We claim:
1. A computer-implemented method for determining a best match of an input signal of interest from a set of candidate signals, wherein two or more of the candidate signals are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate signals;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate signals to calculate a corresponding at least one generalized frequency component value for each of the set of candidate signals;
receiving the input signal of interest;
applying the unified signal transform for the at least one generalized frequency to the input signal of interest to calculate a corresponding at least one generalized frequency component value for the input signal of interest;
determining a best match between the at least one generalized frequency component value of the input signal of interest and the at least one generalized frequency component value of each of the set of candidate signals; and
outputting information indicating a best match candidate signal from the set of candidate signals.
2. The method of claim 1,
wherein said determining a best match between the at least one generalized frequency component value of the input signal of interest and the at least one generalized frequency component value of each of the set of candidate signals comprises:
subtracting each of the respective at least one generalized frequency component values of each candidate signal from the at least one generalized frequency component value of the input signal of interest; and
determining a smallest difference between each of the respective at least one generalized frequency component values of each candidate signal and the at least one generalized frequency component value of the input signal of interest;
wherein a candidate signal corresponding to the smallest difference is the best match candidate signal.
3. The method of claim 1,
wherein the unified signal transform includes a set of basis functions which describe an algebraic structure of the set of candidate signals.
4. The method of claim 1,
wherein the unified signal transform is operable to convert each of the set of candidate signals to a generalized frequency domain.
5. The method of claim 1,
wherein the unified signal transform is operable to convert each of the set of candidate signals into a representation of generalized basis functions, wherein the basis functions represent the algebraic structure of the set of candidate signals.
6. The method of claim 1,
wherein the unified signal transform is operable to decompose the signal into generalized basis functions, wherein the basis functions represent the algebraic structure of the set of candidate signals.
7. The method of claim 1,
wherein all of the candidate signals are uncorrelated with each other.
8. The method of claim 1,
wherein the input signal of interest and the candidate signals are one of 1-dimensional signals, 2-dimensional signals, or 3-dimensional signals.
9. The method of claim 1,
wherein the input signal of interest and the candidate signals are of a dimensionality greater than 3.
10. The method of claim 1,
wherein the input signal of interest and the candidate signals comprise one or more of image data, measurement data, acoustic data, seismic data, financial data, stock data, futures data, business data, scientific data, medical data, insurance data, musical data, biometric data, and telecommunications signals.
11. The method of claim 1,
wherein said determining a unified signal transform for the set of candidate signals comprises:
forming a matrix B from all of the values of the candidate signals, wherein each of the candidate signals comprises a corresponding column of the matrix B;
defining a matrix B, wherein the matrix B comprises a column-wise cyclic shifted matrix B;
defining a matrix A, wherein the matrix A comprises a cyclic shift matrix operator, wherein multiplying matrix A times matrix B performs a column-wise cyclic shift on matrix B, thereby generating matrix B, wherein ABB, wherein ABB1, wherein B1 comprises an inverse matrix of matrix B, and wherein ANan NN identity matrix, I;
performing a Jordan decomposition on ABB1, thereby generating a relation AXBXB1, wherein XB comprises a matrix of normalized columnar eigenvectors of matrix B, wherein comprises a diagonal matrix of eigenvalues of matrix B, and wherein XB1 comprises an inverse matrix of matrix XB; and
calculating matrix XB1, wherein the matrix XB1 comprises the unified signal transform.
12. The method of claim 11,
wherein the set of candidate signals comprises a number of candidate signals, wherein each of the candidate signals comprises a number of values, and wherein the number of values is equal to the number of candidate signals.
13. The method of claim 12, wherein the matrix B is regular.
14. The method of claim 1, further comprising:
receiving an initial set of N candidate signals before said determining a unified signal transform from the set of candidate signals, wherein at least one of said initial set of candidate signals comprises a set of M values, wherein M is greater or less than N;
15. The method of claim 14, wherein M is less than N, the method further comprising:
providing additional NM values for the at least one of said initial set of candidate signals, thereby generating said set of candidate signals, wherein each one of said set of candidate signals comprises N values.
16. The method of claim 15, wherein said providing additional NM values comprises interpolating two or more of the M values to generate the additional NM values.
