A high-precision estimation algorithm for phase difference of sinusoidal signals with strong robustness to frequency error

Abstract

The present invention provides a high-precision estimation algorithm for the phase difference of a sinusoidal signal with strong robustness to frequency error, and belongs to the field of information technology. The algorithm is mainly aimed at two noisy sinusoidal signals with the same frequency. First, a simple algorithm can be arbitrarily selected to obtain a signal frequency estimate; second, the obtained frequency estimate is used to frequency shift the signal; then, the spectrum value of the DFT transform of the frequency-shifted signal at zero frequency is calculated; finally, the phase difference between the two signals is calculated using the obtained zero spectrum line value. The algorithm can still accurately estimate the signal phase difference even when there is a significant error in the signal frequency estimate, effectively overcoming the transfer of frequency estimation error to phase difference estimation, and has a significant advantage in estimation accuracy, especially under high signal-to-noise ratio conditions, and can improve the accuracy by 1 to 2 orders of magnitude compared to traditional algorithms.

Description

Technical Field

[0001] The present invention relates to the field of information technology, and in particular to a parameter estimation problem in signal processing technology. Background Art

[0002] Signal processing is a common requirement in information technology fields such as artificial intelligence and biomedicine. As can be seen from the Fourier series, any periodic signal can be composed of the superposition of sine or cosine waves of different frequencies. Therefore, the sinusoidal signal is the most commonly used basic signal model, and its parameter estimation problem plays a fundamental supporting role in signal processing. Phase difference, as one of the key parameters of the sinusoidal signal, is widely involved in the measurement of distance, displacement, and time delay. It has been widely studied and applied in smart instruments, the Internet of Things, radar communications, electrical engineering, biomedicine and other fields.

[0003] Traditional phase difference estimation methods such as DFT, DTFT, Hilbert transform, and cross-correlation all require the signal to meet certain sampling conditions to ensure the unbiasedness of the estimation. However, these sampling conditions are usually difficult to meet in practical applications. To this end, the multiple cross-correlation method uses Hilbert transform and construction of reference signals to form multiple signal cross-correlations to overcome non-half-periodic sampling. However, new estimation errors are introduced in the process of Hilbert transform and construction of reference signals (Tu Yaqing, Shen Tingao, Li Ming, Zhang Haitao. Phase difference measurement algorithm for non-integer periodic signals based on multiple cross-correlation [J]. Chinese Journal of Scientific Instrumentation, 2014, 35(7): 1578-1585.); the data extension correlation method uses the linear prediction property of the sine function to extend the signal data. By changing the number of signal samples, the signal can meet the half-periodic sampling as much as possible. However, the accurate half-periodic sampling condition is still difficult to meet (Shen Tingao, Tu Yaqing, Li Ming, et al. Phase difference measurement method and verification based on data extension correlation [J]. Chinese Journal of Scientific Instrumentation, 2014, 35(6): 1331-1337.). The negative frequency method overcomes the spectrum interference caused by negative frequencies through analytical derivation, achieving high estimation accuracy under various sampling conditions (Zhang Haitao, Tu Yaqing. A new method for phase difference measurement of low-frequency vibration signals based on DTFT [J]. Journal of Vibration Engineering, 2007, 20(2): 180-184.). Although the above studies have made some progress in overcoming the limitations of sampling conditions, they all rely heavily on prior information about the signal frequency. When the signal frequency is unknown, frequency estimation is bound to have errors. The high computational overhead of high-precision frequency estimation is not conducive to real-time signal processing. At the same time, the signal frequency itself is easily affected by environmental factors such as external vibration or electromagnetic interference. When the frequency estimation has serious errors, the performance of the above research methods will be significantly reduced, and it is difficult to ensure unbiasedness.

[0004] In summary, the existing high-precision phase difference estimation algorithm has a strong dependence on accurate frequency information, which to a certain extent limits the actual effect of the algorithm in engineering applications. Enhancing the robustness of the algorithm to frequency errors and reducing the impact of frequency estimation errors on the phase difference estimation results are crucial to improving the performance of the phase difference estimation algorithm in practical applications. Summary of the Invention

[0005] To address these issues, the present invention proposes a high-precision sinusoidal phase difference estimation algorithm with robust frequency error. This algorithm effectively reduces the dependence of phase difference estimation on precise frequency information, while maintaining a reasonable computational load. It can maintain high phase difference estimation accuracy even when frequency estimation exhibits certain deviations, and can improve accuracy by one to two orders of magnitude compared to traditional algorithms, especially at high signal-to-noise ratios.

