KR20160120977A - Method for enhancing dynamic range of seismec sensor and apparatus thereof - Google Patents

Abstract

The present invention relates to a method for enhancing a dynamic range of a seismometer sensor and a device thereof. According to the present invention, the method for enhancing a dynamic range of a seismometer sensor, comprises: a step of modeling a noise signal included in a seismometer sensor as an automatic regressive moving average (ARMA) model; a step of expressing an output signal of the seismometer sensor defined using the sum of the modeled noise signal and a seismic wave input signal as a state equation using a state variable; and steps of constructing a Kalman filter using the state equation, and estimating the seismic wave input signal using the Kalman filter. According to the method for enhancing a dynamic range of a seismometer sensor and a device thereof, noise components included in the seismometer sensor are minimized, and the dynamic range of the seismometer sensor is enhanced by estimating a seismic wave signal.

Description

TECHNICAL FIELD The present invention relates to a dynamic range of a seismic sensor,

The present invention relates to a dynamic range enhancement method and apparatus for a seismometer sensor, and more particularly, to a dynamic range enhancement method and apparatus for a seismometer sensor capable of improving dynamic range of a seismometer sensor used for measuring a seismic signal will be.

In general, MEMS (Micro Electro Mechanical System) is used as a sensor element for various measurement based on excellent mechanical characteristics and electrical stability of silicon, which is a semiconductor element. In particular, capacitive MEMS sensors are rapidly growing as low-cost sensors for mobile devices because they are suitable for micro-fabrication and batch production.

While MEMS sensors are pursuing miniaturization and lowering costs, efforts are being actively made to replace existing expensive mechanical measurement sensors with MEMS-based sensors. Especially in the case of accelerometers, the SF2006 released by Colibrys in 2011 is approaching the performance of huge mechanical sensors because it has a noise density of only 1.3 / √Hz. As the accuracy of MEMS accelerometers increases, it is possible to replace traditional large-scale, high-cost metrology equipment such as inertial navigation and seismic monitoring with smaller, lower-cost systems.

The output of the seismometer sensor includes both the seismic signal and the noise signal input during the measurement. The types of noise include white noise, noise, random walk, quantization noise, and Markov processor. In the frequency domain, the noise signal can be divided into a low frequency noise added to the seismic signal and a high frequency noise out of this area.

Among them, high-frequency noise can be sufficiently suppressed by a low-pass filter (LPF), but low-frequency noise exists in the same frequency band as the actual seismic signal, so it can not be suppressed by a general low-pass filter.

The technology to be a background of the present invention is disclosed in Korean Patent No. 0594625 (Jun. 30, 2006).

An object of the present invention is to provide a dynamic range enhancement method and apparatus for a seismometer sensor capable of improving a dynamic range of a seismometer sensor by minimizing a noise component of the seismometer sensor while estimating the seismic signal.

The method includes modeling a noise signal included in a seismometer sensor in an ARMA (Auto Regressive Moving Average) model, using the sum of the modeled noise signal and the seismic input signal, Expressing the output signal of the seismic sensor as a state equation using state variables, and constructing a Kalman filter using the state equation and estimating the seismic input signal using the Kalman filter. ≪ / RTI >

The dynamic range enhancement method of the seismometer sensor may further include acquiring the noise signal from output data of the seismometer sensor measured while the input is unmanned.

In addition, the noise signal modeled by the ARMA model can be defined by the following equation.

)(

)

는 백색 가우시안 잡음, nc 및 c_j는 각각 상기 이동평균의 차수 및 계수를 나타낸다.Where b _t is the modeled noise signal, na and a _i are the order and coefficients of the autoregression,

Is the white Gaussian noise, and nc and cj _denote the order and coefficient of the moving average, respectively.

)으로 정의되고, 상기 지진파 입력 신호 u_t는 아래의 수학식으로 정의될 수 있다.In addition, the output signal y _t of the seismometer sensor is calculated by subtracting the sum of the seismic input signal u _t , the modeled noise signal b _t , and the white noise v _t added to the output of the seismometer sensor

), And the seismic input signal u _t can be defined by the following equation.

Where u _t is the seismic input signal defined by the Markov process, α _i is any constant, n α is the Markov process order, and f _t is the white noise included in the seismic input signal.

Further, the state equation can be defined by the following equation including the system equation and the output equation.

