Frequency domain Prony sine parameter estimation method and system based on improved autoregression model, and storage medium

Abstract

The invention discloses a frequency domain Prony sine parameter estimation method and system based on an improved autoregression model, and a storage medium. The method comprises the following steps: firstly, based on a time domain model and a k-order autoregression model of a to-be-estimated FMCW radar signal, solving an autoregression coefficient equation containing a to-be-estimated sine parameter; the Kth sampling point of the signal time domain is used as a starting point to construct an autoregression matrix equation, non-causal items in the equation are eliminated, an optimized autoregression matrix equation is obtained, and K is determined according to the order k of an autoregression model; converting the optimized autoregression matrix equation into a frequency domain to obtain a simplified frequency domain autoregression equation set; solving the frequency domain autoregression equation set based on a least square method to obtain autoregression parameters; and finally, target parameters are solved through the correlation coefficients. According to the method, the calculation process is simplified, the operation time is shortened, the parameter estimation precision is better, the error is smaller under the low signal-to-noise ratio, the hardware system implementation capability and the data real-time resolving capability are achieved, and the method is highly applied to a sine parameter estimation scene.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a frequency domain Prony sine parameter estimation method, system, and storage medium based on an improved autoregressive model. Background Technology

[0002] The original frequency-domain Prony method requires extensive matrix calculations, including constructing windowed weight sequences and time-domain-frequency transformation. Since the dimension of each matrix is ​​positively correlated with the number of discrete sampling points in the time-domain sequence x[n], the computational complexity severely hinders its practical application when the number of time-domain sequences is large. Therefore, this paper proposes a frequency-domain Prony sine parameter estimation method based on an improved autoregressive model. By simplifying the original autoregressive model matrix based on its order, non-causal terms are eliminated, thus avoiding the extensive calculations caused by the windowed weight matrix. Simultaneously, spectral refinement techniques are used to provide more accurate prior spectral information for estimating the undetermined parameters, achieving high-precision estimation of the target parameters. Summary of the Invention

[0003] The purpose of this invention is to provide a frequency domain Prony sine parameter estimation method, system, and storage medium based on an improved autoregressive model.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A frequency domain Prony sine parameter estimation method based on an improved autoregressive model includes the following steps:

[0006] Step 1: Based on the time-domain model and k-th order autoregressive model of the FMCW radar signal to be estimated, solve the autoregressive coefficient equation containing the sinusoidal parameters to be estimated;

[0007] Step 2: Construct an autoregressive matrix equation starting from the Kth sampling point in the time domain of the signal to eliminate non-causal terms in the equation and obtain an optimized autoregressive matrix equation, where K is determined according to the order k of the autoregressive model.

[0008] Step 3: Transform the optimized autoregressive matrix equation to the frequency domain to obtain a simplified set of frequency domain autoregressive equations;

[0009] Step 4: Solve the frequency domain autoregressive equations using the least squares method to obtain the autoregressive parameters;

[0010] Step 5: Calculate the sinusoidal parameters of the FMCW radar signal to be estimated based on the autoregressive coefficients obtained from the solution.

[0011] Furthermore, the time-domain model in step 1 is:

[0012]

[0013] The k-order autoregressive model is:

[0014]

[0015] in, Represents the sampling time. and Represent The values ​​of the signal and noise terms at the sampling time, , … These are the coefficients to be estimated in the autoregressive model; the FMCW radar signal to be estimated is an unknown sinusoidal signal whose frequency is proportional to the target position, and contains the amplitude of the sinusoidal signal to be estimated. ,frequency Damping coefficient Noise term at sampling time , This indicates the phase of a sinusoidal signal.

[0016] The autoregression coefficient equation is:

[0017]

[0018] The autoregressive coefficients to be estimated are: and .

[0019] Furthermore, step 2 is to avoid non-causal terms. … The effect of sinusoidal parameter autoregression model, k=2, yields the optimized autoregression matrix equation as follows:

[0020]

[0021] Where N is the length of the time-domain signal, i.e., the total number of discrete sampling points.

