Method for predicting future function values utilizing derivative samples
First Claim
1. A method for calculating a future function value associated with an object from derivative values associated with the object, to then control operation of the object, comprising the steps of:
- providing a sensor coupled to the object for generating derivative values;
predetermining a sampling interval T of the derivative values;
low pass filtering the derivative values to generate a high frequency value W;
acquiring at least one function value from the sensor;
determining a value for τ
by multiplying 2*T*W, wherein 2 is a Nyquist value, and wherein τ
must always be less than one;
computing a which is the solution vector of predictor coefficients in a (N+1)×
1 size matrix in the form a=[ak(0), a1(1), . . . , aN(1)] for use in a prediction formula, wherein the prediction coefficients are found by minimizing the integral
wherein said prediction formula is in the form of wherein N=the number of data points, wherein n=an integer 1 to N, and wherein k=an integer 1≦
k≦
N used to adjust the calculated result closer to the actual result to generate a future function value f(t); and
utilizing the future function value to control operation of the object.
1 Assignment
0 Petitions
Accused Products
Abstract
A system and method for calculating a future function value, such as velocity, for an object, from derivative values, such as acceleration, includes a sensor, such as an accelerometer, coupled to an object, such as a car. By predetermining a sampling rate of the derivative values and determining the highest frequency in the sampled signal, a set of prediction coefficients can be derived for use in a prediction formula which generates the future function value. A processor, which derives the prediction coefficients and implements the prediction formula may use the future function value to control operation of the object or a related object. By including a past function value in the prediction formula, a highly accurate future function value can be determined.
-
Citations
7 Claims
-
1. A method for calculating a future function value associated with an object from derivative values associated with the object, to then control operation of the object, comprising the steps of:
-
providing a sensor coupled to the object for generating derivative values;
predetermining a sampling interval T of the derivative values;
low pass filtering the derivative values to generate a high frequency value W;
acquiring at least one function value from the sensor;
determining a value for τ
by multiplying 2*T*W, wherein 2 is a Nyquist value, and wherein τ
must always be less than one;
computing a which is the solution vector of predictor coefficients in a (N+1)×
1 size matrix in the form a=[ak(0), a1(1), . . . , aN(1)] for use in a prediction formula, wherein the prediction coefficients are found by minimizing the integral
wherein said prediction formula is in the form ofwherein N=the number of data points, wherein n=an integer 1 to N, and wherein k=an integer 1≦
k≦
N used to adjust the calculated result closer to the actual result to generate a future function value f(t); and
utilizing the future function value to control operation of the object. - View Dependent Claims (2, 3, 4, 5, 6, 7)
computing a=solution vector of a matrix system H·
a=b, where H is a symmetric matrix with diagonal Toeplitz blocks that has the form,
and wherein b=[sinc(kτ
), −
τ
sinc′
(τ
), . . . −
τ
sinc′
(Nτ
)].
-
-
3. The method according to claim 1, wherein said computing step comprises the step of:
computing an eigenvector associated with the smallest eigenvalue of a quadratic form expressed as the integral
-
4. The method according to claim 1, further comprising the step of:
-
correcting the predicted future function by including a current sample of the derivative generated by said sensor by utilizing the following equation
with the prediction formula, wherein the corrector coefficients,
are found by minimizing the integral
-
-
5. The method according to claim 4, wherein the function value and its derivative are velocity and acceleration, respectively.
-
6. The method according to claim 1, further comprising the steps of;
-
calculating the prediction coefficients for preselected values of τ and
W; and
storing the calculated prediction coefficients in a computer-readable medium.
-
-
7. The method according to claim 6, further comprising the steps of
coupling a processor to said sensor to read the derivative and function values; - and
accessing said computer-readable medium by said processor, wherein said processor determines the future function value based upon function values and derivative values and generates an appropriate signal for control of the object.
- and
Specification