CN114665991A - Shortwave time delay estimation method, system, computer device and readable storage medium - Google Patents

Abstract

The present application relates to the field of signal processing, and in particular, to a short-wave time delay estimation method, system, computer device, and readable storage medium, wherein the short-wave time delay estimation method includes: a parameter initialization step of initializing initial parameters of a filter, wherein the initial parameters comprise: weight coefficient vector W, number of iterationsk _max And convergence factorμ(ii) a A signal modulus taking step for obtaining the received two short wave multipath signaly ₁ 、y ₂ For two said short wave multipath signalsy ₁ 、y ₂ Calculating the mean square error after modulus selection; and a time delay estimation result obtaining step, namely performing iterative updating on the weight coefficient vector by using the mean square error minimization as a criterion so as to obtain a time delay estimation result. By the method and the device, the interference of a channel gain function to signals is overcome, and more accurate time comparison of short wave signals is realizedAnd carrying out estimation.

Description

Shortwave time delay estimation method, system, computer device and readable storage medium

technical field

The present application relates to the field of signal processing, and in particular, to a shortwave delay estimation method, system, computer device and readable storage medium.

Background technique

The time delay estimation algorithm is the key research content in the field of signal processing, and it is also the premise for the realization of shortwave time difference-of-arrival positioning technology.

Most of the traditional delay estimation algorithms are based on the dual-element signal processing model. The research focuses on the narrowband signal delay estimation algorithm, the multipath delay estimation algorithm and the delay estimation algorithm in the non-Gaussian noise environment. The problem is how to improve the accuracy of delay estimation and reduce the complexity of the algorithm under complex additive interference noise. However, in the time delay estimation of shortwave signals, since the signal will have severe fading characteristics under the action of the shortwave ionospheric channel, the noise superimposed in the signal includes both the additive noise in the traditional sense (such as high-speed noise or impulse noise). , and there is multiplicative noise interference, which makes the problem of shortwave signal delay estimation extremely complicated.

Taking the classic shortwave channel model Watterson channel as an example, the shortwave channel gain function causes multiplicative interference to the shortwave signal, and the multiplicative interference conforms to the complex Gaussian distribution with zero mean, while the multiplicative interference in the traditional delay estimation model is constant, Therefore, the traditional time delay estimation algorithm is bound to be affected by the shortwave channel gain function. Specifically, when the traditional LMS algorithm (Least Mean Square) is applied to shortwave signal delay estimation, we will find that due to the influence of the channel gain function, the mean square error function in the algorithm only contains noise and does not contain any useful information. Therefore, it cannot be applied to the delay processing of shortwave signals.

At present, no effective solution has been proposed for the influence of the channel gain function on the shortwave signal in the related art.

SUMMARY OF THE INVENTION

Embodiments of the present application provide a shortwave delay estimation method, system, computer device, and computer-readable storage medium, so as to at least overcome the interference of the channel gain function to the signal.

In a first aspect, an embodiment of the present application provides a shortwave delay estimation method, including:

The parameter initialization step is to initialize the initial parameters of the filter, and the initial parameters include: a weight coefficient vector W, a maximum iteration number k _max and a convergence factor μ ;

The signal modulo step is to obtain two received short-wave multipath signals y ₁ , y ₂ , and obtain the mean square error after taking the modulo of the two short-wave multipath signals y ₁ , y ₂ ;

The step of obtaining the delay estimation result is to iteratively update the weight coefficient vector W based on the minimization of the mean square error, so as to obtain the delay estimation result;

Wherein, the km _max ≤ the signal length NR, the initial value W(0) of the weight coefficient vector is a zero vector of order 2 M _f +1, the value of the convergence factor is related to the convergence speed and convergence stability related.

In some of these embodiments, the mean square error is calculated and obtained according to the following model:

为二所述短波多径信号y ₁ 、y ₂ 的误差平方

的期望，

用于表示二所述短波多径信号y ₁ 、y ₂ 的误差函数，k为迭代次数且k=2M _f +1,2M _f ,……,k _max ，T用于表示向量转置，2M _f +1为所述滤波器的阶数，所述阶数可自定义设置，ŷ₁表示为ŷ₁(k)=[y ₁ (k),y ₁ (k-1),…,y ₁ (k-2M _f )]^T。where the mean squared error

is the square of the error of the short-wave multipath signals y ₁ and y ₂

expectations,

It is used to represent the error function of the two shortwave multipath signals y ₁ , y ₂ , k is the number of iterations and k =2 M _f +1,2 M _f ,..., k _max , T is used to represent the vector transposition, 2 M _f +1 is the order of the filter, the order can be customized, ŷ ₁ is represented as ŷ ₁ ( k )=[ y ₁ ( k ), y ₁ ( k-1 ),…, y ₁ ( k-2M _f )] ^T .

