CN114884790A - Doppler frequency shift synchronization method based on four-dimensional track prediction - Google Patents
Doppler frequency shift synchronization method based on four-dimensional track prediction Download PDFInfo
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Abstract
The invention discloses a Doppler frequency shift synchronization method based on four-dimensional track prediction, and belongs to the technical field of communication. Firstly, observing and recording the actual running track of the aircraft to be tested, expressing the actual running track by using a linear mixed model, and carrying out initialization prediction on the four-dimensional track of the aircraft based on a Kalman filtering mode to obtain a system state estimation value of the aircraft at the time t. And then, obtaining an average Doppler frequency shift according to an average system state estimation value of the aircraft in a time window, pre-compensating the received signal, and performing time-frequency synchronization on the compensated received signal by using a cyclic prefix and a synchronization signal. Finally, demodulating the received signals after time-frequency synchronization, obtaining the information of the received signals, feeding the information back to the predicted initial track, correcting the initial track, and performing the next four-dimensional track prediction according to the corrected data. The invention meets the requirement of accurate and rapid time-frequency synchronization between the aircraft and the ground station under the high-speed operation, and saves the cost.
Description
Technical Field
The application relates to the technical field of communication, in particular to a Doppler frequency shift synchronization method based on four-dimensional track prediction.
Background
With the rapid development of civil aviation, the existing narrow-band communication system cannot meet the increasing demand of aviation communication services, upgrading the existing narrow-band communication system of the civil aviation industry to a broadband communication system is a development target in the next stage of the industry, and the national civil aviation bureau also issues a new generation aviation broadband communication technology roadmap of the national civil aviation in 2021 month 5, wherein the new generation aviation broadband communication technology mainly comprises 5G AeroMACS, 5G LDACS, 5G ATG, 5G public network and the like based on the 5G communication technology of the national aviation.
The 5G L wave band Digital airborne communication System (LDACS) technology is mainly applied to air-ground communication scenes in the air route stage of airplanes, works in the L wave band, and is based on the OFDM technology. However, the flying speed of the airplane in the route stage is high and can reach 1000km/h, so that great Doppler frequency shift is caused, the existing receiving equipment cannot receive signals with overlarge frequency shift, and how to solve the signal synchronization under the condition of great Doppler frequency shift is a key problem in the 5G LDACS technology.
Disclosure of Invention
The invention provides a Doppler frequency shift synchronization method based on four-dimensional track prediction, which aims to solve the problem of signal synchronization in a large Doppler frequency shift scene during LDACS application and promote the practical application of civil aviation broadband communication service.
The Doppler frequency shift compensation method based on the four-dimensional track prediction specifically comprises the following steps:
observing and recording an actual running track of an aircraft to be tested, and representing the actual running track by using a linear mixed model;
the linear hybrid model includes an observation equation and a state equation, which are respectively expressed as follows:
the state equation is as follows: x (t) ═ AX (t-1) + BU (t-1) + w (t)
The observation equation: z (t) h (t) x (t) + n (t)
Where x (t) is the true state vector at time t, including the true three-dimensional coordinates of the aircraft, the component velocities in the three directions, and the accelerations in the three directions. X (t-1) is the true state at time t-1; a is a real state transition matrix; w (t) is the noise matrix at the current time; u (t-1) represents the real control vector at the time of t-1; b is a true control matrix representing the transformation of the input true control vector into a state vector;
z (t) is the system true observation at time t; n (t) represents the real observation noise at time t, with a mean of 0 and a covariance of R; h (t) represents the true observation matrix at time t.
Secondly, based on Kalman filtering, combining a linear mixed model, and carrying out initialization prediction on the four-dimensional track of the aircraft to be tested to obtain a system state estimation value of the aircraft at each moment;
the method specifically comprises the following steps:
step 201, according to the real state vector and the real control vector at the t-1 moment, calculating the system state predicted value X at the t moment p (t)；
X p (t)＝A*X p (t-1)+B*U(t-1)
Step 202, using the real system observation value Z (t) and the predicted system state value X p (t) calculating the covariance P - (t)；
P - (t)＝AP(t-1)A T +Q
Q represents the covariance matrix of the noise matrix w (t). P (t-1) represents the covariance of the true state vector at time t-1 and its optimal estimate;
the optimal estimate of the true state value is: and estimating the observation noise to obtain an approximate real state value.
