Calculation method of PPS high-order parameters based on resampled signal components

Abstract

The present invention relates to a method for calculating high-order parameters of a resampled signal component PPS, which belongs to the field of signal processing technology, and in particular to a method for estimating parameters of a polynomial phase signal. The present invention interpolates a polynomial phase signal at a specific position to obtain four interpolated digital signal components. After point multiplication of the four signal components, their digital frequencies are estimated. Finally, the estimated value of the highest-order parameter of the original signal is calculated using the sampling interval, number of sampling points, and digital frequency estimation of the original signal. The algorithm of the present invention has low complexity, and compared with similar algorithms, the mean square error value is the same or lower, and the performance is good.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing methods, and in particular relates to a method for calculating PPS high-order parameters based on resampled signal components. Background Art

[0002] Polynomial phase signal (PPS) is often used in radar, sonar, communication and speech signal processing. For example, in the field of radar detection of airspace targets, the polynomial phase signal model can represent the intermediate frequency echo of maneuvering targets; in the field of radar imaging, the superposition of multiple polynomial phase signals can also represent the echo signals of multiple scattering points of ISAR targets. By estimating the parameters of the polynomial phase signal, the motion parameters of the radar target can be obtained. The R-order polynomial signal model in white noise can be written as

[0003]

[0004] in is complex Gaussian white noise, R is the order of the polynomial phase signal, is the signal sampling interval, is the signal amplitude, is the parameter of the signal and is a real number.

[0005] As early as the 1860s, maximum likelihood was used to estimate the order parameters of polynomial phase signals. Although the mean square error of this estimation method can reach the theoretical lower bound, this estimation method uses a multi-dimensional parameter search and has a high algorithmic complexity. In order to reduce the complexity, a class of methods based on signal nonlinear transformation is used to avoid multi-dimensional search. Among them, the typical method is the parameter estimation method based on the high-order ambiguity function (HAF). This method uses phase differentiation technology. By using multiple phase differential operators, the order of the polynomial phase signal can be reduced to 1, and then the parameter estimation can be completed using fast Fourier transform and one-dimensional search. Although this type of method has low complexity, the multiple phase differential operators greatly improve the signal-to-noise ratio threshold.

[0006] As another nonlinear transformation type estimation method, the parameter estimation method based on the cubic phase function (CPF) has lower nonlinearity than the method based on the high-order fuzzy function, so the estimation accuracy is higher under low signal-to-noise ratio conditions. For example, the estimation method based on the hybrid CPF-HAF function has a lower signal-to-noise ratio threshold than HAF. However, when estimating the parameters of high-order PPS, the nonlinearity of the hybrid CPF-HAF function increases exponentially with the order of the signal.

[0007] In addition, the quasi-maximum likelihood estimation method and its derivative algorithms also have good estimation performance. This method uses the robustness of short-time Fourier transform to noise to greatly reduce the signal-to-noise ratio threshold. However, the multi-dimensional short-time Fourier transform makes the algorithm more complex than the method based on signal nonlinear transformation.

[0008] In view of this, the present invention is proposed. Summary of the invention

[0009] The purpose of the present invention is to provide a method for calculating the high-order parameters of the PPS of the resampled signal component, so as to solve the technical problem that the existing method for estimating the high-order parameters of the sampled signal component is complex and results in a large amount of calculation. The technical solution of this case has many technical benefits, as described below:

[0010] A method for calculating a PPS high-order parameter based on a resampled signal component is provided, the method comprising:

[0011] For length The fourth-order polynomial phase signal Perform fast Fourier transform to obtain frequency domain signal ,in, For discrete signals Sampling point subscript, ; For discrete signals The sampling point subscript of ;

[0012] exist Then fill the preset number of digits with zeros;

[0013] The frequency domain signal after zero padding Perform inverse Fourier transform of the sequence to obtain the frequency domain zero-filled interpolation sequence ,in, For discrete signals The sampling point index of ;

[0014] Determine the frequency domain signal A plurality of insertion points in the sampling points of the signal components are calculated by Lagrange interpolation method;

[0015] Determine the complete signal component of each sampling point after insertion;

[0016] The sampling points of the signal components are multiplied in sequence to obtain a sequence ;

[0017] Based on the fast Fourier transform spectrum estimation method, the sequence Estimated value of digital frequency , determine the highest-order parameter estimate of the fourth-order polynomial phase signal.

