CN117614789A - Carrier phase tracking method and device based on Kalman-like unbiased FIR filter - Google Patents
Carrier phase tracking method and device based on Kalman-like unbiased FIR filter Download PDFInfo
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Abstract
The application relates to the technical field of carrier synchronization, solves the problem that a Kalman carrier tracking algorithm in the prior art is poor in robustness under a high dynamic condition, and discloses a carrier phase tracking method and device based on a Kalman-like unbiased FIR filter, wherein the method comprises the following steps: the method is based on a traditional Kalman carrier tracking model, a Kalman unbiased FIR carrier tracking expansion model without considering state noise information and measurement noise information is built for the first time, a Kalman unbiased FIR carrier synchronization iterative algorithm is provided, and compared with the traditional Kalman carrier tracking algorithm, the method has stronger robustness.
Description
Technical Field
The application relates to the technical field of carrier synchronization, in particular to a carrier phase tracking method and device based on a Kalman-like unbiased FIR filter.
Background
With the rapid development of military and civil aircrafts and missile systems, the radial instantaneous speed, acceleration and jerk between an airborne/missile-borne target and a satellite are larger and larger, and the high-speed carrier has the characteristics of strong nonlinearity, rapid time variation, strong coupling and the like in a dynamic environment, so that the difficulty of accurate carrier synchronization of a high-dynamic receiver is sharply increased.
Classical kalman filters are a simple and globally optimal state estimator of the linear gaussian process, widely used in many fields. The state estimation method of Kalman filtering uses minimum mean square error as the optimal criterion of estimation, adopts a state space model of signal and noise, and the estimation of state variables is updated according to the estimated value of the previous moment and the observed value of the current moment. In order to ensure the optimality of the state estimation value of the Kalman filtering, accurate state noise information and measurement noise information are required to be known, random external interference hardly obeys Gaussian statistics in the practical application process, and once the motion state of a carrier changes or other interference exists, the estimation error of the carrier increases sharply.
Disclosure of Invention
The carrier phase tracking method and device based on the Kalman unbiased FIR filter are provided for solving the problem that a Kalman carrier tracking algorithm in the prior art is poor in robustness under a high dynamic condition.
In a first aspect, a carrier phase tracking method based on a kalman-like unbiased FIR filter is provided, including:
establishing a Kalman carrier tracking model according to the phase difference, the Doppler frequency and the Doppler frequency change rate;
deducing an FIR carrier tracking expansion model according to the N historical data;
deducing a batch processing result output by the unbiased FIR filter according to unbiased constraint conditions;
deriving a Kalman-like unbiased FIR carrier synchronization iterative algorithm;
generating local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter;
and updating the local NCO frequency according to the local NCO frequency control quantity.
Further, the kalman carrier tracking model is:
（1）
（2）
wherein,，/>，/>，/>，，/>，/>，/>for carrier phase deviation>For Doppler frequency deviation, +.>For Doppler frequency difference rate of change, < >>And->Respectively isn-1 carrier phase offset predicted by the time-of-day filter and doppler frequency generated by local NCO replication,/->Update time for carrier loop, process noise +.>Caused by phase deviation of the reference clock of the receiver, frequency deviation and acceleration between the receiver and the moving carrier in the direction of the line of sight>Is the phase difference between the received signal output by the loop phase discriminator and the local reproduction carrier wave, < >>Representing the measured gaussian white noise, the variance isR。
Further, the FIR carrier tracking extension model is:
（3）
（4）
（5）
（6）
（7）
（8）
wherein,，
，/>，/>，，/>，/>。
further, deriving a batch result of the unbiased FIR filter output according to an unbiased constraint, including:
utilization interval [m,n]A kind of electronic deviceN The history data is used as the input of the FIR filterIs expressed as:
（9）
（10）
wherein,for the gain matrix of the FIR filter, when equation (10) is true,/>The estimation is unbiased FIR estimation;
the following is given according to formula (3):
（11）
wherein,、/>respectively is a matrix->And->Is the first of (2)N A row vector;
ignoring the process noise and the measurement noise, the result is according to equation (4), equation (9) and equation (11):
（12）
according to the linear system theory, it is obtained that: the system equation corresponds to the zero input response and zero state response of the system at zero input and zero state, and the system complete response can be obtained by linearly summing the zero input response and the zero state response, which can be divided into for equation (12):
1）the gain matrix of the zero input response satisfies +.>；
2）The gain matrix of the zero state response satisfies +.>；
Gain matrix of zero input response can be calculated according to unbiased constraint conditionGain matrix for zero state response>Satisfy formula (13) and formula (14):
（13）
（14）
the batch form of the unbiased FIR filter response, which is linearly added by the zero input response and the zero state response, is:
（15）。
further, the initial input of the Kalman-like unbiased FIR carrier synchronization iterative algorithmAs calculated by equation (15), the entire iterative process starts with m+v, v=k, ends with v=n-1, and as new observations are continuously entered, new state estimates are updated on the basis of the previous time instant.