Step 203, utilizing the real observation value Z (t-1) at the time of t-1 and the system state prediction value X p Covariance P of (t-1) - (t-1) updating the parameters of Kalman filtering to obtain Kalman filtering gain K:
K＝P - (t-1)H T (HP - (t-1)H T +R) -1
step 204, using Kalman filter gain K and system state predicted value X at time t p (t) calculating an estimated value of the system state at time t
And 205, updating the real value at the time t and the optimal estimated covariance P (t), returning to the step 201 to perform Kalman filtering at the next time, and obtaining the system state estimated value at the next time.
P(t)＝(1-KH)*P - (t-1)
And step three, obtaining the average Doppler frequency shift according to the average system state estimated value of the aircraft in a time window, and pre-compensating the received signal.
The method specifically comprises the following steps:
step 301, taking the current time t as the center, taking the time period h before and after the time t as a time window, and recording the system state estimation value as a slave
To
Averaging to obtain an average system state estimation value in the time window of
302, based on the average system state estimate
Obtaining the average speed v of the aircraft in the time window, substituting the average speed v into a Doppler frequency shift formula to obtain a Doppler frequency shift f d 。
Doppler shift calculation formula: f. of d ＝f m cos(θ)
Theta is an included angle between the relative motion speed direction and a connecting line of the receiving and transmitting ends; f. of m The maximum doppler shift is indicated and the maximum doppler shift,
f c is the carrier center frequency and C is the speed of light.
Step 303, shift the Doppler frequency f d The pre-compensation is used for receiving signals to obtain pre-compensated receiving signals;
assuming that the transmitted signal is s (n), the received signal r (n) is:
r(n)＝s(n-n d )exp(j*2π*n*Δf*Ts)
where j is a constant, Ts is a sampling period, Δ f is the total frequency offset of the signal during transmission, n d Is the time offset of the signal during transmission.
The pre-compensated received signal is: r' (n) ═ s (n-n) d )exp(j*2π*(Δf-f d )*n*Ts)
And step four, after Doppler frequency shift pre-compensation, the frequency shift of the received signal uses a cyclic prefix and a synchronous signal to carry out time-frequency synchronization.
The frequency offset of the signal is divided into an integer multiple of frequency offset (IFO), a Fractional Frequency Offset (FFO), and a residual frequency offset.
(1) Integer multiple frequency offset IFO
Firstly, a plurality of OFDM symbols are subjected to sliding correlation calculation by using cyclic prefixes, the point of obtaining the maximum peak value is the starting point of one OFDM symbol, and the time offset n in the transmission process is obtained d ；
Then, the OFDM symbol time coarse synchronization and the integer frequency offset synchronization of the frequency domain of the system are completed by utilizing the maximum likelihood algorithm.
The correlation function r (n) of the received signal r (n) is:
wherein d represents a timing pointer, N represents the number of subcarriers of an OFDM symbol, and L is the CP length;
then integer frequency offset estimate epsilon IFO Comprises the following steps:
wherein d is ml Is the start time of the OFDM symbol.
(2) Fractional frequency offset FFO
P to be receivedThe SS signal p (n) is divided into two sections, and is subjected to conjugate multiplication with the local unbiased PSS signal s (n) to obtain decimal frequency deviation epsilon FFO ：
(3) Residual frequency offset
And training to use a phase-locked loop to perform frequency offset adjustment on the residual frequency offset.
And step five, demodulating the received signals after time-frequency synchronization is completed, acquiring self-contained speed information, position information and aircraft intention in the received signals, returning to the step two, feeding back to the predicted initial track, correcting the predicted initial track, and performing the next four-dimensional track prediction according to the corrected data.