[0022] Further, step 3 transforms the optimized autoregressive matrix equation into a frequency domain autoregressive equation set matrix as follows:

[0023]

[0024] in, The Fourier transform matrix is... It is a unit array, and The left side of the equation The unit array is eliminated, and Expanding and utilizing the time-shifting property of the Fourier transform, the final autoregressive parametric equation is obtained as follows:

[0025]

[0026] in, It is a frequency domain feature quantity defined based on Fourier coefficients. This represents the noise term from sampling time 2 to N−1. This represents the frequency domain operator corresponding to the time-shift characteristic of the Fourier transform.

[0027] Furthermore, before performing step 4, a spectrum refinement technique is used at the target spectral line to refine the spectrum by a factor of M, obtaining the fine spectral line position k and the corresponding amplitude X(k), which serves as prior information for the least squares solution.

[0028] Furthermore, in step 4, the three Fourier coefficients closest to the initially estimated target frequency are selected, and the local least squares equation is constructed and solved as follows:

[0029]

[0030] Choose the Fourier coefficients that are closest to the target frequency f. As a solution term, and using the three Fourier coefficient window method, the unique solution is obtained as follows:

[0031]

[0032] in, This represents the coefficients to be estimated in a second-order autoregressive model. These represent the three Fourier coefficients that are closest to the target frequency. Indicates the real part, Indicates the imaginary part.

[0033] Furthermore, step 5 involves solving for the coefficients... and Using relational expressions and Solve for the frequency parameters and damping coefficient .

[0034] A computer system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a frequency domain Prony sine parameter estimation method based on an improved autoregressive model.

[0035] A computer device includes a memory, a processor, and a computer program stored in the memory, the processor executing the computer program to implement the steps of a frequency domain Prony sine parameter estimation method based on an improved autoregressive model.

[0036] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements steps of a frequency-domain Prony sine parameter estimation method based on an improved autoregressive model.

[0037] The beneficial effects of this invention are as follows:

[0038] 1. This frequency-domain Prony sine parameter estimation method based on an improved autoregressive model improves the model on the basis of the frequency-domain Prony method. It optimizes the non-cyclic factors in the original model by utilizing the frequency shift invariance of Fourier coefficients. At the same time, it combines with the zero-filling method to simplify the construction, calculation process and computational cost of the windowed weight sequence. Furthermore, through the spectrum refinement technique, it provides more accurate prior information for the Prony method, thereby further improving the accuracy of the algorithm.

[0039] 2. The frequency domain Prony sine parameter estimation method based on the improved autoregressive model has significantly better parameter estimation performance than the original frequency domain Prony algorithm. Its performance is close to that of the I-Rife method. However, at lower signal-to-noise ratios, the frequency domain Prony sine parameter estimation method based on the improved autoregressive model has smaller errors. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the process of the present invention.

[0041] Figure 2 This is a comparison chart of the time complexity of different algorithms of this invention.

[0042] Figure 3 This is a comparison chart of the MSE of different algorithms with signal-to-noise ratios ranging from -10dB to 10dB according to the present invention. Detailed Implementation

[0043] The present invention will now be further described with reference to the accompanying drawings.

[0044] Example 1:

[0045] A frequency domain Prony sine parameter estimation method based on an improved autoregressive model specifically includes the following steps:

[0046] Step 1: Based on the time-domain model and k-th order autoregressive model of the FMCW radar signal to be estimated, solve the general solution of the sinusoidal parameter equation, that is, the autoregressive parameter expression of the sinusoidal parameter model to be estimated.

[0047] The expression for the k-th order autoregressive model is:

[0048]

[0049] in, Represents the sampling time. and Represent The values ​​of the signal and noise terms at the sampling time, , … These are the coefficients to be estimated in the autoregressive model.

