A Robust Heideman Orthogonal Signal Processing Method Combining Morphological Filtering

Abstract

The present invention discloses a robust Heydemann orthogonal signal processing method combined with morphological filtering, comprising step S1: performing morphological filtering preprocessing on two sampled signals to remove outliers; step S2: fitting an ellipse to the filtered signals and calculating the ellipse parameters; and step S3: calculating the DC offset and amplitude-phase errors in the signals based on the ellipse parameters obtained in step S2, and correcting the original signals. This method removes outliers from the sampled signals, improves the signal-to-noise ratio of the signal to be corrected, and effectively addresses the problem of impact jitter affecting signal correction accuracy. Even when the signals are severely interfered with, a stable orthogonal signal can still be obtained, thereby improving the robustness of the Heydemann correction.

Description

Technical Field

[0001] The present invention belongs to the field of orthogonal signal processing, and in particular relates to a robust Heydemann orthogonal signal processing method combined with morphological filtering. Background Art

[0002] Micro-nano positioning technology is fundamental to precision manufacturing and measurement. Precision displacement sensors such as grating sensors, magnetic grating sensors, and laser interferometers are typical micro-nano displacement measurement feedback devices. Theoretically, their typical output signals should be orthogonal signals. However, these signals often contain DC bias, amplitude error, and phase error. Therefore, error correction is crucial for achieving high-precision measurement. The Heydemann model is the most typical method for correcting orthogonal signal errors. This algorithm uses least squares fitting to obtain the parameters of the general equation of an ellipse and establishes a relationship between the ellipse parameters and the errors of each component, thereby correcting signal errors.

[0003] In practical applications, due to factors such as system vibration and local contamination of the grating surface, the measured output signal experiences short-term impact jitter. The Heydemann correction method cannot eliminate the influence of these jitter signals on the iterative results, thereby reducing the measurement accuracy. Morphological filtering is based on integral geometry theory and random set theory. Compared with the Fourier transform commonly used for signal filtering, morphological filtering does not involve complex time-frequency transformations and is more conducive to processing noise that is difficult to separate from effective signals in the frequency domain. Therefore, the present invention proposes a signal processing method combined with morphological filtering to remove jitter or outliers in the sampled signal to improve the robustness of the correction algorithm. The Lissajous figure of the sampled signal after filtering is closer to the ellipse to be fitted than the Lissajous figure of the original sample, which can make the calculation of the ellipse coefficient more accurate, avoid the influence of impact jitter on signal correction, and ensure the accuracy of phase demodulation. Summary of the Invention

[0004] The purpose of the present invention is to overcome the influence of shock jitter in the signal on signal error correction and propose a robust Heydemann orthogonal signal processing method combined with morphological filtering, which can effectively remove outliers and suppress random noise, significantly improve signal quality, and ensure the accuracy of phase decoding.

[0005] In order to achieve the purpose of the present invention, the present invention proposes the following technical solutions:

[0006] A robust Heidemann orthogonal signal processing method combined with morphological filtering, characterized in that the signal processing method comprises the following steps:

[0007] Step S1: Perform morphological filtering preprocessing on the two sampling signals to remove outliers;

[0008] Step S2: Fitting an ellipse to the filtered signal and calculating the ellipse parameters;

[0009] Step S3: Calculate the DC offset and amplitude-phase error in the signal based on the ellipse parameters obtained in step 2, and correct the original signal.

[0010] The robust Heydemann orthogonal signal processing method combined with morphological filtering, the object of preprocessing using morphological filtering in step 1 is two orthogonal signals containing errors and , which can be expressed as

[0011]

[0012]

[0013] in, and is the signal amplitude, is the phase error, and is the DC bias of the two signals, and They are random noise and impact jitter signals in the two signals respectively.

[0014] The robust Heydemann orthogonal signal processing method combined with morphological filtering is characterized in that the step 1 uses morphological filtering to preprocess the error signal, and the alternating hybrid morphological filter used is

[0015]

[0016] in, , , , .