Further, the Kalman-like unbiased FIR carrier synchronization iterative algorithm includes:
the state variables comprise phase difference, frequency difference and frequency change rate between the receiving carrier and the local carrier, so that K=3, initializing historical data points N, and starting from n=N by the Kalman unbiased FIR-like carrier synchronization iterative algorithm;
judging whether N is greater than or equal to N, if not, outputtingThe method comprises the steps of carrying out a first treatment on the surface of the If the judgment result isIf yes, then intermediate variables m and s are calculated by equation (16) and equation (17):
（16）
（17）
calculating an auxiliary gain matrix by equation (18)：
（18）
The prediction vector is calculated according to equation (19) from the observations of [ m, s ]:
（19）
wherein,for prediction vector, ++>，/>；
（20）
（21）
（22）
Judging whether v is in the interval [ K, N-1 ], and if so, performing iterative calculation according to the formula (20), the formula (21) and the formula (22); if the judgment result is negative, outputting:。
further, the calculation formula of the local NCO frequency control amount is as follows:
（23）
wherein,is the local NCO frequency control amount.
In a second aspect, a carrier phase tracking device based on a kalman-like unbiased FIR filter is provided, including:
the model building module is used for building a Kalman carrier tracking model according to the phase difference, the Doppler frequency and the Doppler frequency change rate;
the model expansion module is used for deducing an FIR carrier tracking expansion model according to the N historical data;
the first deducing module is used for deducing the batch processing result output by the unbiased FIR filter according to the unbiased constraint condition;
the second deducing module is used for deducing a Kalman-like unbiased FIR carrier synchronization iterative algorithm;
the computing module is used for generating local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter;
and the updating module is used for updating the local NCO frequency according to the local NCO frequency control quantity.
In a third aspect, a computer readable storage medium is provided, the computer readable medium storing program code for execution by a device, the program code comprising steps for performing the method as in any one of the implementations of the first aspect.
In a fourth aspect, there is provided an electronic device comprising a processor, a memory and a program or instruction stored on the memory and executable on the processor, which when executed by the processor implements a method as in any of the implementations of the first aspect.
The application has the following beneficial effects: based on a traditional Kalman carrier tracking model, a Kalman unbiased FIR-like carrier tracking expansion model without considering state noise information and measurement noise information is established for the first time, a Kalman unbiased FIR-like carrier synchronization iterative algorithm is provided, and simulation results show that compared with the traditional Kalman carrier tracking algorithm, the Kalman unbiased FIR-like carrier tracking algorithm has stronger robustness, and the Kalman unbiased FIR-like carrier tracking loop can still keep stable tracking of phase and frequency under a high dynamic environment with acceleration of 100 g/s.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application, illustrate and explain the application and are not to be construed as limiting the application.
