Zero phase shift IIR digital filtering method and filter for sea-air gravimeter measurement data

Abstract

The invention discloses a zero phase shift IIR (Infinite Impulse Response) digital filtering method and filter for sea-air gravimeter measurement data, and the method comprises the steps: setting two stages of IIR filters which have the same unit impulse response; the method comprises the following steps: collecting measurement data of a sea-air gravimeter, enabling a time sequence of the measurement data of the sea-air gravimeter to pass through an IIR (Infinite Impulse Response) filter to obtain a primary filtering sequence, and performing time sequence inversion and translation on the primary filtering sequence to obtain a new data sequence; and enabling the new data sequence to pass through the same IIR filter to obtain a secondary filtering sequence, and performing time sequence inversion and translation on the secondary filtering sequence to obtain final filtering output. The zero-phase filtering of the sea-air gravimeter is realized by utilizing a forward time sequence and an overturning time sequence through two stages of IIR filters which are mutually offset in phase shift, that is, the filter does not have a time delay problem.

Description

Technical Field

[0001] The present invention relates to the field of surveying and mapping technology, and in particular to a zero-phase-shift IIR digital filtering method and filter for sea and air gravimeter measurement data. Background Art

[0002] The Earth's gravity field is one of the Earth's basic physical fields. It comprehensively reflects the spatial distribution, movement and change state of the Earth's internal matter, and restricts the movement of objects on the Earth's surface and in its adjacent space. Obtaining high-precision and high-resolution Earth gravity field data is not only the basic work necessary for conducting research in disciplines such as geodesy, geophysics, geodynamics, oceanography and space science, but also an essential basic parameter for conducting geological and mineral resource exploration, improving the accuracy of long-range strategic weapons strikes and the reliability of spacecraft launches.

[0003] Gravity measurement by sea and air gravimeters has the advantages of high measurement accuracy and high spatial resolution, and has been widely used in related fields. However, gravity sensors are sensitive to all vertical accelerations. The vertical additional accelerations caused by factors such as carrier turbulence and waves during the measurement process cannot be completely eliminated by the gravimeter. At the same time, there is a lot of measurement noise during the measurement process. In addition, due to the linear motion of the carrier, additional Coriolis forces will inevitably be generated, and there are also influences such as tides, random drift, and platform fluctuations. Therefore, in order to obtain effective gravity anomaly information, it is necessary to filter the gravity measurement data and calculate the final gravity anomaly information based on the spatial distribution model of the gravity field. Therefore, it is necessary to adopt an effective method that can separate motion disturbances from the actual gravity field to improve the accuracy of gravity measurement.

[0004] At present, the digital filtering method used more in sea and air gravimeters is FIR filter, but due to its high filtering order, it brings problems such as slow operation speed and many experimental data discarded by boundary effects. Compared with FIR filter, IIR filter has much lower order and can provide similar amplitude response or lower side lobe with fewer coefficients, so the operation speed is fast and the utilization rate of experimental data is correspondingly improved. However, the phase shift of IIR filter is nonlinear.

[0005] At present, in order to suppress the influence of motion disturbance on gravity measurement, the main method used is the digital filtering method based on the signal frequency domain characteristics to separate the measurement noise from the actual gravity field. Based on this, it is urgent to propose a zero-phase-shift IIR digital filtering technology for gravity measurement data to achieve zero phase shift of the filtering result. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a zero-phase-shift IIR digital filtering method and filter for sea-air gravimeter measurement data in view of the defects in the prior art.

[0007] The technical solution adopted by the present invention to solve its technical problem is:

[0008] The present invention provides a zero-phase shift IIR digital filtering method for sea and air gravimeter measurement data, the method comprising:

[0009] Set up a two-stage IIR filter, the unit impulse response of the two-stage IIR filter is the same;

[0010] Collect the measurement data of the sea and air gravimeter, pass the time series of the sea and air gravimeter measurement data through the IIR filter to obtain a primary filter sequence, and then reverse and shift the primary filter sequence to obtain a new data sequence;

[0011] The new data sequence is passed through the same IIR filter to obtain a secondary filter sequence, and the secondary filter sequence is time-reversed and shifted to obtain the final filter output.

[0012] Furthermore, in the method of the present invention, the first filtering sequence and the second filtering sequence are respectively used for timing inversion using a forward time sequence and a reverse time sequence, and the phase shifts when passing through the filter cancel each other to achieve zero phase shift of the filtering result.