In some of the embodiments, the delay estimation result is calculated and obtained according to the following model:

。

.

In some of these embodiments, when 0 < k ≤ k _max , the weight coefficient vector W is expressed as:

W( k )=W( k -1)+2 μ (| y ₂ ( k -1)|-|ŷ ₁ ( k -1)| ^T W( k -1))ŷ ₁ ( k -1)| .

In some of the embodiments, the step of obtaining the time delay estimation result adopts the steepest descent method to obtain the minimum value of the mean square error, so as to obtain a statistical optimal filter in a sense. At this time, the filter converges, and based on the The delay estimation result is used to calculate the number of iterations corresponding to the maximum value of the model reading weight coefficient vector, so as to obtain the delay estimation result.

In a second aspect, an embodiment of the present application provides a shortwave delay estimation system, including:

A parameter initialization module, used to initialize the initial parameters of the filter, the initial parameters include: a weight coefficient vector W, a maximum iteration number k _max and a convergence factor μ ;

The signal modulo module is used to obtain two received shortwave multipath signals y ₁ , y ₂ , and obtain the mean square error after taking the modulo of the two short wave multipath signals y ₁ , y ₂ ;

a delay estimation result obtaining module, configured to iteratively update the weight coefficient vector according to the criterion of minimizing the mean square error, so as to obtain the delay estimation result;

Wherein, the km _max ≤ the signal length NR, the initial value W(0) of the weight coefficient vector is a zero vector of order 2 M _f +1, the value of the convergence factor is related to the convergence speed and convergence stability related.

In some of these embodiments, the mean square error is calculated and obtained according to the following model:

为二所述短波多径信号y ₁ 、y ₂ 的误差平方

的期望，

用于表示二所述短波多径信号y ₁ 、y ₂ 的误差函数，k为迭代次数且k=2M _f +1,2M _f ,……,k _max ，T用于表示向量转置，2M _f +1为所述滤波器的阶数，所述阶数可自定义设置，ŷ₁表示为ŷ₁(k)=[y ₁ (k),y ₁ (k-1),…,y ₁ (k-2M _f )]^T。where the mean squared error

is the square of the error of the short-wave multipath signals y ₁ and y ₂

expectations,

It is used to represent the error function of the two shortwave multipath signals y ₁ , y ₂ , k is the number of iterations and k =2 M _f +1,2 M _f ,..., k _max , T is used to represent the vector transposition, 2 M _f +1 is the order of the filter, the order can be customized, ŷ ₁ is represented as ŷ ₁ ( k )=[ y ₁ ( k ), y ₁ ( k-1 ),…, y ₁ ( k-2M _f )] ^T .

In some of the embodiments, the delay estimation result obtaining module adopts the steepest descent method to obtain the minimum value of the mean square error, and calculates the model corresponding to the maximum value of the model read weight coefficient vector based on the delay estimation result The number of iterations to obtain the delay estimation result.

In a third aspect, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, when the processor executes the computer program The shortwave delay estimation method as described in the first aspect above is implemented.

In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium on which a computer program is stored, and when the program is executed by a processor, implements the short-wave delay estimation method described in the first aspect above.

Compared with the related art, in order to overcome the interference of the channel gain function to the signal, the embodiment of the present application uses the signal modulo method to improve the traditional LMS algorithm, and proposes a modulus value-based LMS shortwave for the Watterson shortwave channel model. The time delay estimation method, system, computer equipment and readable storage medium, the embodiments of the present application not only consider the influence of the channel gain function but also consider the interference problem of the additive noise on the signal, and realize a more accurate measurement of the relative time delay of the shortwave signal. It is estimated that, through simulation analysis, it is found that the LMS algorithm based on the modulus value has better performance and higher accuracy than the traditional LMS algorithm.

The details of one or more embodiments of the application are set forth in the accompanying drawings and the description below in order to make other features, objects and advantages of the application more apparent.