[0050] The time-domain model of the signal to be estimated is expressed as:

[0051]

[0052] Accordingly, the received signal is an unknown sinusoidal signal whose frequency is proportional to the target position, which includes unknown coefficients amplitude A, frequency ω, damping coefficient ε, and unknown noise term ζ[t]. This indicates the phase of a sinusoidal signal.

[0053] Solving this sine parametric equation yields its general solution:

[0054]

[0055] Wherein, the coefficient to be estimated is and .

[0056] Step 2: Write out the AR model for all times within the time-domain signal observation interval and convert it into the form of an autoregressive matrix equation:

[0057]

[0058] Observe the differential matrix equation; there are non-causal terms in the equation. … .

[0059] Step 3: Optimize the autoregressive parameter equations to obtain the frequency domain autoregressive equation matrix.

[0060] Taking the Kth unit in the time domain of the signal as the starting point of the equation (based on the sinusoidal parametric autoregressive model, k=2), the optimized autoregressive matrix equation can be written as:

[0061]

[0062] Where N is the length of the time-domain signal, i.e., the total number of discrete sampling points;

[0063] The frequency domain autoregressive equation matrix is ​​further obtained as follows:

[0064]

[0065] Here, since W is an identity matrix, and Therefore, the left side of the equation The transformation into an identity matrix eliminates the need for computation, greatly simplifying the calculation process.

[0066] Step 4: Expand F and utilize the time-shifting property of the Fourier transform to obtain the final autoregressive parametric equation.

[0067]

[0068] in, It is a frequency domain feature quantity defined based on Fourier coefficients. This represents the noise term from sampling time 2 to N−1. This represents the frequency domain operator corresponding to the time-shift characteristic of the Fourier transform.

[0069] Step 5: Solve the least squares equation to obtain the parameters to be estimated. , .

[0070] The least squares equation is expressed as follows:

[0071]

[0072] Choose the Fourier coefficients that are closest to the target frequency f. As a solution term, and using the three Fourier coefficient window method, a unique solution is obtained as follows:

[0073]

[0074] in, This represents the coefficients to be estimated in a second-order autoregressive model. These represent the three Fourier coefficients that are closest to the target frequency. Indicates the real part, Indicates the imaginary part.

[0075] Step 6: Use spectral refinement technology at the target spectral line to refine the spectrum by a factor of M, obtaining a more precise spectral line position k and corresponding amplitude X(k).

[0076] To calculate the original frequency domain resolution, assuming the original time domain signal length is N, use a sampling frequency of... By discretely sampling and calculating its Fourier coefficients, its frequency domain resolution is:

[0077]

[0078] Its frequency domain resolution is increased by a factor of M using a spectral refinement method.

[0079]

[0080] Step 7: Use the correlation coefficient obtained from the solution. and According to the relation , Solve for the parameters .

[0081] In particular, in some preferred embodiments of the present invention, a computer device is also provided, including a memory and a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the frequency domain Prony sine parameter estimation method based on the improved autoregressive model described in any of the above embodiments.

[0082] In some other preferred embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program / instruction is stored, wherein when the computer program is executed by a processor, the steps of the frequency domain Prony sine parameter estimation method based on the improved autoregressive model described in any of the above embodiments are implemented.

[0083] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above embodiments of the frequency domain Prony sine parameter estimation method based on the improved autoregressive model, which will not be repeated here.

[0084] Computer-readable storage media encompass a variety of types, including persistent and non-persistent, portable and fixed. These media store information using different technologies, and the content can be machine instructions, data structures, program modules, or other types of data. Some typical examples of computer storage media include: phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), various types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory and other storage technologies, optical storage media such as CD-ROM and digital video disc (DVD), magnetic storage devices such as magnetic tape and disks, and other non-transferable media used to store information accessible to computing devices. It is important to note that the computer-readable media described herein do not include temporary storage media, such as modulated data signals and carrier waves.