, w_t는 프로세스 잡음으로서

, F는 시스템 행렬, G는 프로세스 잡음 행렬, y_t는 지진계 센서의 출력, H는 측정 행렬, v_t는 백색 잡음을 나타낸다.Here, x _t is a state variable

, w _t is the process noise

, F is the system matrix, G is the process noise matrix, y _t is the output of the seismometer sensor, H is the measurement matrix, and v _t is the white noise.

Further, the Kalman filter can be defined by the following equation.

는 시간 t에서의 상태 변수 추정 값,

는 시간 t+1에서의 지진계 센서의 출력을 이용한 상태 변수 추정 값,

는

의 예측 값, K는 칼만 이득 행렬이다.here,

Is the state variable estimate at time t,

Is a state variable estimation value using the output of the seismometer sensor at time t + 1,

The

And K is a Kalman gain matrix.

In addition, the dynamic range enhancement method of the seismometer sensor may further include suppressing high frequency noise using a low-pass filter before or after using the Kalman filter.

The ARMA modeling unit models the noise signal included in the seismometer sensor as an ARMA (Auto Regressive Moving Average) model, and uses the sum of the modeled noise signal and the seismic input signal to define A state space model generator for expressing an output signal of the seismometer sensor by using a state equation using a state variable and a Kalman filter for constructing a Kalman filter using the state equation and estimating the seismic input signal using the Kalman filter, A dynamic range enhancement device for a seismometer sensor including an operation unit is provided.

According to the dynamic range enhancement method and apparatus of a seismometer sensor according to the present invention, a dynamic range of a seismometer sensor can be improved by estimating a seismic signal while minimizing a noise component of the seismometer sensor.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of an apparatus for improving dynamic range of a seismometer sensor according to an embodiment of the present invention; FIG.
2 is a flowchart illustrating a dynamic range enhancement method using the apparatus of FIG.
3 is a diagram illustrating a setup state of a seismograph for testing a method according to an embodiment of the present invention.
4 is a diagram illustrating a frequency response characteristic of a low-pass filter used in an embodiment of the present invention.
FIG. 5 is a diagram for checking whether whitening is possible by a model estimated according to an embodiment of the present invention.
FIG. 6 is a graph comparing output data, low pass filter pass data, and Kalman filter pass data of a seismometer sensor when there is a seismic input signal in the embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention.

The present invention relates to a dynamic range enhancement method and apparatus for a seismometer sensor, and proposes a method for improving the dynamic range of a seismometer sensor by suppressing the influence of noise included in the seismometer sensor.

In general, the most important performance of a seismometer acceleration sensor, ie, a seismometer sensor, is a dynamic range and a dynamic range can be expressed as follows.

As shown in Equation (1), the dynamic range of the seismometer sensor is expressed as a ratio between the maximum value of the sensor signal measured by the seismometer sensor and the standard deviation of the background noise with respect to the predetermined maximum input. In the embodiment of the present invention, a three-axis accelerometer as a seismometer sensor is integrated into a single module by the MEMS process, and 2g determined in the domestic seismograph standard is used as the maximum input.

In general, the theoretical limit to the background noise of the sensor can be explained by the thermodynamic behavior of the inertial mass connected to the spring, and can be expressed by the following equation (2).

단위의 배경잡음 밀도, k_B는 볼츠만(Boltzmann) 상수, T는 온도, ω₀는 2차 진동계의 고유진동수, Q는 quality factor, M은 관성 질량을 의미한다. Where v is

_B is the Boltzmann constant, T is the temperature, ω ₀ is the natural frequency of the secondary vibration system, Q is the quality factor, and M is the inertial mass.

According to Equation (2), the background noise of the MEMS acceleration sensor can be improved by the structure improvement of the sensor and the temperature compensation, but the degree of improvement is limited. Therefore, a digital filtering algorithm is needed to suppress the influence of background noise through separate post-processing of the sensor output.

In the embodiment of the present invention, the noise included in the seismometer sensor is analyzed and the analyzed noise is modeled as ARMA. Then, the modeled noise and the seismic input are included in the Kalman filter expression, The Kalman filter method can estimate the seismic signal while suppressing the noise. In order to improve the estimation performance of the seismic signal, a general low-pass filter may be additionally used before and after the Kalman filter.