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a carrier phase tracking method based on a kalman-like unbiased FIR filter according to embodiment 1 of the present application;
fig. 2 is a schematic diagram of a quasi-kalman unbiased FIR filter recursion in the carrier phase tracking method based on the quasi-kalman unbiased FIR filter according to embodiment 1 of the present application;
FIG. 3 is a flowchart of a Kalman-like unbiased FIR carrier tracking algorithm in the carrier phase tracking method based on Kalman-like unbiased FIR filter according to embodiment 1 of the present application;
fig. 4 is a block diagram of a carrier tracking loop of a kalman-like unbiased FIR in the carrier phase tracking method based on the kalman-like unbiased FIR filter according to embodiment 1 of the present application;
fig. 5 is a diagram of a high dynamic operation model in a carrier phase tracking algorithm of a quasi-kalman unbiased FIR in the carrier phase tracking method based on a quasi-kalman unbiased FIR filter in embodiment 1 of the present application;
fig. 6 is a diagram of a high dynamic operation model in a carrier phase tracking algorithm of a quasi-kalman unbiased FIR in the carrier phase tracking method based on a quasi-kalman unbiased FIR filter in embodiment 1 of the present application;
fig. 7 is a diagram of a high dynamic operation model in a carrier phase tracking algorithm of a kalman-like unbiased FIR in the carrier phase tracking method based on the kalman-like unbiased FIR filter in embodiment 1 of the present application;
fig. 8 is a phase tracking error comparison chart in a kalman-like unbiased FIR carrier tracking algorithm in the kalman-like unbiased FIR filter-based carrier phase tracking method of embodiment 1 of the present application;
fig. 9 is a frequency tracking error comparison chart in a kalman-like unbiased FIR carrier tracking algorithm in the carrier phase tracking method based on the kalman-like unbiased FIR filter of embodiment 1 of the present application;
fig. 10 is a block diagram of a carrier phase tracking device based on a kalman-like unbiased FIR filter according to embodiment 2 of the present application;
fig. 11 is a schematic diagram of the internal structure of the electronic device of embodiment 4 of the present application.
Reference numerals:
100. a model building module; 200. a model expansion module; 300. a first deriving module; 400. a second deriving module; 500. a computing module; 600. and updating the module.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
The carrier phase tracking method based on the Kalman-like unbiased FIR filter according to the embodiment 1 of the application comprises the following steps: establishing a Kalman carrier tracking model according to the phase difference, the Doppler frequency and the Doppler frequency change rate; deducing an FIR carrier tracking expansion model according to the N historical data; deducing a batch processing result output by the unbiased FIR filter according to unbiased constraint conditions; deriving a Kalman-like unbiased FIR carrier synchronization iterative algorithm; generating local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter; according to the local NCO frequency control quantity, the local NCO frequency is updated, a Kalman unbiased FIR-like carrier tracking expansion model without considering state noise information and measurement noise information is established for the first time based on a traditional Kalman carrier tracking model, a Kalman unbiased FIR-like carrier synchronization iterative algorithm is provided, and simulation results show that the algorithm has stronger robustness compared with the traditional Kalman carrier tracking algorithm.
Specifically, fig. 1 shows a flowchart of a carrier phase tracking method based on a kalman-like unbiased FIR filter in application embodiment 1, including:
s101, establishing a Kalman carrier tracking model according to the phase difference, the Doppler frequency and the Doppler frequency change rate;
specifically, a Kalman carrier tracking model is constructed:
（1）
（2）
wherein,，/>，/>，/>，/>，/>，/>，/>for carrier phase deviation>For Doppler frequency deviation, +.>For Doppler frequency difference rate of change, < >>And->Respectively isn-1 carrier phase offset predicted by the time-of-day filter and doppler frequency generated by local NCO replication,/->Update time for carrier loop, process noise +.>Caused by phase deviation of the reference clock of the receiver, frequency deviation and acceleration between the receiver and the moving carrier in the direction of the line of sight>Is the phase difference between the received signal output by the loop phase discriminator and the local reproduction carrier wave, < >>Representing the measured gaussian white noise, the variance isR。
S102, deducing an FIR carrier tracking expansion model according to N historical data;
the FIR filter estimates the state of the nth point using the history data m=n-n+1 to N total N history data as the input to the estimator. Therefore, the FIR carrier tracking model is based on the traditional Kalman carrier tracking model for N-point expansion, and is specifically expressed as follows:
（3）
（4）
（5）
（6）
（7）
（8）
wherein,，
，/>，/>，，/>，/>。
s103, deducing a batch processing result output by the unbiased FIR filter according to unbiased constraint conditions;
specifically, when using interval [m,n]A kind of electronic deviceN When the history data is used as an input to the FIR filter,is expressed as:
（9）
wherein,is the gain matrix of the FIR filter. When formula (10) is true, +.>The estimate is an unbiased FIR estimate.