[0013] Furthermore, the differential equations of the IIR filters in the primary filtering and the secondary filtering of the present invention are as follows:

[0014]

[0015] Where: a k , b k is the filter coefficient; x(n) is the input sequence, i.e., the time series of sea and air gravimeter measurement data; y(n) is the output sequence; the maximum value among M and N is the filter order

[0016] Furthermore, the primary filtering sequence obtained in the method of the present invention is:

[0017] y1[n]=x[n]*h[n]

[0018] Where: h(n) is the impulse response of the IIR filter, x[n] is a time series with a length of N+1, and y1[n] is the primary filter output.

[0019] Furthermore, in the method of the present invention, the first filtering sequence is time-reversed and shifted to obtain a new data sequence:

[0020] y2[n]=y1[Nn]

[0021] Wherein: y2[n] is the new data sequence obtained by time-reversing and shifting the primary filtering sequence y1[n].

[0022] Furthermore, the secondary filtering sequence obtained in the method of the present invention is:

[0023] y3[n]=y2[n]*h[n]

[0024] Where: y3[n] is the secondary filtering output sequence obtained by passing y2[n] through the IIR filter again. Further, the final filtering output in the method of the present invention is:

[0025] y[n]=y3[Nn]

[0026] Where: y[n] is the final filter output obtained by time-reversing and shifting the secondary filter sequence.

[0027] Furthermore, the method of the present invention also includes:

[0028] Perform Fourier transform on x[n], y1[n], y2[n], y3[n], y[n], h[n] respectively; and considering that for the real sequence h[n], H(-ω)=H * (ω), then:

[0029] Y(ω)=e -jωN Y3(-ω)

[0030] =e -jωN Y2(-ω)H(-ω)

[0031] =e -jωN e jωN Y1(ω)H(-ω)

[0032] =Y1(ω)H(-ω)

[0033] =X(ω)H(ω)H(-ω)

[0034] =X(ω)|H(ω) 2

[0035] Where: X(ω), Y1(ω), Y2(ω), Y3(ω), Y(ω), H(ω) are the Fourier transforms of x[n], y1[n], y2[n], y3[n], y[n], h[n] respectively.

[0036] The present invention provides a zero-phase shift IIR digital filter for sea and air gravimeter measurement data, comprising:

[0037] The first-stage IIR filter is used to process the time series of the sea and air gravimeter measurement data to obtain a primary filter sequence, and then the primary filter sequence is time-reversed and translated to obtain a new data sequence;

[0038] The second-stage IIR filter is used to process the new data sequence to obtain a secondary filter sequence, and to perform time inversion and translation on the secondary filter sequence to obtain the final filter output.

[0039] Furthermore, the first-stage IIR filter and the second-stage IIR filter of the present invention are connected in sequence, and the unit impulse responses of the two-stage IIR filters are the same.

[0040] The beneficial effects produced by the present invention are:

[0041] 1. The present invention designs a two-stage IIR filter that utilizes the phase shifts of the forward time series and the flipped time series when they pass through the filter to cancel each other, thereby realizing zero-phase filtering of the sea and air gravimeter, that is, the filter does not have a time delay problem.

[0042] 2. Compared with filters of the same order, the filtering method proposed in the present invention has stronger attenuation in the transition band and stop band than the FIR filter, and has higher filtering accuracy.

[0043] 3. In order to achieve the same filtering effect, the zero-phase IIR digital filter has a lower order, and less data is discarded due to boundary effects, which improves the utilization rate of test data and the calculation speed. There is no delay after filtering, and there is no need to manually time-align the filtering results. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0045] Figure 1 is a filter principle diagram of an embodiment of the present invention;

[0046] Figure 2 4 is a filtering flow chart of an embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0048] Example 1

[0049] In order to improve the measurement accuracy of gravimeter, a zero-phase-shift IIR digital filtering method for sea and air gravimeter measurement data was proposed based on the processing ideas of suppressing the influence of motion disturbance. This technology mainly includes the design of IIR filter and the processing flow design of forward and reverse filtering.

[0050] An embodiment of the present invention provides a zero-phase shift IIR digital filtering method for sea and air gravimeter measurement data, the method comprising:

[0051] Set up a two-stage IIR filter, the unit impulse response of the two-stage IIR filter is the same;

[0052] Collect the measurement data of the sea and air gravimeter, pass the time series of the sea and air gravimeter measurement data through the IIR filter to obtain a primary filter sequence, and then reverse and shift the primary filter sequence to obtain a new data sequence;

[0053] The new data sequence is passed through the same IIR filter to obtain a secondary filter sequence, and the secondary filter sequence is time-reversed and shifted to obtain the final filter output.

