JPH11330911A - Integral arithmetic processing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide the integral arithmetic processing method which can remove an error component by simple algorithm and perform integral processing with high precision without requiring a CPU, etc., to have unreasonable performance. SOLUTION: Detection data of a sensor 1 is converted from analog to digital by a signal processing part 2 and inputted to a numerical arithmetic part 3. Then a threshold value th1 is set and a data part within the threshold value is rounded (step S3). Then the data after the rounding is integrated and then further a threshold value th2 is set; and a data part within this threshold value is rounded (step S4). Further, the data after the rounding is integrated and a threshold value th3 is set; and data within the threshold value is rounded (step S5) and outputted as an integral arithmetic result (step S6).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for digitally sampling analog data and integrating the data two or more times, by setting a threshold value, performing a rounding process of a numerical value, and performing a simple process and a high-speed integration. Suppress the divergence of the error that occurs during the calculation
The present invention relates to a method of numerical calculation that enables high-precision integration calculation.

[0002]

2. Description of the Related Art As a method for removing noise from a signal waveform containing noise detected by a sensor or the like, a filter that cuts the frequency of a noise component is generally used. If so, use a high-pass filter; if low-frequency, use a low-pass filter. However, since these analog filters distort the waveform of the target frequency, the target accuracy may not be obtained in some cases. In addition, white noise which is known stochastically and is uniform in time is most commonly smoothed, and a Kalman filter or the like which is a digital filter calculates a least square error between a target waveform and a waveform including an error. It is often used in such a system because it performs processing to make it smaller.

For example, when 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 an error due to the sensitivity of the other axis. However, unlike the white noise described above, this is not a probability statistical one. An error is also integrated in the distance (or angle) obtained by integrating the acceleration (or angular acceleration) measured by the sensor into the second order, so that the error accumulates with time, and the moving object on which the sensor is mounted. Even after stopping, the distance (or angle) changes, and a measurement result is obtained as if it were moving, even though it was not actually moving.

FIG. 7 shows the result of calculating 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. In the figure, the theoretical values are shown,
With the integration of the error, the angular velocity has a significant value even after the moving body stops, and the angle decreases.

[0005] Second-order integration (Fig. 8) rather than first-order integration (Fig. 7)
It is clear that the result from is a larger error, so distance (or angle) rather than velocity (or angular velocity)
Is required, it is necessary to remove an error component included in the measured value.

[0006]

However, in order to remove an error component using an advanced mathematical method such as the Kalman filter described above, a complicated algorithm is required. Fast and expensive C
A PU (for example, a 32-bit RISC CPU) is required, which significantly increases equipment costs and processing costs.

For this reason, a simple algorithm is required so that a relatively inexpensive CPU can perform high-speed processing. However, if a simple method such as simply averaging is used, the speed is high. However, as described above, even the intended waveform is distorted, so that there is a problem that desired accuracy cannot be obtained.

SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and it is possible to remove an error component with a simple algorithm, and to perform integration processing with high accuracy without requiring excessive performance in a CPU or the like. It is an object of the present invention to provide an integral operation processing method capable of performing the following.

[0009]

According to the present invention, there is provided an integral operation processing method comprising the steps of: setting a predetermined threshold value for digital data; and performing a rounding process on a data portion within the threshold value.
And a second step of performing an integration operation on the data after the rounding processing.

In the case where the integration is performed twice, the integration calculation processing method of the present invention sets a predetermined threshold value for the data after the integration calculation and rounds the data portion within the threshold value to a third value. And a fourth step of performing an integral operation on the data after the rounding processing. Further, a predetermined threshold value is set for the data after the integral operation in the fourth step, and the predetermined threshold value is set within the threshold value. It is preferable to include a fifth step of rounding the data portion.

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 for rounding x by the threshold th is used. (X, th) is represented by the following formulas 1 and 2, where int (a) is a symbol indicating the integer part of the real number a.

[0012]

F (x, th) = int (x / th) × th + th where x / th ≧ int (x / th) + α

[0013]

F (x, th) = int (x / th) × th where x / th <int (x / th) + α Note that when α is 0.5, the error becomes smaller. It is preferable in doing.

[0014]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be specifically described below with reference to the accompanying drawings. FIG. 1 is a block diagram showing an apparatus used in a method according to an embodiment of the present invention. An analog signal detected by the sensor 1, for example, an acceleration or angular acceleration signal S is input to a signal processing unit 2, where the initial condition is determined, and the offset is detected and removed. The digital signal is converted into a digital signal at a predetermined sampling time by a digital converter. 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.

In the numerical operation section 3, the digitally converted acceleration or angular acceleration signal x (digitally sampled measurement data) is subjected to data reception processing (step S1), and after being subjected to correction processing (step S2), a threshold is obtained. The value is set to th1 and subjected to numerical rounding processing (step S1).
3). The numerical value rounding process of the data x is represented by the following Expression 3, and the rounded numerical value is f.

[0016]

F = F (x, th1) When this equation 3 is implemented under the 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 th,
It is all zero, and the integral is zero. Therefore, the speed or the angular speed is obtained by integrating this f with time (step S4). Then, the integral value is rounded with the threshold value as th2 as shown in the following Expression 4.