（10）
The last line can be found according to equation (3):
（11）
wherein,、/>respectively is a matrix->And->Is the first of (2)N A row vector;
ignoring the process noise and the measurement noise, the result is according to equation (4), equation (9) and equation (11):
（12）
according to the linear system theory, it is obtained that: the system equation corresponds to the zero input response and zero state response of the system at zero input and zero state, and the system complete response can be obtained by linearly summing the zero input response and the zero state response, which can be divided into for equation (12):
1）the gain matrix of the zero input response satisfies +.>；
2）The gain matrix of the zero state response satisfies +.>；
Gain matrix of zero input response can be calculated according to unbiased constraint conditionGain matrix for zero state response>Satisfy formula (13) and formula (14):
（13）
（14）
thus, the batch form of the unbiased FIR filter response, which is linearly added by the zero input response and the zero state response, is:
（15）
when the number of points N of the historical data is large, the number of the matrix and the number of the vector in the formula (15) are large, which leads to a sharp increase of the computational complexity, and the problem can be well solved through a Kalman-like iterative process.
S104, deducing a Kalman-like unbiased FIR carrier synchronization iterative algorithm;
specifically, the principle of the Kalman-like unbiased FIR iterative algorithm is shown in FIG. 2. Calculating by the formula (15) to obtain initial input of iterative algorithmAnd starts iterative computation with this. The entire iterative process starts with m+v, v=k and ends with v=n-1. As new observations are continuously entered, new state estimates are updated on the basis of the previous time instant.
The carrier tracking algorithm based on the Kalman-like unbiased FIR filter is shown in fig. 3, and the state variables comprise three quantities of phase difference, frequency difference and frequency change rate between the received carrier and the local carrier, so that K=3, the number of points N of the historical data is initialized, and the whole Kalman-like unbiased FIR carrier synchronization iterative algorithm starts at n=N;
judging whether N is greater than or equal to N, if not, outputtingThe method comprises the steps of carrying out a first treatment on the surface of the If the judgment result is yes, calculating intermediate variables m and s through a formula (16) and a formula (17):
（16）
（17）
calculating an auxiliary gain matrix by equation (18)：
（18）
The prediction vector is calculated according to equation (19) from the observations of [ m, s ]:
（19）
wherein,for prediction vector, ++>，/>；
（20）
（21）
（22）
Judging whether v is in the interval [ K, N-1 ], and if so, performing iterative calculation according to the formula (20), the formula (21) and the formula (22); if the judgment result isNo, output:i.e. when the iteration satisfies v=n-1, the iteration is stopped and the output +.>Namely, the estimated output of the Kalman-like unbiased FIR filter>I.e. the nth output of the filter estimator: />。
S105, generating local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter;
the calculation formula of the local NCO frequency control quantity is as follows:
（23）
wherein,for the local NCO frequency control, a carrier tracking loop for a kalman like unbiased FIR is shown in fig. 4.
And S106, updating the local NCO frequency according to the local NCO frequency control quantity.
The simulation results using the method described in this embodiment are as follows: the high dynamic operation model is shown in fig. 5-7, the phase tracking error is shown in fig. 8, the frequency tracking error is shown in fig. 9, and the simulation result can be seen:
the tracking loop structure of the traditional second-order frequency locking loop auxiliary third-order phase locking loop cannot cope with sudden change of jerk, so that phase deviation is suddenly increased, and the whole sudden change process is continued; meanwhile, when the acceleration of a carrier tracking loop of the traditional Kalman is suddenly changed, the phase deviation changes to have fluctuation, and the duration time is longer; by using the Kalman-like unbiased FIR carrier tracking method, the stable tracking of the phase and the frequency is maintained in the whole high dynamic process, and meanwhile, the method adopted by the method is excellent in the aspect of loop tracking locking time.