[0018] In a preferred or optional embodiment, four interpolation points are set, and the interpolation position expressions are respectively:

[0019] ;

[0020] .

[0021] In a preferred or optional embodiment, the method for determining the complete signal component comprises:

[0022] Let m = 1, 2, 3 ... N, , get the complete signal component , , and ;

[0023] The complete signal component , , and The corresponding sampling points are multiplied to obtain the sequence

[0024] In a preferred or optional embodiment, the method for determining the highest order parameter estimate of the fourth order polynomial phase signal comprises:

[0025] according to Compute the highest-order parameter estimates of a fourth-order polynomial phase signal.

[0026] Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0027] The present invention interpolates the polynomial phase signal at a specific position to obtain four interpolated digital signal components. After point multiplication of the four signal components, the digital frequency is estimated. Finally, the estimated value of the highest order parameter of the original signal is calculated using the sampling interval, the number of sampling points, and the digital frequency estimation of the original signal. The algorithm of the present invention has low complexity, and compared with similar algorithms, the mean square error value is the same or lower, and the performance is good. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0029] Figure 1 It is a flow chart of the fourth-order PPS high-order parameter estimation method of the present invention;

[0030] Figure 2 A comparison chart of the estimation results of the fourth-order PPS high-order parameter estimation method. DETAILED DESCRIPTION

[0031] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0032] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present invention, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0033] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention. The drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0034] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that aspects can be practiced without these specific details. In order to enable those skilled in the art to better understand the scheme of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The terms "first" and "second" are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise stated, "multiple" means two or more.

[0035] The existing technology does not consider the influence of lighting background light during testing, resulting in large noise and affecting the detection deviation. However, by using a point light source, that is, using a point light spot for illumination and detecting the position deviation between the illumination spot and the mask mark, the consistency of the signal-to-noise ratio is improved.

[0036] like Figure 1 The calculation method of the PPS high-order parameters based on the resampled signal component simplifies the estimation method of the PPS high-order parameters by interpolation. The fourth-order PPS high-order parameter estimation method based on the resampled signal component correlation technology includes the following steps:

[0037] Step 1: For the length The fourth-order polynomial phase signal Perform fast Fourier transform to obtain its frequency domain signal , the length is .in For discrete signals Sampling point subscript, ; For discrete signals The sampling point subscript of .

[0038] Step 2, Pad zeros at the end, for example, the number of zeros is .

[0039] Step 3, calculate the inverse fast Fourier transform (IFFT) of the zero-filled sequence. Get the coarse interpolation sequence ,in For discrete signals The sampling point index of .

[0040] Step 4: According to the interpolation position expression

[0041]

[0042] Calculate the signal The interpolated position, where Providing multiple insertion points to the Lagrange interpolation algorithm allows the point product output to be analyzed using the fast algorithm FFT, thereby reducing the complexity of the calculation.

[0043] Step 5: Based on the sequence obtained in step 3 and the interpolation position calculated in step 4, the signal components are calculated using the Lagrange interpolation method. The sampling point , get a sampling point in the component.

[0044] Step 6, let , repeat steps 4 to 5 to get the complete signal components ,in , except for itself.

[0045] Step 7: The remaining 4 interpolation positions are calculated according to the interpolation position expressions

[0046]

[0047]

[0048]

[0049] Repeat steps 4 to 6, output--get the signal component , and .

[0050] Step 8: Convert the signal components , , and The sampling points of .