In this way, the embodiment of the present invention can estimate the seismic signal while minimizing the noise component of the seismometer sensor, thereby improving the dynamic range of the seismometer sensor. Hereinafter, a dynamic range enhancement method of a seismometer sensor according to an embodiment of the present invention will be described in detail.

FIG. 1 is a configuration diagram of a dynamic range enhancement apparatus for a seismometer sensor according to an embodiment of the present invention, and FIG. 2 is a flowchart illustrating a dynamic range enhancement method of a seismometer sensor using the apparatus of FIG.

1 and 2, an apparatus 100 for improving a dynamic range of a seismometer sensor according to an embodiment of the present invention includes a noise acquisition unit 110, an ARMA modeling unit 120, a state space model generation unit 130, A Kalman filter operation unit 140, and a low pass filter unit 150.

First, the noise acquisition unit 110 acquires a noise signal from the output data of the seismometer sensor measured while the input is unmanned (S210).

The embodiment of the present invention obtains the noise signal from the output data of the seismometer sensor measured without applying the input to the seismometer sensor as described above before modeling the noise signal. This is for measuring the background noise component without input to the seismic sensor.

When the noise signal is obtained as described above, the noise signal is expressed by an auto regressive moving average (ARMA) model. That is, the ARMA modeling unit 120 models the noise signal included in the seismometer sensor into the ARMA model (S220).

Here, the process of modeling the noise signal by ARMA is as follows. First, an ARMA model in which an auto regressive (AR) and a moving average (MA) are mixed can be expressed as Equation (3) below.

는 백색 가우시안 잡음, na 및 a_i는 각각 상기 자동회귀의 차수 및 계수(i=1,…,na), nc 및 c_j는 각각 상기 이동평균의 차수 및 계수(j=1,…,nc)를 나타낸다. 그리고 t와 관련한 것은 시간에 대한 인덱스를 나타내는데, t-1은 현재시간 t로부터 한 샘플 이전 시간을 의미한다.Where b _t is the modeled noise signal,

Is white Gaussian noise, na, and a _i are each the autoregressive order and the coefficients (i = 1, ..., na ) of, nc and c _j are respectively the moving average of the order and a coefficient (j = 1, ..., nc ) . And t relates to the time index, where t-1 means one sample time before the current time t.

In this equation (3), the order of the autoregressive na and the coefficient a _i and, to be the estimated moving average degree nc and coefficients c _j of each. Embodiments of the present invention can estimate the order and coefficients using a prediction error method known as an optimal method for noise whitening among system identification methods.

In general, the Kalman filter is known as the optimal filter for estimating state variables in a linear time invariant system. In the embodiment of the present invention, the noise signal represented by the ARMA model is included in the state variable equation as described above, and the seismic input signal is estimated by the Kalman filter.

If the average moving part of Equation (3) is defined as a new variable e _t , Equation (3) is summarized as Equation (4).

이다. 이러한 수학식 4에 정의된 b_t는 수학식 3에 정의한 잡음 신호를 나타내며, a_i는 b_t의 변수(i=1,…,na)를 나타낸다. here,

to be. B _t defined in Equation (4) represents a noise signal defined in Equation (3), and a _i represents a variable (i = 1, ..., na) of b _t .

The noise signal b _t defined above is the ARMA model of the noise obtained when the seismic input is unattended to the seismometer sensor. If the actual seismic input is applied here, the seismic sensor output appears by adding the noise signal b _t and the seismic input. Additionally, the seismic sensor output may include additional white noise.

Accordingly, when defining the seismic input signal into a u _t and defined as a white noise that more may be included in addition to the u _t and b _t a seismic sensor output v _t, the signal y _t is actually outputted by the seismic sensors mathematical below Can be expressed as the sum of u _t , b _t , and v _t as in Equation (5).

Thus, the output y _t of the seismometer sensor can be represented by a simple concept as shown in Equation (5). Of course, this output y _t has the same effect as the seismic input signal, the noise signal modeled by the ARMA model, and the white noise are input and output to the seismometer sensor together.

After modeling the noise signal as in step S220, a state equation is generated based on the model. That is, the state space model generating unit 130 expresses the output signal y _t of the seismometer sensor defined using the modeled noise signal and the seismic input signal as a state equation using the state variable x _t (S230).

The method of constructing the state equation in the embodiment of the present invention will be described in more detail as follows. First, in the embodiment of the present invention, the seismic input signal is assumed to be a Markov process as shown in Equation (6).