Example 2
As shown in fig. 10, a carrier phase tracking device based on a kalman-like unbiased FIR filter according to embodiment 2 of the present application includes:
the model building module 100 is configured to build a kalman carrier tracking model according to the phase difference, the doppler frequency and the doppler frequency change rate;
the model expansion module 200 is configured to derive an FIR carrier tracking expansion model according to the N pieces of history data;
a first deriving module 300, configured to derive a batch processing result output by the unbiased FIR filter according to an unbiased constraint condition;
a second deriving module 400, configured to derive a kalman-like unbiased FIR carrier synchronization iterative algorithm;
the calculation module 500 is used for generating a local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter;
and the updating module 600 is configured to update the local NCO frequency according to the local NCO frequency control amount.
It should be noted that, in the embodiment of the present invention, other specific embodiments of the carrier phase tracking device based on the kalman-like unbiased FIR filter can be referred to the specific embodiments of the carrier phase tracking method based on the kalman-like unbiased FIR filter, and in order to avoid redundancy, the description is omitted here.
Example 3
A computer readable storage medium according to embodiment 3 of the present application stores program code for execution by a device, the program code including steps for performing the method in any one of the implementations of embodiment 1 of the present application;
wherein the computer readable storage medium may be a Read Only Memory (ROM), a static storage device, a dynamic storage device, or a random access memory (random access memory, RAM); the computer readable storage medium may store program code which, when executed by a processor, is adapted to perform the steps of a method as in any one of the implementations of embodiment 1 of the present application.
Example 4
As shown in fig. 11, embodiment 4 of the present application relates to an electronic device, where the electronic device includes a processor, a memory, and a program or an instruction stored on the memory and executable on the processor, where the program or the instruction implements a method as in any one of the implementations of embodiment 1 of the present application when executed by the processor;
the processor may be a general-purpose central processing unit (central processing unit, CPU), microprocessor, application specific integrated circuit (application specific integrated circuit, ASIC), graphics processor (graphics processing unit, GPU) or one or more integrated circuits for executing relevant programs to implement the methods of any of the implementations of embodiment 1 of the present application.
The processor may also be an integrated circuit electronic device with signal processing capabilities. In implementation, each step of the method in any implementation of embodiment 1 of the present application may be implemented by an integrated logic circuit of hardware in a processor or an instruction in a software form.
The processor may also be a general purpose processor, a digital signal processor, an Application Specific Integrated Circuit (ASIC), an off-the-shelf programmable gate array (field programmable gate array, FPGA) or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component. The disclosed methods, steps, and logic blocks in the embodiments of the present application may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present application may be embodied directly in a hardware decoding processor or in a combination of hardware and software modules in the decoding processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in a memory, and the processor reads information in the memory, and in combination with its hardware, performs functions necessary for execution by the units included in the data processing apparatus of the embodiment of the present application, or executes a method in any implementation manner of embodiment 1 of the present application.
The above is only a preferred embodiment of the present application; the scope of protection of the present application is not limited in this respect. Any person skilled in the art, within the technical scope of the present disclosure, shall cover the protection scope of the present application by making equivalent substitutions or alterations to the technical solution and the improved concepts thereof.
Claims (10)
1. A carrier phase tracking method based on a kalman-like unbiased FIR filter, comprising:
establishing a Kalman carrier tracking model according to the phase difference, the Doppler frequency and the Doppler frequency change rate;
deducing an FIR carrier tracking expansion model according to the N historical data;
deducing a batch processing result output by the unbiased FIR filter according to unbiased constraint conditions;
deriving a Kalman-like unbiased FIR carrier synchronization iterative algorithm;
generating local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter;
and updating the local NCO frequency according to the local NCO frequency control quantity.