[0085] Those skilled in the art will further recognize that the operation of the module can be achieved using existing technical protocols or programs, without relying on new computer programs themselves. The units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0086] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented in hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0087] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A frequency domain Prony sine parameter estimation method based on an improved autoregressive model, characterized in that: Step 1: Based on the time-domain model and k-th order autoregressive model of the FMCW radar signal to be estimated, solve the autoregressive coefficient equation containing the sinusoidal parameters to be estimated; Step 2: Construct an autoregressive matrix equation starting from the Kth sampling point in the time domain of the signal to eliminate non-causal terms in the equation and obtain an optimized autoregressive matrix equation, where K is determined according to the order k of the autoregressive model. Step 3: Transform the optimized autoregressive matrix equation to the frequency domain to obtain a simplified set of frequency domain autoregressive equations; Step 4: Solve the frequency domain autoregressive equations using the least squares method to obtain the autoregressive parameters; Step 5: Calculate the sinusoidal parameters of the FMCW radar signal to be estimated based on the autoregressive coefficients obtained from the solution.

2. The frequency domain Prony sine parameter estimation method based on an improved autoregressive model according to claim 1, characterized in that: The time-domain model mentioned in step 1 is: The k-order autoregressive model is: in, Represents the sampling time. and Represent The values ​​of the signal and noise terms at the sampling time, , … These are the coefficients to be estimated in the autoregressive model; the FMCW radar signal to be estimated is an unknown sinusoidal signal whose frequency is proportional to the target position, and contains the amplitude of the sinusoidal signal to be estimated. ,frequency Damping coefficient Noise term at sampling time , This indicates the phase of a sinusoidal signal. The autoregression coefficient equation is: The autoregressive coefficients to be estimated are: and .

3. The frequency domain Prony sine parameter estimation method based on an improved autoregressive model according to claim 2, characterized in that: Step 2 is to avoid non-causal terms. … The effect of sinusoidal parameter autoregression model, k=2, yields the optimized autoregression matrix equation as follows: Where N is the length of the time-domain signal, i.e., the total number of discrete sampling points.

4. The frequency domain Prony sine parameter estimation method based on an improved autoregressive model according to claim 3, characterized in that, Step 3 transforms the optimized autoregressive matrix equation into a frequency domain autoregressive equation set matrix as follows: in, The Fourier transform matrix is... It is a unit array, and The left side of the equation The unit array was eliminated, and Expanding and utilizing the time-shifting property of the Fourier transform, the final autoregressive parametric equation is obtained as follows: in, It is a frequency domain feature quantity defined based on Fourier coefficients. This represents the noise term from sampling time 2 to N−1. This represents the frequency domain operator corresponding to the time-shift characteristic of the Fourier transform.

5. The frequency domain Prony sine parameter estimation method based on an improved autoregressive model according to claim 4, characterized in that, Before performing step 4, a spectrum refinement technique is used at the target spectral line to refine the spectrum by a factor of M, obtaining the fine spectral line position k and the corresponding amplitude X(k), which serves as prior information for the least squares solution.

6. The frequency domain Prony sine parameter estimation method based on an improved autoregressive model according to claim 5, characterized in that, Step 4 selects the three Fourier coefficients that are closest to the initially estimated target frequency, and constructs and solves the local least squares equation as follows: Choose the Fourier coefficients that are closest to the target frequency f. As a solution term, and using the three Fourier coefficient window method, the unique solution is obtained as follows: in, This represents the coefficients to be estimated in a second-order autoregressive model. These represent the three Fourier coefficients that are closest to the target frequency. Indicates the real part, Indicates the imaginary part.

7. The frequency domain Prony sine parameter estimation method based on an improved autoregressive model according to claim 6, characterized in that, Step 5 is based on the coefficients obtained from the solution. and Using relational expressions and Solve for the frequency parameters and damping coefficient .

8. A computer system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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