The invention has the advantages that:
1. on the basis of four-dimensional track prediction, the method meets the requirement that the communication between the aircraft and the ground station needs to be accurate and quick in time-frequency synchronization when the aircraft generates large Doppler frequency shift in high-speed operation.
2. The invention adopts four-dimensional track prediction to estimate the Doppler frequency shift, reduces the requirement on the time-frequency synchronization capability of the equipment by pre-compensating the Doppler frequency shift, and saves the cost.
3. According to the invention, after time-frequency synchronization is completed, signals are demodulated, the position state information and the intention of the aircraft are obtained, the information is fed back to the prediction process, and the rapid convergence of the time-frequency synchronization and the correction of the four-dimensional track prediction are completed.
Drawings
FIG. 1 is a schematic diagram illustrating a four-dimensional track-based Doppler shift compensation method according to the present invention;
fig. 2 is a flowchart of a doppler shift compensation method based on four-dimensional flight path according to the present invention.
Detailed Description
The implementation of the present invention will be further described with reference to the accompanying drawings and embodiments.
Under the air-ground communication scene of civil aviation communication, the aircraft base station is in wireless connection with the fixed ground base station, and real-time communication is realized. When the LDACS is applied to an air-ground communication scene, the Doppler frequency shift is very large due to the fact that the flight speed of an airplane is 800-1200 km/h, normal equipment is difficult to receive, and the Doppler frequency shift needs to be pre-compensated.
The four-dimensional track prediction adopted by the invention is a new generation of air control technology, compared with the traditional three-dimensional track, the four-dimensional track takes the time dimension into consideration on the basis of considering the three-dimensional flight track of the longitude and latitude height of the aircraft, the whole flight process is represented by the longitude and latitude height and the time, the time of passing a waypoint of a flight can be accurately controlled, the information such as the position, the speed and the like of the aircraft at any moment can be accurately obtained, and the Doppler frequency shift is well compensated.
The existing flight path prediction methods of the aircraft are mainly divided into two categories, one is to predict by using performance parameters and meteorological data of the aircraft and the intention of the aircraft, the other is to estimate methods without parameters based on Kalman filtering or machine learning and the like, and the invention takes Kalman filtering as an example to predict the four-dimensional flight path.
A Doppler frequency shift compensation method based on four-dimensional flight path applies civil aviation broadband communication LDACS to time-frequency synchronization when airborne CPE and ground station communicate, as shown in figure 1 and figure 2, the specific steps are as follows:
observing and recording an actual running track of an aircraft to be tested, and representing the running track through a linear mixed model;
the linear hybrid model includes an observation equation and a state equation, which are respectively expressed as follows:
the state equation is as follows: x (t) ═ AX (t-1) + BU (t-1) + w (t)
The observation equation: z (t) h (t) x (t) + n (t)
Where x (t) is a true state vector describing a plurality of states of the aircraft, including true three-dimensional coordinates of the aircraft, three-directional component velocities, and three-directional accelerations. X (t) is the real state at the current time t, and X (t-1) is the real state at the time t-1; a is a real state transition matrix; w (t) is the noise matrix at the current time; u is a real control vector, and U (t-1) represents the real control vector at the moment of t-1; b is a true control matrix representing the transformation of the input true control vector into a state vector;
z (t) is the system true observation at time t; n (t) represents the real observation noise at time t, with a mean of 0 and a covariance of R; h is the true observation matrix, and H (t) represents the true observation matrix at time t.
Secondly, based on a Kalman filtering mode, a linear hybrid model is combined to carry out initialization prediction on the four-dimensional track of the aircraft to obtain a system state estimation value of the aircraft at the t moment
The initialized predicted value of the four-dimensional track of the aircraft is set to 0. The true state X (t) of the system cannot be obtained due to the existence of noise, but the true observed value Z (t) obtained through observation and the predicted value X obtained through prediction p (t) weighting to obtain estimated value of system state close to true value
When the kalman filter is used at this time, the state at the next time can be calculated only by the currently input parameters. Wherein, the noise matrix w (t) of the system has the biggest influence on the accuracy of the Kalman filtering.