2. The carrier phase tracking method based on a kalman-like unbiased FIR filter according to claim 1, wherein the kalman carrier tracking model is:
（1）
（2）
wherein,，/>，for carrier phase deviation>For Doppler frequency deviation, +.>For Doppler frequency difference rate of change, < >>And->Respectively isn-1 carrier phase offset predicted by the time-of-day filter and doppler frequency generated by local NCO replication,/->Update time for carrier loop, process noise +.>Caused by phase deviation of the reference clock of the receiver, frequency deviation and acceleration between the receiver and the moving carrier in the direction of the line of sight>Is the phase difference between the received signal output by the loop phase discriminator and the local reproduction carrier wave, < >>Representing the measured gaussian white noise, the variance isR。
3. The carrier phase tracking method based on a kalman-like unbiased FIR filter according to claim 2, wherein the FIR carrier tracking expansion model is:
（3）
（4）
（5）
（6）
（7）
（8）
wherein,，/>，，。
4. a carrier phase tracking method based on a kalman like unbiased FIR filter as claimed in claim 3, characterized in that deriving the batch result of the unbiased FIR filter output from the constraint of unbiasedness comprises:
utilization interval [m,n]A kind of electronic deviceN The history data is used as the input of the FIR filterIs expressed as:
（9）
（10）
wherein,for the gain matrix of the FIR filter, when equation (10) is true,/>The estimation is unbiased FIR estimation;
the following is given according to formula (3):
（11）
wherein,respectively is a matrix->And->Is the first of (2)N A row vector;
ignoring the process noise and the measurement noise, the result is according to equation (4), equation (9) and equation (11):
（12）
according to the linear system theory, it is obtained that: the system equation corresponds to the zero input response and zero state response of the system at zero input and zero state, and the system complete response can be obtained by linearly summing the zero input response and the zero state response, which can be divided into for equation (12):
1）the gain matrix of the zero input response satisfies +.>；
2）The gain matrix of the zero state response satisfies +.>；
Gain matrix of zero input response can be calculated according to unbiased constraint conditionGain matrix for zero state response>Satisfy formula (13) and formula (14):
（13）
（14）
the batch form of the unbiased FIR filter response, which is linearly added by the zero input response and the zero state response, is:
（15）。
5. the carrier phase tracking method based on a Kalman-like unbiased FIR filter as recited in claim 4, wherein the Kalman-like unbiased FIR carrier synchronization iterated algorithm is initially inputAs calculated by equation (15), the entire iterative process starts with m+v, v=k, ends with v=n-1, and as new observations are continuously entered, new state estimates are updated on the basis of the previous time instant.
6. The carrier phase tracking method based on a kalman-like unbiased FIR filter according to claim 5, characterized in that the kalman-like unbiased FIR carrier synchronization iterative algorithm includes:
the state variables comprise phase difference, frequency difference and frequency change rate between the receiving carrier and the local carrier, so that K=3, initializing historical data points N, and starting from n=N by the Kalman unbiased FIR-like carrier synchronization iterative algorithm;
judging whether N is greater than or equal to N, if not, outputtingThe method comprises the steps of carrying out a first treatment on the surface of the If the judgment result is yes, calculating intermediate variables m and s through a formula (16) and a formula (17):
（16）
（17）
calculating an auxiliary gain matrix by equation (18)：
（18）
The prediction vector is calculated according to equation (19) from the observations of [ m, s ]:
（19）
wherein,for predictive vector +.>，/>；
（20）
（21）
（22）
Judging whether v is in the interval [ K, N-1 ], and if so, performing iterative calculation according to the formula (20), the formula (21) and the formula (22); if the judgment result is negative, outputting:。
7. the carrier phase tracking method based on the kalman-like unbiased FIR filter according to claim 6, wherein the calculation formula of the local NCO frequency control amount is:（23）
wherein,is the local NCO frequency control amount.
8. A carrier phase tracking device based on a kalman-like unbiased FIR filter, comprising:
the model building module is used for building a Kalman carrier tracking model according to the phase difference, the Doppler frequency and the Doppler frequency change rate;
the model expansion module is used for deducing an FIR carrier tracking expansion model according to the N historical data;
the first deducing module is used for deducing the batch processing result output by the unbiased FIR filter according to the unbiased constraint condition;
the second deducing module is used for deducing a Kalman-like unbiased FIR carrier synchronization iterative algorithm;
the computing module is used for generating local NCO frequency control quantity according to the output result of the Kalman-like unbiased FIR filter;
and the updating module is used for updating the local NCO frequency according to the local NCO frequency control quantity.
9. A computer readable storage medium storing program code for execution by a device, the program code comprising steps for performing the method of any one of claims 1-7.
10. An electronic device comprising a processor, a memory, and a program or instruction stored on the memory and executable on the processor, which when executed by the processor, implements the method of any of claims 1-7.
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