Description of drawings

The drawings described herein are used to provide further understanding of the present application and constitute a part of the present application. The schematic embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation of the present application. In the attached image:

1 is a flowchart of a method for estimating shortwave delay according to an embodiment of the present application;

2 is a structural block diagram of a shortwave delay estimation system according to an embodiment of the present application;

Fig. 3 is the traditional LMS algorithm filter weight coefficient vector change curve diagram of background technology;

FIG. 4 is a graph showing the change of a filter weight coefficient vector according to an embodiment of the present application.

In the picture:

1. Parameter initialization module; 2. Signal modulo module; 3. Time delay estimation result acquisition module.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, but not to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

Obviously, the accompanying drawings in the following description are only some examples or embodiments of the present application. For those of ordinary skill in the art, the present application can also be applied to the present application according to these drawings without any creative effort. other similar situations. In addition, it will also be appreciated that while such development efforts may be complex and lengthy, for those of ordinary skill in the art to which the present disclosure pertains, the techniques disclosed in this application Some changes in design, manufacture or production based on the content are only conventional technical means, and it should not be understood that the content disclosed in this application is not sufficient.

Reference in this application to an "embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor a separate or alternative embodiment that is mutually exclusive of other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in this application may be combined with other embodiments without conflict.

Unless otherwise defined, the technical or scientific terms involved in this application shall have the usual meanings understood by those with ordinary skill in the technical field to which this application belongs. Words such as "a", "an", "an", "the" and the like mentioned in this application do not denote a quantitative limitation, and may denote the singular or the plural. The terms "comprising", "comprising", "having" and any variations thereof referred to in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product or process comprising a series of steps or modules (units). The apparatus is not limited to the steps or units listed, but may further include steps or units not listed, or may further include other steps or units inherent to the process, method, product or apparatus. Words like "connected," "connected," "coupled," and the like referred to in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The "plurality" referred to in this application refers to two or more. "And/or" describes the association relationship between associated objects, indicating that there can be three kinds of relationships. For example, "A and/or B" can mean that A exists alone, A and B exist at the same time, and B exists alone. The character "/" generally indicates that the associated objects are an "or" relationship. The terms "first", "second", "third", etc. involved in this application are only to distinguish similar objects, and do not represent a specific order for the objects.

The adaptive filtering delay estimation algorithm has the following characteristics: firstly, the adaptive filtering algorithm can complete the accurate estimation of the delay without knowing any prior information in advance; secondly, the adaptive filter can continuously adjust the relevant parameters in the iterative process , until an optimal criterion is approached, so as to realize the dynamic tracking of the changing input signal.

An embodiment of the present application provides a shortwave delay estimation method. FIG. 1 is a flowchart of the shortwave delay estimation method according to the first aspect of the embodiment of the present application. As shown in FIG. 1 , the flow includes the following steps:

The parameter initialization step S1 is to initialize the initial parameters of the filter. The initial parameters include: a weight coefficient vector W, a maximum iteration number k _max and a convergence factor μ , optionally, the filter is an FIR (Finite Impulse Response) filter ;

The signal modulo step S2 is to obtain two received shortwave multipath signals y ₁ , y ₂ , and to obtain the mean square error after taking the modulo of the two shortwave multipath signals; specifically, the two shortwave multipath signals y ₁ , y ₂ are the signals of the same transmitter received by two relatively distant base stations:

（2-1）

(2-1)

（2-2）

(2-2)

Wherein, the km _max ≤ the signal length NR, the initial value W(0) of the weight coefficient vector is a zero vector of order 2 M _f +1, and the value of M _f can be based on the required delay estimation accuracy Flexible setting, an example is not a limitation, in this embodiment, 2 M _f +1 is set to 32, the value of the convergence factor is related to the convergence speed and convergence stability, x ( n ), x ( n-τ ₁₂ ) are Shortwave signal, n =1,2,...,NR, C ₁ ( n ), C ₂ ( n ) are the channel gain functions in the Watterson channel model, τ ₁₂ is the relative time delay of the signal, e ₁ ( n ) and e ₂ ( n ) are additive white Gaussian noises with a mean value of 0 and a variance of η respectively. The value of η is related to the environment of the channel through which the specific signal passes. It should be noted that x ( n ), e ₁ ( n ) and e ₂ ( n ) are not correlated with each other.