The specific process is as follows:
step 201, according to the real state value and the real control vector at the t-1 moment, calculating the system state predicted value X at the t moment p (t); and calculating a real observation value Z (t) and a system state predicted value X by using the covariance P (t-1) of the real state value and the optimal estimation of the real state value at the t-1 moment p (t) covariance P - (t)；
X p (t)＝A*X p (t-1)+B*U(t-1)
P - (t)＝AP(t-1)A T +Q
Q represents the covariance matrix of gaussian noise.
Step 202, utilizing the t-1 time truthObserved value Z (t-1) and system state predicted value X p Covariance P of (t-1) - (t-1) updating the parameters of Kalman filtering to obtain Kalman filtering gain K:
K＝P - (t-1)H T (HP - (t-1)H T +R) -1
step 203, using Kalman filter gain K and system state prediction value X at time t p (t) calculating an estimated value of the system state at time t
And updating the real value at the time t and the covariance P (t) of the optimal estimation, and returning to the step 201 to perform Kalman filtering at the next time.
P(t)＝(1-KH)*P - (t-1)
The process is automatically triggered each time the observation value Z (t) is received, and ADS-B message information carried by the airplane is input into the Kalman filter as the observation value in the actual navigation process.
And step three, obtaining the average Doppler frequency shift according to the average system state estimated value of the aircraft in a time window, and pre-compensating the received signal.
In a new generation of air management system based on four-dimensional track operation, a concept of predicted arrival time and actual arrival time is provided, a time interval of a period of time before and after a certain time point is defined as a time window, the predicted arrival time is different from the actual arrival time, but the prediction is considered to be accurate when the time window is reached, and the more accurate prediction can control the aircraft to arrive at a certain position, the shorter the time window is.
The method specifically comprises the following steps:
step 301, taking the current time t as the center, taking the time period h before and after the time t as a time window, and recording the estimated value of the system state in the time period h before and after the time period h as a slave, in order to reduce the error as much as possible
To
Averaging to obtain an average system state estimation value in the time window of
302, based on the average system state estimate
Obtaining the average speed v of the aircraft in the time window, substituting the average speed v into a Doppler frequency shift formula to obtain a Doppler frequency shift f d 。
Doppler shift calculation formula: f. of d ＝f m cos(θ)
Theta is the included angle between the relative motion speed direction and the connecting line of the transmitting and receiving ends; f. of m The maximum doppler shift is indicated and the maximum doppler shift,
f c is the carrier center frequency and C is the speed of light.
Step 303, using the doppler shift for pre-compensation of the received signal to obtain a pre-compensated received signal;
initially, assuming that the transmitted signal is s (n), the received signal r (n) is:
r(n)＝s(n-n d )exp(j*2π*n*Δf*Ts)
wherein j is a constant, and j is a constant,
ts is the sampling period, Δ f is the total frequency shift of the signal during transmission, n d Is the time offset of the signal during transmission.
The pre-compensated received signal is: r' (n) ═ s (n-n) d )exp(j*2π*(Δf-f d )*n*Ts)
And step four, after Doppler frequency shift pre-compensation, the frequency shift of the received signal uses a cyclic prefix and a synchronous signal to carry out time-frequency synchronization.
The cyclic prefix CP is a segment of the end of an OFDM symbol added to the symbol, and has good autocorrelation.
The frequency offset of the received signal is divided into an integer multiple of frequency offset (IFO), Fractional Frequency Offset (FFO), and residual frequency offset for the subcarrier spacing.
(1) Integer multiple frequency offset IFO
Firstly, a plurality of OFDM symbols are subjected to sliding correlation calculation by using cyclic prefixes, the point of obtaining the maximum peak value is the starting point of one OFDM symbol, and the time offset n in the transmission process is obtained d ；
Then, the OFDM symbol time coarse synchronization and the integer frequency offset synchronization of the frequency domain of the system are completed by utilizing the maximum likelihood algorithm.
