High-precision time delay estimation method based on frequency domain maximum likelihood

Abstract

The invention discloses a high-precision time delay estimation method based on frequency domain maximum likelihood. A received radio power source signal is processed in a frequency domain, an approximation model is provided, a likelihood function is deduced and established according to the approximation model, and finally iterative solution is performed according to a maximum likelihood criterion, so that high-precision time delay estimation is realized, and the estimation precision exceeds a sampling interval. According to the method, the problem that the estimation precision of a time delay estimation algorithm is limited in a radio astronomical scene is well solved, and the effectiveness of an optimization algorithm is verified through a simulation experiment.

Description

Technical Field

[0001] The present invention relates to a high-precision time delay estimation method in a radio astronomy scenario, belongs to the technical field of radar signal processing, and particularly relates to a high-precision time delay estimation method based on frequency domain maximum likelihood. Background Art

[0002] In radio astronomy, radio stars are often used as calibration sources when calibrating radars. Radio star signals are usually modeled as complex Gaussian white signals, which are used to estimate the delay difference between radar arrays. The estimation accuracy is a key indicator.

[0003] Traditional delay estimation methods are generally based on the correlation method, which calculates the delay by correlating two received signals and searching for the correlation peak position. However, due to the limitation of sampling rate, the delay estimation accuracy of the correlation method can only reach the sampling interval. Therefore, it is necessary to study high-precision delay estimation methods.

[0004] Most of the existing literature has conducted research from the algorithmic perspective to improve the accuracy of delay estimation. Yang Jianhui from Lanzhou Jiaotong University proposed using interpolation in the time domain, which is equivalent to increasing the sampling rate, thereby improving the accuracy of delay estimation. Linas Svilainis from Kaunas University of Technology proposed using phase spectrum features in the frequency domain to estimate delay, breaking through the limitations of the time domain method and also improving the accuracy of delay estimation.

[0005] Calibration in radio astronomy usually requires extremely high precision, and it is also hoped that online calibration can be completed quickly. However, in order to achieve extremely high precision, the existing algorithms using interpolation require extremely high computational costs, making it difficult to achieve rapid calibration; the existing methods using phase spectrum features often cannot achieve high accuracy. Among the currently available technologies, no method can meet the calibration requirements in radio astronomy scenarios. Summary of the invention

[0006] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, which requires extremely high computational cost or the estimation accuracy is not high enough, and it is difficult to achieve high-precision time delay estimation. A high-precision time delay estimation method based on frequency domain maximum likelihood is proposed, which has low computational cost and extremely high estimation accuracy, and solves the problem that it is difficult to achieve high-precision time delay estimation in radio astronomy calibration. The method proposes an approximate model for the received radio source signal, and establishes a likelihood function based on the derivation of the approximate model, and finally solves it based on the criterion of frequency domain maximum likelihood to achieve high-precision time delay estimation, and the estimation accuracy exceeds the sampling interval.

[0007] The technical solution of the present invention is: A high-precision delay estimation method based on frequency domain maximum likelihood, the method comprising the steps of: Step S1, establishing models of two-way signals received by two radars; Step S2, performing Fourier transform on the two signals obtained in step S1 to obtain two frequency domain signals, and then performing conjugate multiplication; Step S3, proposing an approximate model based on the conjugate multiplication result obtained in step S2, and calculating the likelihood function of the phase according to the model; Step S4, based on the likelihood function obtained in step S3, a cost function is established using the maximum likelihood criterion, and the optimal solution is iteratively solved, which is the delay estimation result of the method.

[0008] Furthermore, in step S1, the specific method of establishing a signal model for the two signals received by the two radars is as follows: Assume that the signal received by a single radar is , expressed as: (1) in represents the signal frequency, , represents the sampling frequency, represents the center frequency, Indicates the number of sampling points, represents the signal spectrum; Consider the existence of two signals received by two radars The delay difference, The phase difference and noise considerations lead to the two signals received by the two radars: (2) (3) in ; , Receive gain for both radars; , Represents the unit noise of the two radars, which is generally Gaussian white noise.