In some of these embodiments, in the aforementioned signal modulo step S2, the mean square error is obtained by calculating the error function and the square of the error after the modulo of the second shortwave multipath signal. The specific solution process is as follows:

The error function is calculated according to the following model (2-3):

（2-3）

(2-3)

The squared error is calculated according to the following model (2-4):

（2-4）

(2-4)

The mean squared error is calculated according to the following model (2-5):

（2-5）

(2-5)

为二所述短波多径信号y ₁ 、y ₂ 的误差平方

的期望，T用于表示向量转置，

用于表示二所述短波多径信号y ₁ 、y ₂ 的误差函数，k为迭代次数且k=2M _f +1,2M _f ,……,k _max ，ŷ₁表示为ŷ₁(k)=[y ₁ (k),y ₁ (k-1),…,y ₁ (k-2M _f )]^T。where the mean squared error

is the square of the error of the short-wave multipath signals y ₁ and y ₂

The expectation of , T is used to denote the vector transpose,

It is used to represent the error function of the two shortwave multipath signals y ₁ , y ₂ , k is the number of iterations and k =2 M _f +1,2 M _f ,..., k _max , ŷ ₁ is represented as ŷ ₁ ( k )=[ y ₁ ( k ), y ₁ ( k-1 ),…, y ₁ ( k-2M _f )] ^T .

After substituting the expressions (2-1, 2-2) of y ₁ and y ₂ into the mean square error expression, the mean square error can be expressed as:

（2-6）

(2-6)

In formula (2-6):

、

,

、

,

。

.

In step S3 of obtaining the time delay estimation result, the weight coefficient vector is iteratively updated according to the criterion of minimizing the mean square error, so as to obtain the time delay estimation result. Among them, based on the above expression (2-6) of the mean square error, it can be known that after the signal is modulo taken, the mean square error is a quadratic function of the weight coefficient vector W, and is a parabolic type with a unique lowest point surface.

Based on this, in step S3 of this embodiment, the steepest descent method is used to obtain the minimum value of the mean square error, so as to obtain a statistical optimal filter in the sense, and the filter converges at this time. At the same time, in the steepest descent method, the weight coefficient vector W is updated by iteration. Then, step S3 calculates, based on the delay estimation result, the maximum value of the model read weight coefficient vector, that is, the peak value, and the corresponding iteration times, so as to obtain the delay estimation result. Specifically, the delay estimation result is calculated and obtained according to the following model (3-1):

（3-1）

(3-1)

Specifically, the weight coefficient vector in the iterative process is expressed as:

W( k +1)=W( k )- μ ▽( k ) (3-2)

对W求导的结果；考虑到对

求导过于复杂，实际应用时，不便于实现，本实施例采用

表示

，则▽(k)可表示为：That is to say, the weight coefficient vector W( k +1) of each iteration is the product of the weight coefficient vector W( k ) of the previous iteration and the mean square error gradient ▽( k ) and the convergence factor, where ▽( k ) is

The result of derivation with respect to W; taking into account the

The derivation is too complicated, and it is inconvenient to realize in practical application. This embodiment adopts

express

, then ▽( k ) can be expressed as:

（3-3）

(3-3)

Then the weight coefficient vector is further expressed as:

（3-4）

(3-4)

Substitute the error function expression (2-3) into this weight coefficient vector expression (3-4), we can get:

When 0 < k ≤ k _max , the weight coefficient vector W is expressed as:

In order to verify the actual effect of the embodiments of the present application, with reference to FIGS. 3 to 4 , the present application simulates and analyzes the traditional LMS algorithm under the shortwave channel and the present application, and assumes that the signal modulation mode is BPSK modulation, the symbol rate is 2400 Hz, and the sampling rate is 2400 Hz. The rate is 9600Hz, the Doppler frequency shifts of the two multipath signals are 1Hz and 2Hz respectively, the Doppler frequency spread is 0.5Hz, the relative delay is 2ms, the number of delay points is 19, and the signal-to-noise ratio is both 10dB. The data length is 1000. Figure 3 is a graph of the change of the weight coefficient vector of the traditional LMS algorithm filter in the background art. As shown in Figure 3, the weight coefficient vector of the traditional LMS algorithm has a multi-peak phenomenon. The peak has an impact and the position of the maximum peak is significantly different from the real delay value. This indicates that due to the existence of the channel gain function, the minimum mean square error criterion of the traditional LMS algorithm has been invalidated. FIG. 4 is a graph showing the change of the filter weight coefficient vector according to the embodiment of the present application. As shown in FIG. 4 , the weight coefficient vector of the embodiment of the present application only has a single peak value, and the peak position is exactly the real delay value, which means that the After taking the modulo of the signal, the mean value of the channel gain in the mean square error function can be made non-zero, so that the weight coefficient vector can be effectively updated in each iteration.