The correlation function r (n) of the received signal r (n) is:
wherein d represents a timing pointer, N represents the number of subcarriers of an OFDM symbol, and L is the CP length;
then integer frequency offset estimate epsilon IFO Comprises the following steps:
wherein d is ml Is the start time of the OFDM symbol.
(2) Fractional frequency offset FFO
PSS (Primary Synchronization Signal) is utilized to carry out decimal frequency offset estimation, a received PSS Signal p (n) is divided into a front section and a rear section, conjugate multiplication is respectively carried out on the front section and the rear section and the local unbiased PSS Signal s (n), and then decimal frequency offset epsilon is obtained FFO Comprises the following steps:
(3) residual frequency offset
In an actual situation, after the FFO and the IFO estimation are completed, some residual frequency offset still exists, and the frequency offset adjustment is performed on the residual frequency offset by training and using a phase-locked loop.
And step five, demodulating the received signals after time-frequency synchronization is completed, acquiring self speed information, position information and aircraft intention in the received signals, returning to the step two, feeding back to the predicted initial track, correcting the predicted initial track, and performing next four-dimensional track prediction according to the corrected data.
In a general linear hybrid model equation, z (t) is an observed value at the current time, and noise n (t) exists, but a sub-error is derived from a measuring instrument and cannot be estimated. The noise matrix w (t) existing in the state equation can be estimated through the real value of the state at the previous moment and the estimated value of the state at the previous moment obtained after the signal is demodulated, so that the prediction is more accurate, and the pre-compensation estimation of the Doppler frequency shift is more accurate.
Examples
In this embodiment, the doppler shift compensation method based on four-dimensional flight path includes the following specific steps:
step one, considering a real observation equation and a state equation, and completing prediction of an initial flight path based on Kalman filtering;
the state equation and the observation equation are respectively:
X(t)＝AX(t-1)+BU(t-1)+w(t)
Z(t)＝H(t)X(t)+n(t)
in the state information received by the receiving end, the speed and the position of the aircraft at the last moment are known, and the real state value representing the last moment can be known. In the state equation, a noise term w (t) is arranged in the system state equation X (t), when time reaches the time k, the actual state value at the time k-1 can be known, the predicted value is also recorded, and the difference between the actual state value and the predicted value can be compared at the time, so that the noise magnitude can be obtained. Considering that the noise is gaussian noise, the mean is 0 but covariance exists, and the noise can be calculated by calculating a covariance matrix at this time.
In an actual process, the covariance matrix of the noise may be constantly changed, and in view of this point, the variance ratio of covariance proof may be calculated by differentiating the covariance matrix at the previous time, so as to complete estimation of the covariance matrix at the next time, and then the estimated covariance matrix is brought into the state equation, so that a better result may be obtained.
The prediction of the initial track is completed based on Kalman filtering, and the specific process is as follows:
the state matrix of the aircraft is an n-dimensional column vector, set X T (t)＝[v x ,v y ,v z ,p x ,p y ,p z ,a x ,a y ,a z ]；
Wherein, [ v ] x ,v y ,v z ]Is the velocity component in the three directions of the aircraft xyz, [ p ] x ,p y ,p z ]Is the three position coordinates of the aircraft, [ a ] x ,a y ,a z ]Are the acceleration components in three directions of the aircraft.
For the state transition matrix a, a is an n × n matrix, the state of the aircraft at the next time can be estimated according to the existing state of the aircraft, and is obtained according to the motion formula:
wherein b is 1/2k 2 And k is the time interval between the last time and the current time.
The control matrix B is used to input entries for various human intervention movements of the aircraft, such as steering and landing control actions. The control matrix is typically an n-dimensional column vector and has values only in three terms of acceleration. For simplicity, the control vector is set here as a unit matrix of order n.