17. The method of claim 15, wherein said providing additional NM values comprises extrapolating two or more of the M values to generate the additional NM values.
18. The method of claim 14, wherein M is less than N, the method further comprising:
fitting a curve to the M values for the at least one of said initial set of candidate signals;
sampling the curve to generate N values for the at least one of said initial set of candidate signals, thereby generating said set of candidate signals, wherein each one of said set of candidate signals comprises N values.
19. The method of claim 1, further comprising:
receiving an initial set of M candidate signals before said determining a unified signal transform from the set of candidate signals, wherein each of said initial set of candidate signals comprises a set of N values, and wherein M is less than N.
20. The method of claim 19, the method further comprising:
providing an additional NM candidate signals to said initial set of candidate signals, thereby generating said set of candidate signals, wherein said set of candidate signals comprises N candidate signals, and wherein each one of said set of candidate signals comprises N values.
21. The method of claim 19, wherein said providing additional NM candidate signals to said initial set of candidate signals comprises providing NM arbitrary candidate signals.
22. The method of claim 1, wherein said outputting information comprises displaying the information on a display screen.
23. The method of claim 1, wherein said outputting information comprises storing the best match candidate signal in a memory medium of a computer system.
24. The method of claim 1, further comprising:
processing the best match candidate signal to determine if the best match candidate is an acceptable match.
25. The method of claim 1, further comprising:
processing the best match candidate signal to determine characteristics of the received input signal of interest.
26. A memory medium comprising program instructions which are executable to determine a closest match between an input signal of interest and one of a set of candidate signals, wherein two or more of the candidate signals are uncorrelated, wherein the program instructions are executable to perform:
determining a signal transform for the set of candidate signals;
calculating one or more values of the signal transform applied to each of the set of candidate signals at at least one generalized frequency
receiving the input signal of interest;
calculating one or more values of the signal transform applied to the input signal of interest at the at least one generalized frequency;
determining a best match between the one or more values of the transformation of the input signal of interest and the one or more values of the transformation for each of the set of candidate signals; and
outputting information indicating a closest match candidate signal of the set of candidate signals.
27. The memory medium of claim 26,
wherein the signal transform includes a set of basis functions which describe an algebraic structure of the set of candidate signals.
28. The memory medium of claim 26,
wherein the signal transform is operable to convert each of the set of candidate signals to a generalized frequency domain.
29. The memory medium of claim 26,
wherein the signal transform is operable to convert each of the set of candidate signals into a representation comprising generalized basis functions, wherein the basis functions represent the algebraic structure of the set of candidate signals.
30. The memory medium of claim 26,
wherein the signal transform is operable to decompose the signal into a form represented by generalized basis functions, wherein the basis functions represent the algebraic structure of the set of candidate signals.
31. The memory medium of claim 26,
wherein the signal transform is the unified signal transform.
32. The memory medium of claim 26,
wherein all of the candidate signals are uncorrelated with each other.
33. The memory medium of claim 26,
wherein the input signal of interest and the candidate signals are one of 1-dimensional signals, 2-dimensional signals, or 3-dimensional signals.
34. The memory medium of claim 26,
wherein the input signal of interest and the candidate signals are of a dimensionality greater than 3.
35. The memory medium of claim 26,
wherein the input signal of interest and the candidate signals comprise one or more of image data, measurement data, acoustic data, seismic data, financial data, stock data, futures data, business data, scientific data, medical data, insurance data, musical data, biometric data, and telecommunications signals.
36. The memory medium of claim 26, wherein said outputting information comprises displaying the information on a display screen.
37. The memory medium of claim 26, wherein said outputting information comprises storing the best match candidate signal in a memory medium of a computer system.
38. A computer-implemented method for determining a best match of an input image of interest from a set of candidate images, wherein two or more of the candidate images are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate images;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate images to calculate a corresponding at least one generalized frequency component value for each of the set of candidate images;
receiving the input image of interest;
applying the unified signal transform for the at least one generalized frequency to the input image of interest to calculate a corresponding at least one generalized frequency component value for the input image of interest;
determining a best match between the at least one component value of the input image of interest and the at least one component value of each of the set of candidate images; and
outputting information indicating a best match candidate image from the set of candidate images.