To sum up, the embodiment of the present application adopts the method of taking the modulo of the signal to effectively avoid the influence of the zero mean value of the channel gain on the mean square error function.

It should be noted that the steps shown in the above flow or the flow chart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical sequence is shown in the flow chart, in the In some cases, steps shown or described may be performed in an order different from that herein.

This embodiment also provides a shortwave delay estimation system. As used below, the terms "module," "unit," "subunit," etc. may be a combination of software and/or hardware that implements a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, implementations in hardware, or a combination of software and hardware, are also possible and contemplated.

FIG. 2 is a structural block diagram of a shortwave delay estimation system according to an embodiment of the present application. As shown in FIG. 2 , the system includes:

The parameter initialization module 1 is used to initialize the initial parameters of the filter, and the initial parameters include: a weight coefficient vector W, a maximum iteration number k _max and a convergence factor μ ;

The signal modulo module 2 is used to obtain two received shortwave multipath signals y ₁ , y ₂ , and obtain the mean square error after taking the modulo of the two short wave multipath signals y ₁ , y ₂ ;

The delay estimation result obtaining module 3 is configured to iteratively update the weight coefficient vector W based on the criterion of minimizing the mean square error, so as to obtain the delay estimation result, where k _max ≤ signal length NR.

Based on the above-mentioned modules, the system is used to implement the shortwave delay estimation method of the embodiment of the present application, which has already been described and will not be described again.

It should be noted that each of the above modules may be functional modules or program modules, and may be implemented by software or hardware. For the modules implemented by hardware, the above-mentioned modules may be located in the same processor; or the above-mentioned modules may also be located in different processors in any combination.

In addition, the shortwave delay estimation method in the embodiment of the present application described in conjunction with FIG. 1 may be implemented by a computer device. A computer device may include a processor and a memory storing computer program instructions.

Specifically, the above-mentioned processor may include a central processing unit (CPU), or a specific integrated circuit (Application Specific Integrated Circuit, ASIC for short), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

Among other things, the memory may include mass storage for data or instructions. By way of example and not limitation, the memory may include a Hard Disk Drive (HDD), a floppy disk drive, a Solid State Drive (SSD), a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a Universal Serial Bus ( Universal SerialBus, or USB for short) drive or a combination of two or more of these. Storage may include removable or non-removable (or fixed) media, where appropriate. Where appropriate, the memory may be internal or external to the data processing device. In certain embodiments, the memory is non-volatile (Non-Volatile) memory. In a specific embodiment, the memory includes a read-only memory (Read-Only Memory, referred to as ROM for short) and a random access memory (Random Access Memory, referred to as RAM for short). In a suitable case, the ROM may be a mask-programmed ROM, a programmable ROM (Programmable Read-Only Memory, referred to as PROM), an erasable PROM (Erasable Programmable Read-Only Memory, referred to as EPROM), an electrically erasable Except PROM (Electrically Erasable Programmable Read-Only Memory, referred to as EEPROM), Electrically Rewritable ROM (Electrically Alterable Read-Only Memory, referred to as EAROM) or Flash (FLASH) or a combination of two or more of these. In appropriate cases, the RAM may be Static Random-Access Memory (SRAM for short) or Dynamic Random Access Memory (DRAM for short), where DRAM may be a fast page Mode dynamic random access memory (Fast Page Mode Dynamic Random Access Memory, referred to as FPMDRAM), Extended Date Out Dynamic Random Access Memory (Extended Date Out Dynamic Random Access Memory, referred to as EDODRAM), Synchronous Dynamic Random Access Memory (Synchronous Dynamic Random Access Memory) Random-Access Memory, referred to as SDRAM) and so on.

The memory may be used to store or cache various data files required for processing and/or communication use, and possibly computer program instructions executed by the processor.

The processor reads and executes the computer program instructions stored in the memory to implement any one of the shortwave delay estimation methods in the foregoing embodiments.

In addition, in combination with the shortwave delay estimation method in the foregoing embodiments, the embodiments of the present application may provide a computer-readable storage medium for implementation. Computer program instructions are stored on the computer-readable storage medium; when the computer program instructions are executed by the processor, any one of the shortwave delay estimation methods in the foregoing embodiments is implemented.

