JP4097318B2 - Integral calculation processing method - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
In the present invention, when analog data is digitally sampled and integrated two or more times, a threshold value is set and a rounding process of numerical values is performed. The present invention relates to a numerical calculation method that suppresses divergence and enables highly accurate integral calculation.
[0002]
[Prior art]
As a method for removing noise from a signal waveform including noise detected by a sensor or the like, it is common to use a filter that cuts the frequency of the noise component. If the target waveform is high frequency, a high-pass filter, For low frequencies, use a low-pass filter. However, since these analog filters distort even the waveform of the target frequency, the target accuracy may not be obtained. Also, white noise that is statistically known and uniform in time is most commonly smoothed. Kalman filters, which are digital filters, reduce the least square error between the target waveform and the waveform that contains the error. This is often used in the case of such a system in order to perform processing to make it smaller.
[0003]
For example, when an acceleration (or angular acceleration) is measured using an acceleration sensor (or angular acceleration sensor), a result as shown in FIG. 6 is obtained. An input from a direction other than the measurement direction affects as an error due to the sensitivity of the other axis, but this is not a probability statistic unlike the white noise described above. The distance (or angle) obtained by second-order integration of the acceleration (or angular acceleration) measured by the sensor is also integrated with the error. Therefore, this error accumulates with time, and the moving body on which the sensor is mounted Even after stopping, the distance (or angle) changes, and a measurement result as if moving is obtained even though it is not actually moving.
[0004]
FIG. 7 shows the result of obtaining the angular velocity by integrating the measurement result of FIG. 6 once, and FIG. 8 shows the result of obtaining the angle by further integrating. Although the theoretical values are shown in the figure, the angular velocity has a significant value even after the moving body stops, and the angle decreases with the integration of the error.
[0005]
Since it is clear that the result of the second order integration (FIG. 8) is a larger error than the first order integration (FIG. 7), it requires distance (or angle) rather than speed (or angular velocity). In some cases, it is necessary to remove an error component included in the measurement value.
[0006]
[Problems to be solved by the invention]
However, when an advanced mathematical method such as the aforementioned Kalman filter is used to remove an error component, a complicated algorithm is required. For this processing, a high-speed and expensive CPU (for example, a 32-bit RISC) is required. CPU) is required, and the apparatus cost and processing cost are significantly increased.
[0007]
For this reason, a simple algorithm is required so that even a relatively inexpensive CPU can perform processing at high speed. However, if a simple method such as simply averaging is used, it is fast, but In this way, even the target waveform is distorted, so that there is a difficulty that a desired accuracy cannot be obtained.
[0008]
The present invention has been made in view of such a problem, and it is possible to remove an error component with a simple algorithm, without requiring excessive performance in a CPU or the like, and to perform integration processing with high accuracy. An object is to provide an arithmetic processing method.
[0009]
[Means for Solving the Problems]
The integration calculation processing method according to the present invention includes a first step of setting a predetermined threshold value for digital data and rounding the data portion within the threshold value, and a first step of integrating the rounded data. A second step, a third step of setting a predetermined threshold value for the data after the integration calculation and rounding the data portion within the threshold value; and a fourth step of further integrating the rounded data. And a fifth step of setting a predetermined threshold value for the data after the integration calculation in the fourth step and rounding the data portion within the threshold value .
[0011]
In the first, third, or fifth step, when the digital data is x, the threshold is th, and α is a positive number less than 1, a function F (x, th) is expressed by Equations 1 and 2 below, where int (a) is a symbol indicating the integer part of the real number a.
[0012]
[Expression 1]
F (x, th) = int (x / th) × th + th
However, when x / th ≧ int (x / th) + α
[Expression 2]
F (x, th) = int (x / th) × th
However, in the case of x / th <int (x / th) + α, it is preferable that α is 0.5 in order to further reduce the error.
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. FIG. 1 is a block diagram showing an apparatus used in an embodiment method of the present invention. An analog signal detected by the sensor 1, for example, an acceleration or angular acceleration signal S is input to the signal processing unit 2. The signal processing unit 2 determines an initial condition and detects and removes an offset. It is converted into a digital signal by a digital converter at a predetermined sampling time. The digital signal is input to the numerical operation unit 3 and after a predetermined integration operation is performed, the operation result is output to an external output device 4 such as a display.
[0015]
In the numerical calculation unit 3, the digitally converted acceleration or angular acceleration signal x (digitally sampled measurement data) is subjected to data reception processing (step S1) and corrected (step S2), and then the threshold value is set to th1. Is subjected to a numerical value rounding process (step S3). The numerical value rounding process of the data x is expressed by the following mathematical formula 3, and the rounded numerical value is f.
[0016]
[Equation 3]
f = F (x, th1)
When Equation 3 is implemented under Equations 1 and 2, the data within the threshold value becomes 0 as shown in FIG. That is, as shown in FIG. 2, even if the data fluctuates within the threshold value th, it is all 0 and the integral value is 0. Therefore, the speed or angular velocity is obtained by integrating f with time (step S4). Then, the integral value is rounded with a threshold value of th2, as shown in the following Equation 4.
[0017]
[Expression 4]