Where u _t is the seismic input signal defined by the Markov process, α _i is any constant, n α is the Markov process order, and f _t is the white noise included in the seismic input signal. α _i requires tuning appropriately when configuring the filter.

By combining the modeled noise signal b _{t according to} equation (4), the seismic input signal u _{t according} to equation (6), and the equation (5) representing the output y _t of the seismometer sensor, the equation of state of equation .

The state equation of Equation (7) is a system equation (first equation of Equation (7)) representing the time propagation of the state variable x _t , and an output equation of the output of the seismometer sensor (The second expression in Equation 7).

이다. 그리고, 프로세스 잡음 w_t 즉, 공정 잡음은

이다.Specifically, in the system equation (Equation (7)) of Equation (7), x _t is a state variable indicating the state of the system and is composed of a noise signal b _t and a seismic input signal u _t ,

to be. Then, the process noise w _t, that is, the process noise,

to be.

Also, in the system equation, F is expressed as a system matrix, and G is expressed as a process noise matrix as shown in Equation (8) below.

In equation (7), y _t is the output of the sensor, H is the measurement matrix, and v _t is the white noise.

H is expressed by the following equation (9).

The state variable of the state equation can be estimated by constructing the Kalman filter using the state equation generated as shown in Equation (7). That is, in Equation (7), x _t represents all the information on the current state of the system, but since it can not be measured directly, x _t can be estimated using the output of a sensor with a mixed noise type .

Accordingly, the Kalman filter operation unit 140 estimates the state variable from the output signal of the seismometer sensor through the Kalman filter constructed by using the state equation of Equation (7), and consequently obtains the estimated value of the seismic input signal (S240). Here, the Kalman filter can be expressed by Equation (10).

는 시간 t에서의 상태 변수 추정 값,

는 시간 t+1에서의 지진계 센서의 출력 신호를 이용한 상태 변수 추정 값이다.

는

의 예측 값으로서 상태 변수 추정 값

를 통해 구할 수 있다. 더 상세하게는 시간 갱신(time update)으로 구해진 상태 변수 추정 값

로부터

를 이용하여 계산될 수 있다. K는 칼만이득 행렬로서 시스템 및 측정 행렬과 잡음의 분산으로부터 계산된다. K를 구하는 과정은 칼만 필터 이론으로부터 기 공지되어 있으므로 상세한 설명은 생략한다.here,

Is the state variable estimate at time t,

Is the state variable estimation value using the output signal of the seismometer sensor at time t + 1.

The

The state variable estimation value < RTI ID = 0.0 >

. More particularly, the present invention relates to a state variable estimation value obtained by time update

from

. ≪ / RTI > K is the Kalman gain matrix and is calculated from the variance of the system and measurement matrix and noise. Since the process of obtaining K is well known from the Kalman filter theory, detailed description is omitted.

The Kalman filter estimates the seismic input while suppressing noise from the seismic sensor output, which can improve the dynamic range of the seismic sensor.

By using a low pass filter in addition to the Kalman filter, the estimation of the seismic input signal can be more accurate. That is, the low-pass filter unit 150 is positioned before or after the use of the Kalman filter to suppress high-frequency noise. Specifically, before using the Kalman filter, a method of passing the output signal of the seismometer sensor through a low-pass filter and then constructing a Kalman filter or passing the estimated value of the seismic input signal obtained through the Kalman filter to a low-pass filter .

The ripple in the passband must be minimized in order to prevent distortion of the seismic signal in the low frequency band through which the lowpass filter passes. An elliptic filter can be used as the filter to minimize the ripple. The passband can be 0 ~ 50Hz, which is the frequency standard of the domestic seismometer.

The embodiment of the present invention can estimate the seismic signal while suppressing the noise using the Kalman filter method after modeling the noise with the ARMA model, thereby improving the dynamic range of the seismometer sensor. The improvement of dynamic range can be verified through the following test results. For reference, the embodiment described below is a case where the low-pass filter is placed in front of the Kalman filter.

3 is a diagram showing a setup state of a seismograph for testing a method according to an embodiment of the present invention. FIG. 3 (a) is a seismometer sensor used in the test, which is a MEMS process integrating a three-axis accelerometer into one module, which can input a maximum of 2 g or more. 3 (b) shows a state where a seismograph is attached to the upper part of the vibrator mounted on the vibration-free table.