[0017] represents the corrosion operator, represents the dilation operator, represents the opening operation, represents the closing operation, is the signal to be processed, is the morphological filter structure element.

[0018] Reasonably set the size and shape of the structural elements, and the structural elements used The shape is sinusoidal, the width is set to 50, and the amplitude is set to 0.05.

[0019] The robust Heydemann orthogonal signal processing method combined with morphological filtering is characterized in that the ellipse fitting in step 2 is specifically the sampling points after preprocessing Satisfies the general equation of an ellipse , the filtered sampling signal is brought into the ellipse equation, and the ellipse parameters are obtained by fitting the least square method based on the best linear unbiased estimate .

[0020] The robust Heydemann orthogonal signal processing method combined with morphological filtering is characterized in that the error correction method in step S3 is Heydemann correction, and the specific steps include:

[0021] S3.1, based on the relationship between the ellipse parameters and the errors of each part, calculate the DC bias, amplitude error and phase error respectively, where the relationship between the ellipse parameters and the errors is:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] S3.2, substitute the calculated error into the signal to correct it. The correction formula is as follows:

[0028]

[0029]

[0030] in, and Represents the signal after error correction.

[0031] Advantages and beneficial effects of the present invention:

[0032] The present invention applies morphological filtering to the orthogonal signal processing process. First, the signal is preprocessed by morphological filtering to remove outliers in the sampled signal, improve the signal-to-noise ratio of the signal to be corrected, and effectively solve the problem that the impact jitter in the signal affects the accuracy of Heydemann correction.

[0033] The present invention can obtain a relatively stable orthogonal signal even when the signal is severely interfered with, ensuring the accuracy of the correction algorithm and phase demodulation. Furthermore, when the signal interference is severe, the Lissajous figure of the signal after morphological filtering is closer to the ellipse to be fitted, which can reduce the number of iterations in the fitting process. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 Schematic diagram of the signal processing method of the present invention;

[0036] Figure 2 Filtering effect diagram of structural elements of different sizes;

[0037] Figure 3 The signal diagrams before and after morphological filtering;

[0038] Figure 4 The Lissajous figure shows the signal before and after morphological filtering;

[0039] Figure 5 The Lissajous figure shows the signal after error correction;

[0040] Figure 6 Comparison of displacement calculation errors with and without morphological filtering preprocessing. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings.

[0042] like Figure 1 As shown, a robust Heydemann orthogonal signal processing method combined with morphological filtering of the present invention comprises the following steps:

[0043] Step S1: Perform morphological filtering preprocessing on the two sampling signals to remove outliers;

[0044] The objects of the preprocessing using morphological filtering in step S1 are two orthogonal signals containing errors. and , which can be expressed as

[0045]

[0046]

[0047] in, and is the signal amplitude, is the phase error, and is the DC bias of the two signals, and They are random noise and impact jitter signals in the two signals respectively.

[0048] The alternating mixed morphological filter used for morphological filtering is

[0049]

[0050] in, , , , .

[0051] represents the corrosion operator, represents the dilation operator, represents the opening operation, represents the closing operation, is the signal to be processed, It is the morphological filter structure element. The structure element is reasonably set according to the characteristics of the signal to be processed. The size and shape of the structural elements used The shape is sinusoidal.

[0052] like Figure 2 As shown in the figure, the filtering effects of structural elements of different scales are different. The contour lines are the signal-to-noise ratio of the filtered signal. The higher the value, the better the filtering effect. In this embodiment, a grating ruler with a grating pitch of 20 microns is used, the sampling rate of the NI data acquisition card is 70KHz, the test piece moves at a speed of 0.1mm / s, and a total of 14,000 data are sampled in one cycle. Figure 2 When the width of the structural element is constant, the signal-to-noise ratio increases gradually with the increase of the amplitude and eventually stabilizes; when the amplitude is constant, the signal-to-noise ratio increases first and then decreases with the increase of the structural element width. A higher signal-to-noise ratio is achieved when the structural element width is greater than 80 and the amplitude is small. Considering that the filtering time increases with the increase of the structural element width, Set the width to 50 and the amplitude to 0.05.