The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity, all possible combinations of the technical features in the above-described embodiments are not described. However, as long as there is no contradiction between the combinations of these technical features, All should be regarded as the scope described in this specification.

The above-mentioned embodiments only represent several embodiments of the present application, and the descriptions thereof are specific and detailed, but should not be construed as a limitation on the scope of the invention patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which all belong to the protection scope of the present application. Therefore, the scope of protection of the patent of the present application shall be subject to the appended claims.

Claims (10)

1. A short-wave time delay estimation method is characterized by comprising the following steps:

a parameter initialization step of initializing initial parameters of a filter, wherein the initial parameters comprise: weight coefficient vector W, maximum number of iterationsk _max And convergence factorμ；

A signal modulus taking step for obtaining the received two short wave multipath signaly ₁ 、y ₂ For two said short wave multipath signalsy ₁ 、y ₂ Calculating the mean square error after modulus selection;

a time delay estimation result obtaining step, which is to carry out iterative update on the weight coefficient vector W by using the mean square error minimization as a criterion so as to obtain a time delay estimation result, wherein the time delay estimation result is obtainedk _max Less than or equal to the signal length NR.

2. The short wave time delay estimation method according to claim 1, wherein the mean square error is calculated according to the following model:

wherein the mean square error

Is twoThe short wave multipath signaly ₁ 、y ₂ Square of error of

In the expectation of the above-mentioned method,

for representing two said short-wave multipath signalsy ₁ 、y ₂ Is determined by the error function of (a),kis the number of iterations andk=2M _f +1,2M _f ,……,k _max t is used to denote vector transposition, ŷ₁Is shown as ŷ₁(k)=[y ₁ (k),y ₁ (k-1),…,y ₁ (k-2M _f )]^T，2M _f +1 is the order of the filter, which can be set by user.

3. The short-wave time delay estimation method according to claim 2, wherein the time delay estimation result is obtained by calculation according to the following model:

。

4. the short wave time delay estimation method according to claim 3, wherein when 0 <, the time delay is less than 0 < >k≤k _max Then, the weight coefficient vector W is represented as:

W(k)=W(k-1)+2μ(|y ₂ (k-1)|-|ŷ₁(k-1)|^TW(k-1))ŷ₁(k-1)|。

5. the short-wave time delay estimation method according to claim 3, wherein the time delay estimation result obtaining step obtains the minimum value of the mean square error by using a steepest descent method, and calculates the iteration number corresponding to the maximum value of the model reading weight coefficient vector based on the time delay estimation result, thereby obtaining the time delay estimation result.

6. A short wave delay estimation system, comprising:

a parameter initialization module, configured to initialize initial parameters of a filter, where the initial parameters include: weight coefficient vector W, maximum number of iterationsk _max And convergence factorμ；

A signal module for obtaining the received two-short wave multipath signaly ₁ 、y ₂ For two said short wave multipath signalsy ₁ 、y ₂ Calculating the mean square error after modulus selection;

a delay estimation result obtaining module, configured to iteratively update the weight coefficient vector W according to a criterion of minimizing a mean square error, so as to obtain a delay estimation result, where the delay estimation result is obtainedk _max ≦ Signal Length NR.

7. The short wave delay estimation system of claim 6, wherein: the mean square error is calculated according to the following model:

whereinThe mean square error

For two said short wave multipath signalsy ₁ 、y ₂ Square of error of

In the expectation of the above-mentioned method,

for representing two said short-wave multipath signalsy ₁ 、y ₂ Is determined by the error function of (a),kis the number of iterations andk=2M _f +1,2M _f ,……,k _max t is used to denote vector transposition, ŷ₁Is shown as ŷ₁(k)=[y ₁ (k),y ₁ (k-1),…,y ₁ (k-2M _f )]^T，2M _f +1 is the order of the filter, which can be set by user.

8. The short wave delay estimation system of claim 7, wherein: and the time delay estimation result acquisition module acquires the minimum value of the mean square error by adopting a steepest descent method, and calculates the iteration times corresponding to the maximum value of the model reading weight coefficient vector based on the time delay estimation result so as to obtain the time delay estimation result.

9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the short wave delay estimation method according to any one of claims 1 to 5 when executing the computer program.

10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the short wave delay estimation method according to any one of claims 1 to 5.

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