39. A computer-implemented method for determining a best match of an input data set of interest from a set of candidate data sets, wherein two or more of the candidate data sets are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate data sets;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate data sets to calculate a corresponding at least one generalized frequency component value for each of the set of candidate data sets;
receiving the input data set of interest;
applying the unified signal transform for the at least one generalized frequency to the input data set of interest to calculate a corresponding at least one generalized frequency component value for the input data set of interest;
determining a best match between the at least one component value of the input data set of interest and the at least one component value of each of the set of candidate data sets; and
outputting information indicating a best match candidate data set from the set of candidate data sets.
40. A computer-implemented method for determining a best match of an input biometric signal of interest from a set of candidate biometric signals, wherein two or more of the candidate biometric signals are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate biometric signals;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate biometric signals to calculate a corresponding at least one generalized frequency component value for each of the set of candidate biometric signals;
receiving the input biometric signal of interest;
applying the unified signal transform for the at least one generalized frequency to the input biometric signal of interest to calculate a corresponding at least one generalized frequency component value for the input biometric signal of interest;
determining a best match between the at least one component value of the input biometric signal of interest and the at least one component value of each of the set of candidate biometric signals; and
outputting information indicating a best match candidate biometric signal from the set of candidate biometric signals.
41. A computer-implemented method for determining a best match of an input stock history waveform of interest from a set of candidate stock behavior waveforms, wherein two or more of the candidate stock behavior waveforms are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate stock behavior waveforms;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate stock behavior waveforms to calculate a corresponding at least one generalized frequency component value for each of the set of candidate stock behavior waveforms;
receiving the input stock history waveform of interest;
applying the unified signal transform for the at least one generalized frequency to the input stock history waveform of interest to calculate a corresponding at least one generalized frequency component value for the input stock history waveform of interest;
determining a best match between the at least one component value of the input stock history waveform of interest and the at least one component value of each of the set of candidate stock behavior waveforms; and
outputting information indicating a best match candidate stock history waveform from the set of candidate stock behavior waveforms.
42. A computer-implemented method for determining a best match of an input telecommunications signal of interest from a set of candidate telecommunications signals, wherein two or more of the candidate telecommunications signals are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate telecommunications signals;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate telecommunications signals to calculate a corresponding at least one generalized frequency component value for each of the set of candidate telecommunications signals;
receiving the input telecommunications signal of interest;
applying the unified signal transform for the at least one generalized frequency to the input telecommunications signal of interest to calculate a corresponding at least one generalized frequency component value for the input telecommunications signal of interest;
determining a best match between the at least one component value of the input telecommunications signal of interest and the at least one component value of each of the set of candidate telecommunications signals; and
outputting information indicating a best match candidate telecommunications signal from the set of candidate telecommunications signals.
43. A computer-implemented method for determining a best match of an input medical image of interest from a set of candidate medical images, wherein two or more of the candidate medical images are uncorrelated, the method comprising:
determining a unified signal transform from the set of candidate medical images;
applying the unified signal transform for at least one generalized frequency to each of the set of candidate medical images to calculate a corresponding at least one generalized frequency component value for each of the set of candidate medical images;
receiving the input medical image of interest;
applying the unified signal transform for the at least one generalized frequency to the input medical image of interest to calculate a corresponding at least one generalized frequency component value for the input medical image of interest;
determining a best match between the at least one component value of the input medical image of interest and the at least one component value of each of the set of candidate medical images; and
outputting information indicating a best match candidate medical image from the set of candidate medical images.