[0006] The technical solution of the present invention is a sinusoidal signal phase difference estimation algorithm with strong frequency error robustness. The overall technical solution includes: firstly, using any computationally simple frequency estimation algorithm to obtain two channels of same-frequency noisy sinusoidal signal samples x i Initial frequency estimate of (n)(i=1,2) Then use For signal x i (n) Perform frequency shift to concentrate the signal energy at the DFT zero spectrum line to improve the anti-noise performance. Taking the negative frequency energy concentration as an example, the corresponding frequency shift signal is expressed as According to the frequency estimate Sure Select two symmetrical integer points l2 and l3 about l1 (usually l2 = l1-2, l3 = l2+2) to calculate the negative frequency DFT spectrum line Y at zero frequency i- (0); Finally, use Y i- (0) The phase difference estimation value can be obtained by the corresponding relationship with the signal phase difference

[0007] The zero-frequency DFT spectrum line Y i- The calculation steps of (0) specifically include:

[0008] (1) Substitute l2 and l3 to calculate and

[0009]

[0010] (2) Substitution and Calculate Y i- (0):

[0011]

[0012] The signal phase difference estimation result The specific calculation formulas are:

[0013]

[0014] The algorithm proposed in the present invention can directly adopt the Pisarenko harmonic decomposition method with extremely low computational complexity as the frequency estimator, greatly reducing the computational complexity and delay generated by the frequency estimation. At the same time, under the significant frequency estimation error caused by the frequency estimator, accurate phase difference estimation can still be achieved. The performance advantage is particularly obvious under high signal-to-noise ratio. Under the premise of the same frequency estimation, the estimation accuracy can be improved by 1 to 2 orders of magnitude compared with the traditional algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] To clearly illustrate the technical solution of the present invention, the following are the drawings and brief descriptions required for describing the embodiments. Obviously, the drawings shown are only some embodiments of the present invention, and those skilled in the art can create other similar drawings based on the drawings without inventive effort. The drawings shown in the present invention are:

[0016] Figure 1 Schematic diagram of the algorithm of the present invention;

[0017] Figure 2 Comparison of the root mean square error of frequency estimation between the present invention and other algorithms under different signal-to-noise ratio values;

[0018] Figure 3 Comparison of the root mean square error of frequency estimation between the present invention and other algorithms at different frequency values;

[0019] Figure 4 The root mean square error of frequency estimation under different signal length values ​​is compared between the present invention and other algorithms. DETAILED DESCRIPTION

[0020] The following is a detailed technical description of the present invention in conjunction with the accompanying drawings and examples. This example provides a detailed implementation method and calculation process based on the technical solution of the present invention. However, the protection scope of the present invention is not limited to the following examples. It should be understood that the examples are only for illustrating the present invention, not for limiting the protection scope of the present invention.

[0021] according to Figure 1 The signal processing flow shown in the figure considers the input of two sinusoidal sampling signals with the same frequency x i (n) = a i cos(ωn+θ i )+z i (n), i=1, 2, where a i and θ i are the amplitude and initial phase of the i-th signal respectively, ω is the angular frequency of the two signals; zi (n) is the zero mean variance of the superimposed signal of the i-th channel, and its value is σ 2 The number of signal samples is N.

[0022] Taking the Pisarenko harmonic decomposition method as an example for frequency estimation, the specific calculation formula is:

[0023]

[0024] in,

[0025]

[0026] Depend on The two signals can be frequency shifted, that is At the same time, you can obtain Preferably, according to the principle of symmetrical point selection, l2=l1-2, l3=l2+2 can be set, and then the DFT zero spectrum line value Y of the two frequency-shifted signals can be further calculated. i- (0):

[0027]

[0028] Finally, using Y i- (0) The estimated phase difference between the two signals can be calculated:

[0029]

[0030] To illustrate the estimation performance of the algorithm of the present invention, this embodiment uses numerical simulation experiments to compare the algorithm of the present invention with several other typical algorithms, including multiple cross-correlation, data extension correlation, and negative frequency algorithm. The experiments all use the Pisarenko harmonic decomposition method, which is simple to calculate but has a large estimation error, to obtain the frequency estimation value. Without loss of generality, it is assumed that the signal amplitude a1=a2=1, the initial phase of the first signal is θ1~U[-π,π], the initial phase of the second signal is θ2=θ1+Δθ, the phase difference is set to Δθ=π / 6, and N=53 and ω=0.4585rad unless otherwise specified. At this time, the signal half-cycle sampling and coherent sampling conditions are not met.