The noise matrix w (t) is a 9-dimensional column vector whose content is consistent with x (t), represents the noise on the position velocity and acceleration components, and is gaussian noise with a mean value of 0 and a covariance matrix of Q.
The observed value Z (t) in the Kalman filtering process is a three-dimensional column vector and records the observed value of the xyz coordinate position of the aircraft.
Observation matrix
The observation noise n (t) is a 3-dimensional column vector whose content is consistent with the observation value z (t), represents the noise of the aircraft position, and is gaussian noise with a mean value of 0 and a covariance of R.
Step two, after the initialization prediction of the flight path is finished by Kalman filtering, the compensation of Doppler frequency shift is carried out;
the formula for calculating the doppler shift is:
theta is the included angle between the relative motion speed direction and the connecting line of the transmitting and receiving ends.
Assuming that the transmission signal is s (n) and the reception signal is r (n), it can be known that r (n) is s (n-n) d ) exp (j × 2 pi × Δ f × n × Ts), where Δ f represents the frequency shift due to doppler shift and other factors, n d Representing the time domain deviation in the transmission.
The pre-compensated signal is r' (n) s (n-n) d )exp(j*2π*(Δf-f d )*n*Ts)，f d The estimated value of the Doppler frequency shift is obtained by track prediction, and then only normal time-frequency synchronization is needed to receive signals.
The precompensation of the Doppler frequency shift is completed through the track prediction, compared with the traditional method of directly performing time-frequency synchronization, the method has the advantages that the requirement on the time-frequency synchronization capability of a receiving end is reduced, some devices with low original frequency offset correction capability can also receive signals with large Doppler frequency shift, the requirement on the time-frequency synchronization capability of the devices is reduced, and the manufacturing cost is also reduced. Secondly, the convergence process of time-frequency synchronization is accelerated, the frequency of the signal is closer to the correct frequency through the pre-compensation of Doppler frequency shift, the time for synchronizing to the correct frequency is reduced, and in the aspect of synchronization maintenance, when the frequency of the aircraft deviates due to execution of various actions or other changes, the frequency of the signal can be tracked more accurately.
And step three, after the signal reception is finished, the content in the received signal can be demodulated, and after the state information of the aircraft is also put into the signal, the track prediction can be further perfected through the state information, so that the Doppler frequency shift can be estimated more accurately.
Claims (3)
1. A Doppler frequency shift synchronization method based on four-dimensional track prediction is characterized by comprising the following specific steps:
firstly, observing and recording the actual running track of an aircraft to be tested, and expressing the actual running track by using a linear mixed model; based on a Kalman filtering mode, a linear mixed model is combined to carry out initialization prediction on the four-dimensional track of the aircraft to obtain a system state estimation value of the aircraft at each moment
Then, obtaining an average Doppler frequency shift according to an average system state estimation value of the aircraft in a time window, and pre-compensating a received signal; performing time-frequency synchronization on the frequency deviation of the received signal after the Doppler frequency shift precompensation by using a cyclic prefix and a synchronization signal;
finally, demodulating the received signal after time-frequency synchronization is completed, acquiring self-contained speed information, position information and aircraft intention in the received signal, feeding back to the predicted initial track, correcting the predicted initial track, and performing next four-dimensional track prediction according to the corrected data;
the linear hybrid model comprises an observation equation and a state equation which are respectively expressed as follows:
the state equation is as follows: x (t) ═ AX (t-1) + BU (t-1) + w (t)
The observation equation: z (t) h (t) x (t) + n (t)
Wherein, x (t) is a real state vector including real three-dimensional coordinates of the aircraft, component velocities in three directions, and accelerations in three directions; x (t) is the true state at time t, and X (t-1) is the true state at time t-1; a is a real state transition matrix; w (t) is the noise matrix at the current time; u (t-1) represents the real control vector at the time of t-1; b is a true control matrix representing the transformation of the input true control vector into a state vector;