Here, when the standard deviation of the background noise is obtained, the data is collected in a static state where the operation of the exciter is stopped. And the seismic input signal by the exciter uses the sinusoidal input of 2g size which is the maximum input specified by the domestic seismograph standard. The frequency of the sinusoidal wave is 27Hz which is half of the frequency range defined by the seismograph standard. In order to collect data, an NI-9239 DAQ device with a 24-bit ADC was used. Data was transmitted from the NI-9239 DAQ to a PC and an algorithm according to an embodiment of the present invention was performed on the PC. Of course, such an algorithm can also be implemented in a form embedded in a seismic sensor itself.

4 is a diagram illustrating a frequency response characteristic of a low-pass filter used in an embodiment of the present invention. In the embodiment of the present invention, an oval filter is used as a low-pass filter for eliminating high-frequency noise. Referring to FIG. 4, the low-pass filter used is designed to suppress high-frequency noise by 120 dB or more, and this characteristic is sufficient to eliminate high-frequency noise.

First, high-frequency noise is removed by passing a low-pass filter from the measured data of the sensor obtained in the static state without the seismic input, and then the coefficients of the ARMA model are estimated using the prediction error method.

In an embodiment of the present invention, an auto correlation function comparison is performed to confirm whether the estimated noise model can be sufficiently whitened, and the result is shown in FIG. 5 below.

FIG. 5 is a diagram for checking whether whitening is possible by a model estimated according to an embodiment of the present invention. FIG. 5A shows noise data having passed through the low-pass filter, and FIG. 5B shows the autocorrelation function results for the noise data ARMA modeled after the low-pass filter. From the result of FIG. 5, it can be seen that the ARMA modeled data after passing through the low-pass filter is very close to the whitening, unlike the data simply passing through the low-pass filter, and it is confirmed that the estimated ARMA model is valid .

Next, the Kalman filter is constructed using the coefficients of the estimated ARMA model and the results of estimating the seismic input signal are described. First, we explain the estimation result in dynamic state without seismic input. In the absence of seismic input, the estimated value corresponds to background noise and its standard deviation is shown in Table 1 below.

Standard deviation (g) Sensor output 2.04e-5 After passing the low-pass filter 1.02e-5 After passing through the Kalman filter 7.72e-6

Referring to Table 1, it can be seen that the background noise estimated after passing through the low-pass filter is less than the background noise directly estimated from the sensor output, and the standard deviation thereof is reduced to about 0.5 times. After passing through the Kalman filter, And it is decreased to the times when it is decreased. As a result, it can be confirmed that the background noise approaches the whitening due to the passage of the Kalman filter.

Next, we explain the estimation result in the state where the seismic wave input is applied. A sinusoidal wave of 27 Hz was applied to the input of 2 g, and the results after passing through the low-pass filter and after the estimation of the Kalman filter were compared, respectively.

FIG. 6 is a graph comparing output data, low pass filter pass data, and Kalman filter pass data of a seismometer sensor when there is a seismic input signal in the embodiment of the present invention. The results in FIG. 6 show that the estimated values of the Kalman filter agree well with the sensor output data and the lowpass filter pass-through data.

In order to obtain the dynamic range of the seismometer sensor, which is a characteristic to be confirmed in the embodiment of the present invention, the maximum value of each output data is obtained from FIG. 6, and as a result, . Table 2 shows the results of calculating the dynamic range of the sensor by applying each maximum value to Equation (1).

Dynamic range (dB) Sensor output 99 After passing the low-pass filter 105 After passing through the Kalman filter 108

Referring to Table 2, it can be seen that the dynamic range is improved by about 6 dB after passing through the low-pass filter, and by about 9 dB after passing through the Kalman filter. As a result, the method according to the embodiment of the present invention was applied to a three-axis acceleration type seismometer based on MEMS and the performance was verified. As a result, the dynamic range could be improved by 3 dB compared with the case using a low pass filter. That is, according to the ARMA modeling method and the Kalman filter method according to the embodiment of the present invention, the dynamic range can be significantly improved as compared with the low-pass filter method that is commonly used.