[0053] The result of signal preprocessing by morphological filtering is as follows Figure 3 As shown in , the morphological filter can effectively remove outliers and significantly reduce noise. The Lissajous figure of the filtered signal is closer to the ellipse to be fitted, as shown in Figure 4 shown.

[0054] Step S2: Fitting an ellipse to the filtered signal and calculating the ellipse parameters;

[0055] The ellipse fitting in step S2 is specifically the sampling points after preprocessing Satisfies the general equation of an ellipse , the filtered sampling signal is brought into the ellipse equation, and the ellipse parameters are obtained by fitting the least square method based on the best linear unbiased estimate .

[0056] Step 3: Calculate the DC offset and amplitude-phase errors in the signal based on the ellipse parameters obtained in step S2, and correct the original signal.

[0057] The error correction method in step S3 is Heydemann correction, and the specific steps include:

[0058] Step S3.1, based on the relationship between the ellipse parameters and the errors of each part, the DC bias, amplitude error and phase error are calculated respectively. The relationship between the ellipse parameters and the errors is:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] In step S3.2, the calculated error is substituted into the signal for correction. The correction formula is as follows:

[0065]

[0066]

[0067] in, and Represents the signal after error correction. The correction result is as follows Figure 5 shown.

[0068] The displacement values are calculated based on the corrected signals and the calculation results with and without morphological filtering are compared, e.g. Figure 6 As shown in Figure 3, morphological filtering can suppress the impact of shock jitter on signal correction and improve the robustness of Heydemann correction.

Claims

1. A robust Heidemann orthogonal signal processing method combined with morphological filtering, characterized in that: The signal processing method comprises the following steps: Step S1: Perform morphological filtering preprocessing on the two sampling signals to remove outliers; In step S1, the objects preprocessed by morphological filtering are two sampling signals containing errors, including orthogonal signals μ0 and v0, which are expressed as: μ0=R1cosθ+p+Δ1 v0=R2sin(θ+δ)+q+Δ2 Where R1 and R2 are the signal amplitudes, δ (-π / 2 < δ < π / 2) is the phase error, p and q are the DC offsets of the two signals, Δ1 and Δ2 are the random noise and impact jitter signals in the two signals, respectively. Step S2: Fitting an ellipse to the filtered signal and calculating the ellipse parameters; In step S2, the fitting ellipse is specifically that the pre-processed sampling points (μ0, v0) satisfy the general ellipse equation μ0 2 +Bv0 2 +Cμ0v0+Dμ0+Ev0+F=0, the filtered sampling signal is substituted into the ellipse equation, and the ellipse parameters B~F are obtained by the least squares fitting based on the best linear unbiased estimate; Step S3: Calculate the DC offset and amplitude and phase errors in the signal based on the ellipse parameters obtained in step 2, and perform error correction on the original signal; The error correction method in step S3 is Heydemann correction, and the specific steps include: Step S3.1, based on the relationship between the ellipse parameters and the errors of each part, the DC bias, amplitude error and phase error are calculated respectively. The relationship between the ellipse parameters and the errors is: p=(2BD-EC) / (C 2 −4B) q=(2E-DC) / (C 2 -4B) In step S3.2, the calculated error is substituted into the signal for correction. The correction formula is as follows: μ=(μ0-p) / R1 where μ and v represent the error-corrected signals.

2. The robust Heidemann orthogonal signal processing method combined with morphological filtering according to claim 1, characterized in that: In step S1, the morphological filtering adopts an alternating mixed morphological filter, and the alternating mixed morphological filter used is in, represents the corrosion operator, represents the dilation operator, represents the opening operation, represents the closing operation, f(n) is the signal to be processed, and g(n) is the morphological filter structure element; The size and shape of the structural element g(n) are reasonably set. The shape of the structural element g(n) used is sinusoidal, with a width of 50 and an amplitude of 0.05.

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