do not take into account dynamic factors. The use of hydrodynamic models (HDM) is time-consuming, and the results depend significantly on the used a priori hypotheses about the geological structure of objects and the properties of fluids. Thus, there is a practical need for an analytical tool that would rely on the most reliable and available data and would allow solving the problem of separating the volumes of produced fluid and injected water with sufficient accuracy. Such a tool should take into account the dynamics of changes in reservoir pressure and have a low (compared to the hydrodynamic model) need for computing resources. A promising candidate for the role of such a tool is the CRMP-ML6 model — a fundamentally new author’s modification of the previously known CRMP model. The CRMP model is a functional dependence of the well fluid flow rate on the injectivity of the surrounding injection wells. The unknown parameters of this dependence are determined in such a way as to minimize the discrepancy between the simulated and actual values of production rates at the selected date interval. Fundamentally new features of the CRMP-ML6 model are the regularization of the problem through the use of a priori information on the permeability of reservoirs in the vicinity of production wells and the requirement for the proximity of reservoir pressures calculated using the material balance model and from the Dupuis equation. To assess the performance of the new model, a number of numerical simulation experiments were carried out, and the simulation results were compared with the HDM. The possibility of the CRMP-ML6 model is demonstrated to take into account the dynamic separation of production and injection, taking into account additional constraints and a priori information, and while meeting all the requirements for models of the CRM family.

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