[0051] Step 9: Use the spectrum estimation method based on fast Fourier transform to obtain the sequence Estimated value of digital frequency .

[0052] Step 10, follow Compute the highest-order parameter estimates of a fourth-order polynomial phase signal, is the sampling interval of the original signal, For sequence An estimate of the frequency of the numbers.

[0053] The method of the present invention is applicable to the fields of estimation of motion parameters of maneuvering targets in radar signal processing. The polynomial phase signal is interpolated at a specific position to obtain four interpolated digital signal components. After the four signal components are point-multiplied, their digital frequencies are estimated. Finally, the estimated value of the highest-order parameter of the original signal is calculated using the sampling interval, number of sampling points, and digital frequency estimation of the original signal. The algorithm of the present invention has low complexity, and compared with similar algorithms, the mean square error value is the same or lower, and the performance is good.

[0054] The effect of the present invention can be further illustrated by the following simulation experiment:

[0055] 1) Simulation experiment environment and content

[0056] Experimental environment: MATLAB 7.5.0, Intel(R) Pentium(R) 2 CPU 3.0 GHz, Window XP Professional.

[0057] Experimental content: Simulate and generate a fourth-order polynomial phase signal, where the order parameters are , , , The number of signal sampling points is 513, and the sampling interval is 0.05 seconds. The proposed method, the quasi-maximum likelihood estimation method, the hybrid CPF-HAF method, the method based on the higher-order fuzzy function (HAF), and the algorithm based on PD-NURO are used to estimate the highest-order parameters under different signal-to-noise ratio environments, and the mean square error of the estimate is compared with the Clemero bound.

[0058] 2) Experimental results:

[0059] The results are as follows Figure 2 , it can be seen that under the same signal-to-noise ratio, the mean square error of the estimator of the detection method proposed in the present invention is lower than that of the methods other than the quasi-maximum likelihood estimation method (with the highest algorithm complexity), and the estimation performance is better. CRLB is a theoretical value, and the method in this case is closer to the theoretical value and reduces the amount of calculation.

[0060] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

[0061] The above is a detailed introduction to the product provided by the present invention. Specific examples are used in this article to illustrate the principle and implementation method of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of invention, several improvements and modifications can be made to the invention, and these improvements and modifications also fall within the scope of protection of the invention claims.

Claims

1. A method for calculating PPS high-order parameters based on resampled signal components, characterized in that: The method comprises: For length The fourth-order polynomial phase signal Perform fast Fourier transform to obtain frequency domain signal ,in, For discrete signals Sampling point subscript, ; For discrete signals The sampling point subscript of ; exist Then fill the preset number of digits with zeros; The frequency domain signal after zero padding Perform inverse Fourier transform of the sequence to obtain the frequency domain zero-filled interpolation sequence ,in, For discrete signals The sampling point index of ; Determine the frequency domain signal A plurality of insertion points in the sampling points of the signal components are calculated by Lagrange interpolation method; Determine the complete signal component of each sampling point after insertion; The sampling points of the plurality of signal components are multiplied in sequence to obtain the sequence ; Based on the fast Fourier transform spectrum estimation method, the sequence Estimated value of digital frequency , determine the highest-order parameter estimate of the fourth-order polynomial phase signal.

2. The calculation method according to claim 1, characterized in that: Set 4 interpolation points, and the interpolation position expressions are: ； 。 3. The calculation method according to claim 2, characterized in that: The method of determining the complete signal component comprises: Let m = 1, 2, 3...N, and get the complete signal components , , and ; The complete signal component , , and The corresponding sampling points are multiplied to obtain the sequence .

4. The calculation method according to claim 3, characterized in that: A method for determining a highest order parameter estimate of a fourth order polynomial phase signal includes: according to Compute the highest-order parameter estimates of a fourth-order polynomial phase signal, is the sampling interval of the original signal, For sequence An estimate of the frequency of the numbers.

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