[0009] Furthermore, in step S2, the specific method of performing Fourier transform on the two frequency domain signals obtained in step S1 to obtain the two frequency domain signals and then performing conjugate multiplication is as follows: The two signals obtained from S1 , Perform Fourier transform to obtain two frequency domain signals: (4) (5) in , Indicates noise , spectrum.

[0010] For the convenience of analysis, , conjugate multiplication gives (6)

[0011] Furthermore, in step S3, the method of calculating the likelihood function of the phase according to the conjugate multiplication result obtained in step S2 and the approximate model is: Will Decomposition into signal components and noise component ,in (7) (8) in , It can be solved by combining (7)(8).

[0012] Furthermore, in step S3, the approximate model is specifically: ignoring The higher order moments of Approximate and establish an approximate model for complex Gaussian distribution; for any , about the unknown variable , The probability density function of is: (9) in (10) Actually Represents the phase difference between the two radar signals. ,Will The probability density function of is integrated along a ray starting from the origin, and we can get The probability density function of is: (11) in Represents the right tail function of the Gaussian distribution, the unknown quantity Available Alternative.

[0013] The likelihood function of the phase can be expressed as: (12) in represents the natural logarithm, Indicates the number of sampling points.

[0014] Furthermore, in step S4, according to the likelihood function obtained in step S3, the cost function is established using the maximum likelihood criterion, and the method of iteratively obtaining the optimal solution is: According to the maximum likelihood criterion, the cost function is established as: (13) For unknown variables , The Newton iteration method is used to obtain the optimal solution, which is the delay estimation result of this method.

[0015] Beneficial Effects The present invention proposes a high-precision delay estimation method based on frequency domain maximum likelihood, which has the following beneficial effects: (1) In the method of the present invention, delay estimation is performed in the frequency domain, rather than in the time domain as in the prior art. Delay estimation in the frequency domain can break through the limitations of the time domain method, and the estimation accuracy exceeds the sampling interval.

[0016] (2) In the prior art, when performing delay estimation in the frequency domain, the problem of phase deambiguation usually arises, which may cause estimation errors and reduce estimation accuracy. In the method of the present invention, delay estimation is performed in the frequency domain and phase deambiguation is not required.

[0017] (3) The present invention has effectively solved the problem of difficulty in high-precision time delay estimation in radio astronomy scenarios and has certain engineering significance. The estimation effect of the high-precision time delay estimation method in radio astronomy scenarios has been verified through simulation experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a signal processing flow chart of the method of the present invention; Figure 2 This is a diagram of the root mean square error of delay estimation between the present invention and the comparative method; Figure 3 This is a graph showing the average error of delay estimation between the present invention and the comparative method. DETAILED DESCRIPTION

[0019] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific examples and with reference to the accompanying drawings.

[0020] The present invention proposes a high-precision delay estimation method based on frequency domain maximum likelihood, the signal processing flow is as follows: Figure 1 As shown, the steps are as follows: Step S1, establishing models of two-way signals received by two radars; Step S2, performing Fourier transform on the two signals obtained in step S1 to obtain two frequency domain signals, and then performing conjugate multiplication; Step S3, proposing an approximate model according to the conjugate multiplication result obtained in step S2, and calculating the likelihood function of the phase according to the model; Step S4, based on the likelihood function obtained in step S3, a cost function is established using the maximum likelihood criterion, and the optimal solution is iteratively solved, which is the delay estimation result of the method.

[0021] The following is an example of using the above method to perform high-precision delay estimation.

[0022] Example In step S1, the specific method of establishing a signal model for the two signals received by the two radars is as follows: Assume that the signal received by a single radar is , expressed as: (14) in represents the signal frequency, , represents the sampling frequency, represents the center frequency, Indicates the number of sampling points, Represents the signal spectrum.

[0023] The signal parameters are shown in Table 1: Table 1 Signal parameters variable Numeric Carrier frequency 3GHz Sampling frequency 50MHz bandwidth 10MHz Signal-to-Noise Ratio 0~20dB Number of data points 100 Consider the existence of two signals received by two radars The delay difference, The phase difference and noise considerations lead to the two signals received by the two radars: (15) (16) in ; , Receive gain for both radars; , Represents the unit noise of the two radars, which is generally Gaussian white noise.