[0017]

G = F (∫fdt, th2) Next, as shown in the following Expression 5, the obtained data g is integrated at time t, and similarly, the threshold value is set to th3, and rounding is performed by the function F ( Step S5).

[0018]

H = F (∫gdt, th3) Then, the second-order integral value h is output to the outside of the numerical operation unit 3 (step S6), and the output device 4 such as a display is output.
To be displayed. Note that the numerical operation unit 3 can be constituted by one integrated circuit (IC), but the signal processing unit 2 for performing sampling can also be incorporated in this IC.

In the method of this embodiment having the above-described structure, in order to solve the conventional disadvantage, first, the value x of the acceleration or angular acceleration measured by the sensor 1 is set to the threshold value th.
A process of numerically rounding with the function F using 1 is performed.
This rounding process is performed as shown in Expressions 1 and 2 and FIG.
The numerical value within the threshold value th1 is set to 0. As a result, as shown in FIG. 3, the data f has a small variation.

Next, this data f is integrated at time t,
Further, a similar rounding process is performed using the threshold value th2.
The result is the first-order integration (step S4). Then, the obtained data g is integrated at time t, and the same rounding process is further performed using the threshold value th3 to obtain a second-order integration result (step S5).

The data h after the second-order integration according to this embodiment
Is shown in FIG. As shown in FIG. 4, the same data as the theoretical values can be obtained with high accuracy by performing the integration processing according to the method of the present embodiment. On the other hand, the result of the second-order integration by the conventional method (see FIG. 8) is also shown in FIG. 4. In the case of the conventional method, when the angle is constant and the operation is stopped, the error increases with time and increases. Will be done. Therefore, as shown in FIG. 5, in the case of the present embodiment, an extremely small error occurs when the motor is stopped, and this error does not increase. As time goes on, the error increases.

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. Especially when the moving object is stopped,
The above effects are remarkable.

It is needless to say that the present invention is not limited to the above embodiment. For example, in the above embodiment,
Although the rounding processing is based on the function F represented by Expressions 1 and 2, it is not limited to this, and the rounding processing can be performed by rounding down or rounding up. As described above, any function or operation that removes an error can be used in the numerical rounding processing of the present invention.

Further, in the above-described embodiment, the example in which the angular velocity and the angle are calculated from the output of the angular acceleration sensor 1 has been described. However, the present invention can be applied to any system requiring the second-order integration. For example, the present invention can be applied to a case where a speed and a distance are calculated using an acceleration sensor.

Furthermore, the above-described embodiment relates to the second-order integration, but it goes without saying that the present invention may be applied to the first-order integration. However, application to the second-order integration is more effective than application to the first-order integration. Further, when the present invention is applied to third order integration or more, more excellent effects can be obtained.

The integration operation itself may be performed by a known method, and various methods can be used.

[0027]

As described above, according to the present invention,
An error in the integration processing of the digital data is small, and accumulation of this error can be avoided, so that the integration processing can be performed with extremely high accuracy. Also, when the output of the sensor is 0
Even in the case of (2), that is, even when the moving body is stopped, the divergence of the integrated data is prevented. In addition, since the algorithm is simple, the operation can be performed at a higher speed as compared with other algorithms, and the performance of the CPU, the memory and the like 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 a method according to an embodiment of the present invention.

FIG. 2 is a diagram illustrating the principle of a rounding process.

FIG. 3 is a diagram showing data rounded by a function F;

FIG. 4 is a graph showing data obtained by performing second-order integration by a method according to an embodiment of the present invention in comparison with theoretical values and conventional data.

FIG. 5 is a graph comparing the error between the embodiment method and the conventional method.

FIG. 6 is a graph showing a measurement result of an angular acceleration by a sensor.

FIG. 7 is a graph showing data after performing an integration operation once by a conventional method.

FIG. 8 is a graph showing data after performing an integral operation twice by a conventional method.

FIG. 9 is a graph showing an error caused by a conventional integration operation method.

[Explanation of symbols]

 1: Sensor 2: Signal processing unit 3: Numerical operation unit 4: Output device

Claims (5)

[Claims] 1. A first step of setting a predetermined threshold value for digital data and rounding a data portion within the threshold value, and a second step of performing an integration operation on the data after the rounding processing. An integration calculation processing method characterized by having: 2. A third step in which a predetermined threshold value is set for the data after the integration operation, and a data portion within the threshold value is rounded, and a third step in which the rounded data is further integrated. 4. The method according to claim 1, wherein the method includes four steps. 3. The method according to claim 1, further comprising a fifth step of setting a predetermined threshold value for the data after the integration operation in the fourth step and rounding a data portion within the threshold value. 3. The integration calculation processing method according to 2. 4. In the first, third or fifth step,
When the digital data is x, the threshold value is th, and α is a positive number less than 1, a function F (x, th) for performing a process of rounding x with the threshold value th is obtained by converting int (a) to a real number a. As a symbol indicating an integer part, when x / th ≧ int (x / th) + α, F
(X, th) = int (x / th) × th + th, where x / th
<Int (x / th) + α, F (x, th) = int (x
/ Th) × th.
3. The method according to claim 1. 5. The method according to claim 4, wherein α is 0.5.