acceleration more than 1 g it is possible to select
the reference signals whose values do not exceed 1 g.
1. A characteristic of the input-output of convertor is presented as a row as
Macloren row
The output parameter f is brought to the input parameter, or in other words it
is expressed in units of the input parameter, by dividing
or
The value y is an reading x, which is different from it only by the inaccuracy
value. In the same way the speed is determined
and the speed reading
2. Since to the input of the convertor "n" reference signals are
supplied, it is possible to determine "n" coefficients of the above
presented row, while practically only one coefficient b1 is needed. There is the following system of equations:
From this system of equations the above mentioned determinators are found, and
the value of b1 is found.
3. The input signal acts in the (t) can be judged only by the output signal, or
in other words by the value y. It is possible to directly compute initial
moments of the output signal Mi[y].
The output signal is caused by the input signal x[t], but mathematically it is
possible to present a reverse function, or in other words the input signal as a
function of the output signal. This function can be disintegrated in the
Macloren row with the disintegration coefficient di. This
disintegration formula is 
When "n" reference signals are available, the following can be
written
Since Xi and Yi are known, the value di can be found. The
system of equation is linear and it is determined by the above mentioned
determinators. The value d.sub.i is found in accordance with the previously
presented equation. Since Y is a value of
X, d1 is close to I but not always equal to Y.
4. Knowing the initial moments of the value y, it is possible to find initial
moments of the value x. The following formulas are utilized for this purpose.
The initial order of the moment of the power "m" is
Where p(x) is a density of probability of x or
Then the first initial moment or the mathematical expectation is
where
and d2, d3
. . . characterized non linearity, and its product is a value of the upper order
of the smallness which is neglectable. Then, finally the following is received
Analogously, it is possible to obtain
and in a common case
The system of equations
is obtained from the previous system of equations, (USSR Inventor's
Certificates 1,453,418; 1,547,635) but the maximum value "m" is not
equal to 2n-1, but instead is equal to n-1, or in other words it is necessary
to have twice the number of the previous signals. For the simple case of three
reference signals the following can be written.
While the invention has been illustrated and described as embodied in method
and device of determination of an input signal which changes in time, it is not
intended to be limited to the details shown, since various modifications and
structural changes may be made without departing in any way from the spirit of
the present invention.
Without further analysis, the foregoing will so fully reveal the gist of the
present invention that others can, by applying current knowledge, readily adapt
it for various applications without omitting features that, from the standpoint
of prior art, fairly constitute essential characteristics of the generic or
specific aspects of this invention.
What is claimed as new and desired to be protected by Letters Patent is set
forth in the appended claims.
* * * * *