[0031] Figure 2 The corresponding relationship between the root mean square error of phase difference estimation and the signal-to-noise ratio in two scenarios is given. Figure 2 In (a), the signal frequency is known. In this case, multiple cross-correlation and data extension correlation algorithms cannot completely eliminate the correlation error under non-half-cycle sampling conditions, and thus cannot achieve unbiased estimation. However, the negative frequency algorithm and the algorithm of the present invention can achieve unbiased estimation. When the frequency is unknown, the frequency estimation performance is as follows: Figure 2As shown in the neutron diagram (b), the frequency estimation value shows obvious deviation from 20 dB. At this time, the negative frequency algorithm is affected by the frequency estimation error, and its phase difference estimation performance is also significantly reduced. In comparison, the algorithm of the present invention can well overcome the influence of the frequency estimation error, and its performance advantage is very obvious under high signal-to-noise ratio.

[0032] Figure 3 The relationship between the root mean square error of phase difference estimation and signal frequency is given under two signal-to-noise ratios. Considering the case where the frequency is unknown, the frequency estimation performance is as follows: Figure 3 As shown in the sub-figures in (a) and (b), it can be seen that no matter the signal-to-noise ratio is 20dB or 50dB, there is an obvious deviation in the frequency estimation. When SNR=20dB, except for the multiple cross-correlation and data extension related algorithms, other algorithms can achieve higher estimation accuracy, especially the algorithm of the present invention can maintain good estimation performance within a larger frequency change range. As the signal-to-noise ratio increases, when SNR=50dB, the frequency estimation accuracy is limited by the performance flatness and cannot be improved with the signal-to-noise ratio. At this time, except for the algorithm of the present invention, the other algorithms are affected to varying degrees by the frequency estimation error, and the root mean square error of their phase difference estimation fluctuates with the fluctuation of the frequency estimation performance, and the estimation accuracy decreases significantly. In contrast, the algorithm of the present invention is not significantly affected by the frequency estimation error, and can still stably obtain accurate estimation results as the signal-to-noise ratio increases.

[0033] Figure 4 The relationship between the root mean square error of phase difference estimation and signal length (log2N) is given under two different signal-to-noise ratios. When the frequency is unknown, the frequency estimation performance is shown in the sub-figure. As the signal length increases from 32 to 1024, the frequency estimation always has a large estimation error. Figure 4 It can be seen that under the two signal-to-noise ratio settings, the phase difference estimation performance of algorithms such as multiple cross-correlation, data extension correlation, and taking negative frequency into account fluctuates slightly with the change of frequency estimation, while the algorithm of the present invention is greatly reduced in being affected by the frequency estimation error and can always maintain a high phase difference estimation accuracy.

[0034] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It is apparent that various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the present invention. Thus, the present invention is intended to encompass such modifications and variations as long as they fall within the scope of the claims and their equivalents.

Claims

1. A high-precision method for estimating the phase difference of a sinusoidal signal with strong robustness to frequency error, characterized in that: The method steps are: ① using a simple frequency estimation algorithm to obtain a signal frequency estimation value The simple frequency estimation algorithm is the Pisarenko harmonic decomposition method, which greatly reduces the amount of calculation and delay generated by frequency estimation. The specific calculation formula for frequency estimation using the Pisarenko harmonic decomposition method is: in, The number of signal samples is N; ② Use the frequency estimation value to frequency shift the two signals to obtain the frequency shift signal The input is two sinusoidal sampling signals with the same frequency x i (n) = a i cos(ωn+θ i )+z i (n), i = 1, 2, a i and θ i are the amplitude and initial phase of the i-th signal respectively, ω is the angular frequency of the two signals; z i (n) is the zero mean variance of the superimposed signal of the i-th channel, and its value is σ 2 Additive Gaussian white noise; ③Calculate the DFT spectrum line value Y at zero frequency based on the frequency shift signal i- (0); ④ Obtain the phase difference estimation result by calculating the obtained zero-frequency DFT spectrum line value; In the calculation of the zero-frequency DFT spectral line value in step ③, the idea of ​​symmetrical point error correction is applied: Select center point Then select two integer points l2 and l3 symmetric about l1 and calculate and Then we can get y i (n) The negative frequency DFT spectrum line value Y corresponding to the zero frequency i- (0); The above algorithm for symmetrical point error correction and simultaneous error cancellation can still achieve accurate phase difference estimation under the significant frequency estimation error caused by the frequency estimator. The specific calculation formula is:

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