44. A computer-implemented method for determining a best match of an input signal of interest from a set of candidate signals, wherein two or more of the candidate signals are uncorrelated, the method comprising:
receiving the input signal of interest;
applying a unified signal transform for at least one generalized frequency to the input signal of interest to calculate a corresponding at least one generalized frequency component value for the input signal of interest, wherein the unified signal transform is determined from the set of candidate signals;
determining a best match between the at least one generalized frequency component value of the input signal of interest and at least one generalized frequency component value of each of the set of candidate signals; and
outputting information indicating a best match candidate signal from the set of candidate signals.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method of controlling a towing vehicle connected to a vehicle trailer, the method comprising:
determining a set of vehicle targets for the towing vehicle, the set of vehicle targets including a plurality of target values each corresponding to a different one of a plurality of vehicle sensors positioned on the towing vehicle;
sensing a set of vehicle conditions indicative of movements exhibited by the towing vehicle caused by the vehicle trailer, the set of vehicle conditions including a plurality of condition values each sensed by a different one of the plurality of vehicle sensors;
determining a plurality of differences between the set of vehicle targets and the set of vehicle conditions;
determining a trend of the plurality of differences;
determining, by a symmetric braking control system, a symmetric force to apply to the vehicle based at least in part on the set of vehicle targets and the set of vehicle conditions;
determining, by an asymmetric braking control system, an asymmetric force to apply to the vehicle based at least in part on the set of vehicle targets and the set of vehicle conditions;
selecting between the symmetric control system and the asymmetric control system based on the trend; and
actuating a vehicle system according to the selected symmetric control system or the asymmetric control system to apply the symmetric force or the asymmetric force to the towing vehicle to decrease the plurality of differences.
2. The method of claim 1, wherein determining a trend of the plurality of differences comprises:
determining a rate of change of the plurality of differences as compared to a previous plurality of differences;
indicating the trend to be increasing when the rate of change comprises a positive value; and
indicating the trend to be decreasing when the rate of change comprises a negative value.
3. The method of claim 1, wherein determining a trend of the plurality of differences comprises:
determining a peak value from a previous plurality of differences;
indicating the trend to be increasing when one of the plurality of differences is above the peak value; and
indicating the trend to be decreasing when all of the plurality of differences are less than the peak value.
4. The method of claim 1, wherein selecting between the symmetric control system and the asymmetric control system comprises:
selecting the asymmetric control system when the trend indicates increasing differences, between the set of vehicle targets and the set of vehicle conditions; and
selecting the symmetric control system when the trend indicates decreasing differences between the set of vehicle targets and the set of vehicle conditions.
5. The method of claim 1, wherein actuating a vehicle system comprises applying at least one of a symmetric braking and an asymmetric braking based on the selected control system.
6. The method of claim 1, further comprising band-pass filtering the plurality of differences, and wherein determining a trend comprises determining a trend of the plurality of filtered differences.
7. The method of claim 1, wherein actuating a vehicle system comprises generating at least one of a symmetric torque and an asymmetric torque based on the selected control system.
8. A system for controlling a towing vehicle connected to a vehicle trailer, the system comprising:
a plurality of sensors positioned on the towing vehicle configured to sense a set of vehicle conditions indicative of movements exhibited by the towing vehicle caused by the vehicle trailer, the set of vehicle conditions including a plurality of condition values each sensed by a different one of the plurality of vehicle sensors;
a comparator configured to determine a plurality of differences between the set of vehicle conditions and a set of vehicle targets, the set of vehicle targets including a plurality of target values each corresponding to a different one of the plurality of vehicle sensors;
a trend module configured to determine a trend of the plurality of differences;
a symmetric control system configured to determine a symmetric force to apply to the vehicle based at least in part on the set of vehicle targets and the set of vehicle conditions;
an asymmetric control system configured to determine an asymmetric force to apply to the vehicle based at least in part on the set of vehicle targets and the set of vehicle conditions;
a switch configured to select between the symmetric control system and the asymmetric control system based on the trend; and
a vehicle system configured to be actuated by the selected control system to apply the symmetric force or the asymmetric force to the towing vehicle.
9. The system of claim 8, wherein the trend comprises a rate of change of the plurality of differences, and wherein the system is further configured to indicate the trend to be increasing when the rate of change comprises a positive value, and to indicate the trend to be decreasing when the rate of change comprises a negative value.
10. The system of claim 8, wherein the trend module comprises a peak seeker configured to determine a peak value of the plurality of differences, and wherein the controller is further configured to indicate the trend to be increasing when one of the plurality of differences is above a previously determined peak value, and to indicate the trend to be decreasing when all of the plurality of differences are less than the previously determined peak value.