g = F (∫fdt, th2)
Next, as shown in Equation 5 below, the obtained data g is integrated at time t, and similarly rounded by the function F with the threshold value set to th3 (step S5).
[0018]
[Equation 5]
h = F (∫gdt, th3)
Then, the second-order integral value h is output to the outside of the numerical calculation unit 3 (step S6) and displayed on the output device 4 such as a display. The numerical operation unit 3 can be constituted by one integrated circuit (IC), but the signal processing unit 2 that performs sampling can also be incorporated in the IC.
[0019]
In the method of this embodiment configured as described above, in order to eliminate the conventional drawbacks, first, the acceleration or angular acceleration value x measured by the sensor 1 is expressed numerically using the threshold value th1. A process of rounding by F is performed. In this rounding process, the numerical value in the threshold value th1 is set to 0 as shown in Equations 1 and 2 and FIG. 2, but as a result, as shown in FIG. Become.
[0020]
Next, the data f is integrated at time t, and the same rounding process is further performed using the threshold value th2 to obtain a first-order integration result (step S4). Then, the obtained data g is integrated at time t, and the same rounding process is performed using the threshold value th3 to obtain a second-order integration result (step S5).
[0021]
FIG. 4 shows data h after second-order integration according to this embodiment. As shown in FIG. 4, data similar to the theoretical value can be obtained with high accuracy by performing integration processing according to the method of this embodiment. On the other hand, the result of second-order integration by the conventional method (see FIG. 8) is shown in FIG. 4, but in the case of this conventional method, the error is amplified with time when the angle is constant and stopped. Will be. Therefore, as shown in FIG. 5, in the case of the present embodiment, only a very small error is generated when the vehicle is stopped, and this error does not increase. The error increases with time.
[0022]
As described above, in this embodiment, the error is extremely small as compared with the prior art, and the error does not increase due to the accumulation of the error. For this reason, the method of this embodiment has extremely high calculation accuracy. In particular, when the moving body is stopped, the above-described effect is remarkable.
[0023]
Needless to say, the present invention is not limited to the above embodiments. For example, in the above-described embodiment, the rounding process is performed by the function F expressed by the mathematical formulas 1 and 2. However, the rounding process is not limited to this, and rounding may be performed by rounding down or rounding up. In this way, any function or operation that removes an error can be used in the numerical rounding processing of the present invention.
[0024]
Moreover, in the said Example, although the example which calculates an angular velocity and an angle from the output of the angular acceleration sensor 1 was shown, this invention is applicable to all the systems which require a 2nd-order integration. For example, the present invention can be applied to the case where the speed and distance are calculated using an acceleration sensor.
[0025]
Furthermore, although the said Example is about 2nd-order integration, of course, you may apply this invention to 1st-order integration. However, the application to the second order integration is more effective than the application to the first order integration. Further, when the present invention is applied to the third order integration or more, a further excellent effect can be obtained.
[0026]
The integration operation itself may be a known method, and various methods can be used.
[0027]
【The invention's effect】
As described above, according to the present invention, errors in integrating digital data are small, and accumulation of these errors can be avoided, so that integration processing can be performed with extremely high accuracy. Even when the output of the sensor is 0, that is, when the moving body is stopped, the divergence of the data after integration is prevented. In addition, since the algorithm is simple, it is possible to perform calculations at a higher speed than other algorithms, and it is sufficient that the performance of the CPU and memory is low, and the device can be configured at low cost.
[Brief description of the drawings]
FIG. 1 is a block diagram of an apparatus used in an embodiment method of the present invention.
FIG. 2 is a diagram for explaining the principle of rounding processing;
FIG. 3 is a diagram illustrating data rounded by a function F;
FIG. 4 is a graph showing data obtained by second-order integration by an embodiment method of the present invention in comparison with theoretical values and conventional data.
FIG. 5 is a graph for comparing errors between an example method and a conventional method.
FIG. 6 is a graph showing measurement results of angular acceleration by a sensor.
FIG. 7 is a graph showing data after an integration operation is executed once by a conventional method.
FIG. 8 is a graph showing data after an integration operation is executed twice by a conventional method.
FIG. 9 is a graph showing an error caused by a conventional integral calculation method.
[Explanation of symbols]
1: Sensor 2: Signal processing unit 3: Numerical calculation unit 4: Output device

Claims (3)

A first step of setting a predetermined threshold for the digital data and rounding the data portion within the threshold; a second step of integrating the rounded data; and the data after the integration calculation A third step of setting a predetermined threshold value for the data and rounding the data portion within the threshold value, a fourth step of integrating the rounded data, and an integration operation by the fourth step And a fifth step of setting a predetermined threshold value for the subsequent data and rounding the data portion within the threshold value . In the first, third, or fifth step, when the digital data is x, the threshold is th, and α is a positive number less than 1, a function F (x, When th / is a symbol indicating the integer part of the real number a, and x / th ≧ int (x / th) + α, F (x, th) = int (x / th) × th + th 2. The integration operation according to claim 1 , wherein, when x / th <int (x / th) + α, F (x, th) = int (x / th) × th. Processing method. The integration calculation processing method according to claim 2 , wherein α is 0.5.

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