z (t) is the system true observation at time t; n (t) represents the real observation noise at time t, with a mean of 0 and a covariance of R; h (t) represents the true observation matrix at time t;
the pre-compensation is carried out on the received signal, and the specific process is as follows:
step 301, taking the current time t as the center, taking the time period h before and after the time t as a time window, and recording the system state estimation value as a slave
To
Averaging to obtain an average system state estimation value in the time window of
302, based on the average system state estimate
Obtaining the average speed v of the aircraft in the time window, substituting the average speed v into a Doppler frequency shift formula to obtain a Doppler frequency shift f d ；
Doppler shift calculation formula: f. of d ＝f m cos(θ)
Theta is an included angle between the relative motion speed direction and a connecting line of the receiving and transmitting ends; f. of m The maximum doppler shift is indicated and the maximum doppler shift,
f c is the carrier center frequency, C is the speed of light;
step 303, using the doppler shift for pre-compensation of the received signal to obtain a pre-compensated received signal;
assuming that the transmitted signal is s (n), the received signal r (n) is:
r(n)＝s(n-n d )exp(j*2π*n*Δf*Ts)
wherein the content of the first and second substances,
ts is the sampling period, Δ f is the total frequency shift of the signal during transmission, n d Is the time offset of the signal during transmission;
the pre-compensated received signal is: r' (n) ═ s (n-n) d )exp(j*2π*(Δf-f d )*n*Ts)。
2. The Doppler frequency shift synchronization method based on four-dimensional track prediction according to claim 1, wherein the estimated value of the system state of the aircraft at each moment is obtained in a Kalman filtering manner
The specific process is as follows:
step 201, according to the real state vector and the real control vector at the t-1 moment, calculating the system state predicted value X at the t moment p (t)；
X p (t)＝A*X p (t-1)+B*U(t-1)
Step 202, using the real system observation value Z (t) and the predicted system state value X p (t) calculating the covariance P - (t)；
P - (t)＝AP(t-1)A T +Q
Q represents the covariance matrix of the noise matrix w (t); p (t-1) represents the covariance of the true state vector at time t-1 and its optimal estimate;
the optimal estimate of the true state value is: estimating the observation noise to obtain an approximate real state value;
step 203, utilizing the real observation value Z (t-1) at the time of t-1 and the system state prediction value X p Covariance P of (t-1) - (t-1) updating the parameters of Kalman filtering to obtain Kalman filtering gain K:
K＝P - (t-1)H T (HP - (t-1)H T +R) -1
step 204, using Kalman filter gain K and system state predicted value X at time t p (t) calculating an estimated value of the system state at time t
Step 205, updating the real value at the time t and the covariance P (t) of the optimal estimation, returning to the step 201 to perform Kalman filtering at the next time, and obtaining the system state estimation value at the next time;
P(t)＝(1-KH)*P - (t-1)。
3. the doppler shift synchronization method according to claim 1, wherein the frequency offset of the received signal is divided into an integer multiple of frequency offset (IFO), a Fractional Frequency Offset (FFO), and a residual frequency offset, and the time-frequency synchronization process is performed by:
(1) integer multiple frequency offset IFO
Firstly, a plurality of OFDM symbols are subjected to sliding correlation calculation by using cyclic prefixes, the point of obtaining the maximum peak value is the starting point of one OFDM symbol, and the time offset n in the transmission process is obtained d ；
Then, the OFDM symbol time coarse synchronization and the integer frequency offset synchronization of the frequency domain of the system are completed by utilizing a maximum likelihood algorithm;
the correlation function r (n) of the received signal r (n) is:
then integer frequency offset estimate epsilon IFO Comprises the following steps:
wherein d is ml Is the start time of the OFDM symbol;
(2) fractional frequency offset FFO
Dividing the received PSS signal p (n) into two sections, and performing conjugate multiplication with the PSS signal s (n) without local deviation to obtain decimal frequency deviation epsilon FFO ：
(3) Residual frequency offset
And training to use a phase-locked loop to perform frequency offset adjustment on the residual frequency offset.
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