11. The system of claim 8, wherein the switch is further configured to select the asymmetric control system when the trend indicates increasing differences between the set of vehicle conditions and the set of vehicle targets, and to select the symmetric control system when the trend indicates decreasing differences between the set of vehicle conditions and the set of vehicle targets.
12. The system of claim 8, wherein the vehicle system comprises a hydraulic braking system, and wherein the hydraulic braking system is configured to apply symmetric braking or asymmetric braking based on the selected control system.
13. The system of claim 8, further comprising a band-pass filter configured to filter the plurality of differences, and wherein the system is further configured to determine the trend of the plurality of differences based on the plurality of filtered differences.
14. The system of claim 8, wherein the vehicle system comprises a hydraulic system, and wherein the hydraulic system is configured to generate symmetric torque or asymmetric torque for the towing vehicle based on the selected control system.
15. A method of controlling a towing vehicle connected to a vehicle trailer, the method comprising:
determining a set of vehicle targets for the towing vehicle, the set of vehicle targets including a plurality of target values each corresponding to a different one of a plurality of vehicle sensors positioned on the towing vehicle;
sensing a set of vehicle conditions indicative of movements exhibited by the towing vehicle caused by the vehicle trailer, the set of vehicle conditions including a plurality of condition values each sensed by a different one of the plurality of vehicle sensors;
determining a plurality of differences between the set of vehicle targets and the set of vehicle conditions;
determining a trend of the plurality of differences;
determining a switching signal based on the trend; and
selectively applying either symmetric braking or asymmetric braking based on the switching signal to decrease the plurality of differences.
16. The method of claim 15, further comprising determining a model of the towing vehicle based on a plurality of dynamics, wherein the model comprises at least one of a proportional-integral-derivative (\u201cPID\u201d) controller model, a proportional controller model, a proportional-derivative (\u201cPD\u201d) controller model, a proportional-integral (\u201cPI\u201d) controller model, a filtering model, a trend model, a comparison model, and a peak seeking model.
17. The method of claim 16, further comprising:
determining a plurality of differences between the set of vehicle targets and the set of vehicle conditions with the comparison model;
determining a peak value of the plurality of differences with the peak seeking model;
filtering the plurality of differences with the filtering model;
determining the trend of the plurality of differences with the trend model; and
determining the switching signal with one of the PID controller model, the proportional controller model, the PD controller model, and the PI controller model.
18. The method of claim 16, wherein the plurality of dynamics of the towing vehicle comprise a wheel speed, a steering angle, a yaw rate, a body slip angle, a lateral acceleration, a front wheel torque, and a rear wheel torque.
19. The method of claim 15, further comprising:
determining a peak value from a previous plurality of differences;
indicating an increasing trend when one of the plurality of differences is above the peak value; and
indicating a decreasing trend when all of the plurality of differences are less than the peak value.
20. The method of claim 19, wherein determining the switching signal comprises:
generating an asymmetric signal when the trend comprises an increasing trend; and
generating a symmetric signal when the trend comprises a decreasing trend.
21. The method of claim 15, further comprising:
determining a rate of change of the plurality of differences;
indicating an increasing trend when the rate of change comprises a positive value; and
indicating a decreasing trend when the rate of change comprises a negative value.
22. The method of claim 15, wherein selectively applying at least one of a symmetric braking and an asymmetric braking comprises generating at least one of a symmetric torque and an asymmetric torque.
23. The method of claim 15, further comprising
determining, by a symmetric braking control system, a symmetric force to apply to the vehicle based at least in part on the set of vehicle targets and the set of vehicle conditions; and
determining, by an asymmetric braking control system, an asymmetric force to apply to the vehicle based at least in part on the set of vehicle targets and the set of vehicle conditions,
wherein determining a switching signal based on the trend includes determining a switching signal that switches between the symmetric braking control system and the asymmetric braking control system, and
wherein selectively applying either symmetric braking or asymmetric braking includes controlling a vehicle system according to either the symmetric braking control system or the asymmetric braking control system based on the switching signal.
24. The method of claim 23, wherein the symmetric braking control system is a first proportional-integral-derivative (\u201cPID\u201d) controller and the asymmetric braking control system is a second proportional-integral-derivative (\u201cPID\u201d) controller.