Boots – shoes – and leggings
Patent
1996-11-26
1999-08-03
Grant, William
Boots, shoes, and leggings
364131, 36447401, 36447411, 364151, 702185, G05B 1500, G05B 1304, G06F 1900
Patent
active
059333529
DESCRIPTION:
BRIEF SUMMARY
The present invention relates to a method and a system for non-linear optimal estimation of dynamic processes in real time.
BACKGROUND OF THE INVENTION
The method of the invention is based on replicating a large number of simulated random particles, and the system for implementing the method is such that it makes it possible by digital computation to restitute the estimated state of such processes on the basis of sampled measurement signals taken by a sensor suitable for receiving information characteristic of the state of said dynamic process.
The estimation is said to be "non-linear" since it cannot be reduced to linear operations, and it is said to be "optimal" since the process and the measurements are subject to disturbances or noise which make probabilistic optimization of said restitution necessary. Finally, by their very nature, the recurrent methods of the method and of the system make it possible for them to operate and to be applied in real time.
The technical field of the invention is the field of making measurement and computation systems for estimating in real time the current state of a dynamic process and for forecasting future states thereof, on the basis of successive imperfect observations of the process as provided by means of one or more sensors.
Applications of the invention include restitution, tracking, and forecasting, e.g. of the trajectory of an aircraft with the help of a radar, and also the state of a chemical reaction on the basis of fragmentary measurements of product concentrations, or they may include processing signals received from a positioning satellite to extract the position of the moving body receiving the satellite, etc. . . . .
FIG. 1 is a diagram of a known method and system for Kalman linear estimation.
FIG. 2 shows an example of an electromechanical application for tracking and forecasting the trajectory of an aircraft.
FIG. 3 shows an example of an application in the biochemical field for tracking and forecasting fermentation.
FIG. 4 is a diagrammatic view of the general structure both of the method (flow chart) and of the system of the invention.
It is recalled that if the way in which a physical process varies over time is known, then it is possible to deduce what will be observed by the, or each, sensor associated with the process at any instant. Estimating the behavior of such a dynamic process in order to restitute and track the corresponding succession of different states consists in solving the inverse of the above problem: that constitutes the problem posed by the present invention which, itself provides the solution which is "best" in the probabilistic sense. Since the real behavior of the process is unknown, the idea is to make an estimate at each instant that corresponds best with the present and past observations made by the sensor(s). Such estimation consists in computing the values of a set of unknown variables also referred to as the "components" or the "state vectors" of said process, and in using them in the model of the behavior thereof. More precisely, the idea is to construct the probability distribution of said state, conditional on the set of measurements taken over time. Any prediction of future behavior is then the result of extrapolating said state vector, on the basis of said distribution, and depending on the model for the behavior of the dynamic process.
When it is desired actually to perform optimal estimation of a general dynamic process, the problem as described above does not have a solution that can be constructed on the basis of known digital methods or systems, because of the resulting dimensional and combinatory explosion.
A single exception to the above rule has been known for a long time. This is Kalman linear estimation which relies on linear models of the process described by:
a state transition matrix O(t,t-1); and
a matrix H of measurements taken.
In that case, the simple algorithmic solution can be executed by a conventional computer machine. The method is well known and can be summarized as follows, with reference
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Baumgardner Carolyn T.
Grant William
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