As described above, embodiments of the present invention model the noise as an ARMA model and then suppress the noise and estimate the seismic signal using the Kalman filter method. That is, the method includes modeling the sensor noise in the unmanned state with the ARMA model, identifying the corresponding model, and then including the modeled noise and the seismic input in the Kalman filter expression to estimate the seismic input by the Kalman filter . As a result, according to the dynamic range enhancement method and apparatus of a seismometer sensor according to the present invention, dynamic range of a seismometer sensor can be improved by estimating a seismic signal while minimizing a noise component of the seismometer sensor.

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: Dynamic range enhancement device of a seismic sensor
110: noise acquisition unit 120: ARMA modeling unit
130: state space model generation unit 140: Kalman filter operation unit
150: Low pass filter section

Claims (14)

Modeling a noise signal included in the seismometer sensor into an automatic regressive moving average (ARMA) model;
Expressing an output signal of the seismometer sensor defined by using the sum of the modeled noise signal and the seismic input signal as a state equation using a state variable; And
And constructing a Kalman filter using the state equation and estimating the seismic input signal using the Kalman filter. The method according to claim 1,
Further comprising the step of acquiring the noise signal from output data of the seismometer sensor measured while the input is unmanned. The method according to claim 1 or 2,
Wherein the noise signal modeled by the ARMA model is defined by the following equation:

(

)
Where b _t is the modeled noise signal, na and a _i are the order and coefficients of the autoregression,

Is the white Gaussian noise, and nc and cj _denote the order and coefficient of the moving average, respectively. The method of claim 3,
The output signal y _t of the seismometer sensor is obtained by:
The sum of the seismic input signal u _t , the modeled noise signal b _t , and the white noise v _t added to the output of the seismometer sensor

),
Wherein the seismic input signal u _t is defined by the following equation:

Where u _t is the seismic input signal defined by the Markov process, α _i is any constant, n α is the Markov process order, and f _t is the white noise included in the seismic input signal. The method of claim 4,
Wherein the state equation is defined by the following equation including a system expression and an output expression:

Here, x _t is a state variable

, w _t is the process noise

, F is the system matrix, G is the process noise matrix, y _t is the output of the seismometer sensor, H is the measurement matrix, and v _t is the white noise. The method of claim 5,
Wherein the Kalman filter is defined by the following equation:

here,

Is the state variable estimate at time t,

Is a state variable estimation value using the output of the seismometer sensor at time t + 1,

The

And K is a Kalman gain matrix. The method according to claim 1,
Further comprising suppressing high frequency noise using a low pass filter before or after using the Kalman filter. An ARMA modeling unit for modeling the noise signal included in the seismometer sensor as an automatic regressive moving average (ARMA) model;
A state space model generation unit for expressing an output signal of the seismometer sensor defined by using the sum of the modeled noise signal and the seismic input signal as a state equation using a state variable; And
And a Kalman filter operator for constructing a Kalman filter using the state equation and estimating the seismic input signal using the Kalman filter. The method of claim 8,
And a noise acquiring unit for acquiring the noise signal from output data of the seismometer sensor measured in a state where the input is unmanned. The method according to claim 8 or 9,
Wherein the noise signal modeled by the ARMA model is defined by the following equation:

(

)
Where b _t is the modeled noise signal, na and a _i are the order and coefficients of the autoregression,

Is the white Gaussian noise, and nc and cj _denote the order and coefficient of the moving average, respectively. The method of claim 10,
The output signal y _t of the seismometer sensor is obtained by:
The sum of the seismic input signal u _t , the modeled noise signal b _t , and the white noise v _t added to the output of the seismometer sensor

),
The seismic input signal u _t is defined by the following equation:

Where u _t is the seismic input signal defined by the Markov process, α _i is any constant, n α is the Markov process order, and f _t is the white noise included in the seismic input signal. The method of claim 11,
Wherein the state equation is defined by the following equation including a system expression and an output expression:

Here, x _t is a state variable

, w _t is the process noise

, F is the system matrix, G is the process noise matrix, y _t is the output of the seismometer sensor, H is the measurement matrix, and v _t is the white noise. The method of claim 11,
Wherein the Kalman filter is defined by the following equation:

here,

Is the state variable estimate at time t,

Is a state variable estimation value using the output of the seismometer sensor at time t + 1,

The

And K is a Kalman gain matrix. The method of claim 8,
Further comprising a low-pass filter portion for suppressing high-frequency noise using a low-pass filter before or after using the Kalman filter.

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