[0054] In a preferred embodiment of the present invention, the zero-phase-shift IIR digital filtering method for sea and air gravimeter measurement data includes a two-stage low-pass filter, and the unit impulse response of the two-stage filter is the same. The specific filtering process is to first pass the sea and air gravimeter measurement data time series x[n] with a length of N+1 through an IIR filter to obtain a primary filter sequence y1[n], and then perform time inversion and translation on the primary filter sequence y1[n] to obtain a new data sequence y2[n], and then pass the new data sequence y2[n] through the same IIR filter to obtain a secondary filter sequence y3[n], and finally perform time inversion and translation on the secondary filter sequence to obtain the final filter output y[n]. The corresponding filter principle is as follows: Figure 1 shown.

[0055] Example 2

[0056] The gravity signal distributed along a certain trajectory near the earth's surface is a spatially continuous signal, which has spectral energy at all spatial resolutions. Sea and air gravity measurement is a discrete spatial sampling of the continuous gravity field, and the obtained value is a band-limited estimate of the continuous gravity field. Since different spatial resolutions correspond to different spectral energies, in sea and air gravity measurement, the accuracy of the survey line results refers to the measurement accuracy at a certain spatial resolution. In addition, since the original gravity measurement value inevitably contains measurement noise caused by the measurement environment, carrier movement and the observation instrument itself, these errors generally show high-frequency characteristics, and the energy of the gravity signal is mainly concentrated in the low-frequency band, it is necessary to low-pass filter the original gravity measurement value. The spatial resolution of sea and air gravity measurement depends on the cutoff frequency of the low-pass filter. When the spatial resolution of a set of gravity measurement data is λ, it always means that the spatial sampling interval of the set of data is λ. According to the Nyquist sampling theorem, the set of data only contains gravity field information with a wavelength greater than 2λ, so the spatial resolution and half wavelength can be regarded as the same concept. In sea and air gravity measurement, the sampling data of the original gravity field can be obtained by sampling at equal intervals. Assuming the sampling frequency is f T , then the spatial resolution corresponding to the original observation data is v represents the carrier's velocity. Since the original sampled value contains a lot of high-frequency noise, it is necessary to use a low-pass filter to filter it out, that is, to smooth the data. The spatial resolution of the filtered sea and air gravity measurement data is λ c and the filter cutoff frequency f c The relationship is

[0057] In the process of gravity measurement, the original sensor signal usually has a high-frequency sampling frequency of 50 to 500 Hz. The signal contains both useful gravity information and various interference information. Since gravity information is concentrated in the low-frequency band, while interference information is concentrated in the high-frequency band, low-pass filtering is used to process gravity measurement data. In experience, the useful gravity information of sea and air gravity measurement data is mainly concentrated below F = 0.01 Hz, that is, the passband of the gravity signal is taken as 0 to FHz.

[0058] like Figure 2 As shown, in a preferred embodiment of the present invention, the processing flow and design method of the zero-phase IIR digital filter for sea-air gravimeter measurement data are as follows:

[0059] In order to improve the utilization rate of test data and increase the calculation speed, IIR filters are used for primary and secondary filtering. The differential equation of IIR filters is as follows:

[0060]

[0061] Where: a k , b k is the filter coefficient; x(n) is the input sequence; y(n) is the output sequence; the maximum value of M and N is the filter order. The cutoff frequency f of the ideal filter is c From F and sampling frequency f T The calculation formula is as follows:

[0062]

[0063] Assuming that the impulse response of the designed IIR filter is h(n), the time series x[n] with a length of N+1 passes through the filter, and the obtained first filtering output is the sequence:

[0064] y1[n]=x[n]*h[n]

[0065] Then reverse and translate the sequence y1[n] to get the sequence y2[n], that is:

[0066] y2[n]=y1[Nn]

[0067] Pass y2[n] through the IIR filter again to obtain the secondary filtering output sequence y3[n], that is:

[0068] y3[n]=y2[n]*h[n]

[0069] Finally, the secondary filter sequence is time-reversed and shifted to obtain the final filter output y[n], that is:

[0070] y[n]=y3[Nn]

[0071] Assume that the Fourier transforms of x[n], y1[n], y2[n], y3[n], y[n], and h[n] are X(ω), Y1(ω), Y2(ω), Y3(ω), Y(ω), and H(ω), respectively, and consider that for the real sequence h[n], H(-ω)=H * (ω), then:

[0072] Y(ω)=e -jωN Y3(-ω)

[0073] =e -jωN Y2(-ω)H(-ω)

[0074] =e -jωN e jωN Y1(ω)H(-ω)

[0075] =Y1(ω)H(-ω)

[0076] =X(ω)H(ω)H(-ω)

[0077] =X(ω)|H(ω)| 2

[0078] Therefore, the above method realizes the zero-phase-shift IIR digital filtering of the sea-air gravimeter.