[0024] In step S2, the specific method of performing Fourier transform on the two frequency domain signals obtained in step S1 to obtain the two frequency domain signals and then performing conjugate multiplication is as follows: The two signals obtained from S1 , Perform Fourier transform to obtain two frequency domain signals: (17) (18) in , Indicates noise , spectrum.

[0025] For the convenience of analysis, , conjugate multiplication gives (19)

[0026] In step S3, according to the conjugate multiplication result obtained in step S2, the method for calculating the likelihood function of the phase according to the approximate model is: Will Decomposition into signal components and noise component ,in (20) (twenty one) in , It can be solved by combining (20)(21).

[0027] In step S3, the approximate model is specifically: ignoring The higher order moments of Approximate and establish an approximate model for complex Gaussian distribution; for any , about the unknown variable , The probability density function of is: (twenty two) in (twenty three) Actually Represents the phase difference between the two radar signals. ,Will The probability density function of is integrated along a ray starting from the origin, and we can get The probability density function of is: (twenty four) in Represents the right tail function of the Gaussian distribution, the unknown quantity Available Alternative.

[0028] The likelihood function of the phase can be expressed as: (25) in represents the natural logarithm, Indicates the number of sampling points.

[0029] In step S4, according to the likelihood function obtained in step S3, the cost function is established using the maximum likelihood criterion, and the method of iteratively obtaining the optimal solution is: According to the maximum likelihood criterion, the cost function is established as: (26) For unknown variables , The Newton iteration method is used to obtain the optimal solution, which is the delay estimation result of this method.

[0030] The proposed method is compared with the traditional correlation interpolation method and phase spectrum method. The results are as follows: Figure 2 , Figure 3 shown.

[0031] It can be seen that with the improvement of signal-to-noise ratio, the proposed method can break through the performance boundary and have higher estimation accuracy.

[0032] The present invention may also have other various embodiments, and the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A high-precision delay estimation method based on frequency domain maximum likelihood, characterized in that: The steps of the method include: Step S1, establishing models of two-way signals received by two radars; Step S2, performing Fourier transform on the two signals obtained in step S1 to obtain two frequency domain signals, and then performing conjugate multiplication; Step S3, proposing an approximate model based on the conjugate multiplication result obtained in step S2, and calculating the likelihood function of the phase according to the model; Step S4, based on the likelihood function obtained in step S3, a cost function is established using the maximum likelihood criterion, and the optimal solution is iteratively solved, which is the delay estimation result of the method.

2. A high-precision delay estimation method based on frequency domain maximum likelihood as claimed in claim 1, characterized in that: In step S3, the method of calculating the likelihood function of the phase according to the conjugate multiplication result obtained in step S2 and the approximate model is: Will Decomposition into signal components and noise component ,in (1) (2) in , It can be solved by combining (1) and (2).

3. A high-precision delay estimation method based on frequency domain maximum likelihood as claimed in claim 2, characterized in that: The approximate model in step S3 is specifically: neglect The higher order moments of Approximate and establish an approximate model for complex Gaussian distribution. For any , about the unknown variable , The probability density function of is: (3) in (4) Actually Represents the phase difference of two radar signals; for any ,Will The probability density function of is integrated along a ray starting from the origin, and we can get The probability density function of is: (5) in Represents the right tail function of the Gaussian distribution, the unknown quantity Available Replacement; The likelihood function of the phase can be expressed as: (6) in represents the natural logarithm, Indicates the number of sampling points.

4. The high-precision delay estimation method based on frequency domain maximum likelihood according to claim 1, characterized in that: In step S4, based on the likelihood function obtained in step S3, the cost function is established using the maximum likelihood criterion, and the method for iteratively obtaining the optimal solution is: According to the maximum likelihood criterion, the cost function is established as: (7) For unknown variables , The Newton iteration method is used to obtain the optimal solution, which is the delay estimation result of this method.

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