[0079] Example 3

[0080] Based on Embodiments 1 and 2, the embodiment of the present invention provides a zero-phase-shift IIR digital filter for sea-air gravimeter measurement data, including:

[0081] The first-stage IIR filter is used to process the time series of the sea and air gravimeter measurement data to obtain a primary filter sequence, and then the primary filter sequence is time-reversed and translated to obtain a new data sequence;

[0082] The second-stage IIR filter is used to process the new data sequence to obtain a secondary filter sequence, and to perform time inversion and translation on the secondary filter sequence to obtain the final filter output.

[0083] Preferably, the output signal of the sea-air gravimeter may be connected before the first-stage IIR filter.

[0084] Preferably, the first-stage IIR filter and the second-stage IIR filter are connected in sequence, and the unit impulse responses of the two-stage IIR filters are the same.

[0085] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0086] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data, characterized in that: The method includes: Set up a two-stage IIR filter, the unit impulse response of the two-stage IIR filter is the same; Collect the measurement data of the sea and air gravimeter, pass the time series of the sea and air gravimeter measurement data through the IIR filter to obtain a primary filter sequence, and then reverse and shift the primary filter sequence to obtain a new data sequence; The new data sequence is passed through the same IIR filter to obtain a secondary filter sequence, and the secondary filter sequence is time-reversed and shifted to obtain the final filter output.

2. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 1, characterized in that: In this method, the first filtering sequence and the second filtering sequence are respectively used for time inversion using a forward time sequence and a reverse time sequence, and the phase shifts when passing through the filter are offset to achieve zero phase shift of the filtering result.

3. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 1, characterized in that: The difference equations of the IIR filter in the primary and secondary filtering of this method are as follows: Where: a k 、b k is the filter coefficient; x(n) is the input sequence, i.e., the time series of sea and air gravimeter measurement data; y(n) is the output sequence; the maximum value among M and N is the filter order.

4. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 1, characterized in that: The primary filtering sequence obtained in this method is: y1[n]=x[n]*h[n] Where: h(n) is the impulse response of the IIR filter, x[n] is a time series with a length of N+1, and y1[n] is the primary filtering output.

5. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 4, characterized in that: In this method, the first filter sequence is reversed and shifted to obtain a new data sequence: y2[n]=y1[Nn] Wherein: y2[n] is the new data sequence obtained by time-reversing and shifting the primary filtering sequence y1[n].

6. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 5, characterized in that: The secondary filtering sequence obtained in this method is: y3[n]=y2[n]*h[n] Where: y3[n] is the secondary filtering output sequence obtained by passing y2[n] through the IIR filter again.

7. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 6, characterized in that: The final filtering output in this method is: y[n]=y3[Nn] Where: y[n] is the final filter output obtained by time-reversing and shifting the secondary filter sequence.

8. The zero-phase-shift IIR digital filtering method for sea-air gravimeter measurement data according to claim 7, characterized in that: The method also includes: Perform Fourier transform on x[n], y1[n], y2[n], y3[n], y[n], h[n] respectively; and considering that for the real sequence h[n], H(-ω)=H * (ω), then: Y(ω)=e -jωN Y3(-ω) =e -jωN Y2(-ω)H(-ω) =e -jωN e jωN Y1(ω)H(-ω) =Y1(ω)H(-ω) =X(ω)H(ω)H(-ω) =X(ω)|H(ω)| 2 Where: X(ω), Y1(ω), Y2(ω), Y3(ω), Y(ω), H(ω) are the Fourier transforms of x[n], y1[n], y2[n], y3[n], y[n], h[n] respectively.

9. A zero-phase-shift IIR digital filter for sea-air gravimeter measurement data, used to implement the method according to any one of claims 1 to 8, characterized in that: include: The first-stage IIR filter is used to process the time series of the sea and air gravimeter measurement data to obtain a primary filter sequence, and then the primary filter sequence is time-reversed and translated to obtain a new data sequence; The second-stage IIR filter is used to process the new data sequence to obtain a secondary filter sequence, and to perform time inversion and translation on the secondary filter sequence to obtain a final filter output.

10. The zero-phase-shift IIR digital filter for sea-air gravimeter measurement data according to claim 9, characterized in that: The first-stage IIR filter and the second-stage IIR filter are connected in sequence, and the unit impulse responses of the two-stage IIR filters are the same.

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