阅读说明：本技术 一种分路径水声信道跟踪方法 (Sub-path underwater acoustic channel tracking method ) 是由 李维 顾佳倩 詹伟程 李秀清 于 2020-03-03 设计创作，主要内容包括：本发明提供了一种分路径水声信道跟踪方法,包括以下步骤：S1、基于收发机之间的相对运动给出分路径的时延和多普勒因子时变状态模型；S2、利用基于随机有限集的概率密度假设滤波器进行多路径参数跟踪,获得分路径信息。本发明的有益效果是：结合水声信道基本物理特性及多目标跟踪技术设计在随机有限集框架下的水声多径信道跟踪器,实现了多径信道特征参数的分路径跟踪。(The invention provides a sub-path underwater acoustic channel tracking method, which comprises the following steps: s1, giving time-varying state models of time delay and Doppler factors of the branch paths based on the relative motion between the transceivers; and S2, performing multi-path parameter tracking by using a probability density hypothesis filter based on a random finite set to obtain branch path information. The invention has the beneficial effects that: the underwater acoustic multipath channel tracker under the random finite set frame is designed by combining the basic physical characteristics of the underwater acoustic channel and the multi-target tracking technology, and the path-splitting tracking of the multipath channel characteristic parameters is realized.)

1. A method for tracking a sub-path underwater acoustic channel, comprising the steps of:

s1, giving time-varying state models of time delay and Doppler factors of the branch paths based on the relative motion between the transceivers;

and S2, performing multi-path parameter tracking by using a probability density hypothesis filter based on a random finite set to obtain branch path information.

2. The method of claim 1, wherein the method comprises: in step S1, the relationship between the delay and doppler factor at each time and the previous time is calculated to obtain a state model of the underwater acoustic channel parameters.

3. The method of claim 2, wherein the method comprises: in step S2, a random finite set of underwater acoustic channel state information in a shallow sea underwater acoustic environment is established.

4. The method of claim 3, wherein the method comprises: in step S1, the delay and doppler of the path i at time k are obtained from the properties of the right triangle:

time delayDoppler device

Finishing to obtain:

setting intermediate variable under the k time path i

Then the delay and doppler for path i at time k +1 are:

noting the state vector asThe equation of state is

The measurement equation is

Wherein the content of the first and second substances,

c is 1500m/s, and the propagation speed of sound in water is c;

D_i(k) the equivalent distance of the path i at the kth moment in the connecting line direction of the signal source S and the receiver R;

d_2ithe equivalent distance of the path i at the kth moment in the vertical direction of the connecting line of the signal source S and the receiver R;

is the included angle of the path i at the k moment in the moving direction of the receiver R;

the distance between the sea surface and the seabed is d meters;

t is tracking interval time;

the signal source S and the receiver R are always parallel to the sea surface and the seabed and are d1 meters away from the sea surface, and the initial distance is dsr meters; the receiver R is far away from the transmitter at v m/s.

5. The method of claim 2, wherein the method comprises: in step S2, constructing a random finite set of multipath channel state information based on Random Finite Set (RFS) theory;

it is known that in underwater acoustic communication, the probability that a certain path continues to exist or disappear at the next time is random, and whether a new path is generated at the next time cannot be confirmed, wherein the randomness mainly represents the change of the number of multipaths and channel state information at a certain time, and the channel state information RFS at the time k is recorded as

In the formula x_k,iThe state vector of the ith multipath at time k,

N_k-the number of multipaths at time k is a random number;

X_k-1-channel state information RFS at time k;

_k-k isPunctuated new emerging channel information RFS;

-multipath channel state information RFS surviving at time k-1 to time k;

it is known that the measured values of the multipath channel state information are also random, because it is uncertain whether each channel generates an observed value or is missed to be detected at the receiving end, and whether the receiver is false alarm information, so the number of the measured values is random, and the change of the channel state information affected by the communication environment is also random, and the channel state information measurement RFS at the time k is represented as:

in the formula z_k,i-measurement vector of ith multipath at time k;

M_k-the number of multipaths at time k is a random number;

K_k-clutter information RFS at time k;

Θ_k(x) -measurement RFS of multipath channel at time k;

the most recursive formula based on the multi-target Bayesian filter of the formula (6) and the formula (7) is as follows:

p_k|k-1(X_k|Z_1:k-1)＝∫f_k|k-1(X_k|X)p_k-1(X|Z_1:k-1)μ_S(dX) (8)

in the formula p_k(·|Z_1:k) -multi-objective posterior probability;

f_k|k-1(. I.) -multi-target transition probability;

g_k(. I.) -multiple target likelihoods;

the Probability Hypothesis Density Filter (PHD) algorithm is adopted to transfer the posterior intensity to replace the multi-target posterior Probability, and the method is an approximation method based on the first-order statistical moment of the multi-target state;

basic assumptions for the PHD filtering algorithm include:

① the status and measurement of each target are not related to each other;

② the clutter is independent of the target measurement and obeys Poisson distribution;

③ the newborn target is independent of the surviving target;

the assumption of multi-target tracking PHD in linear gaussian mode becomes more rigid:

a1: assuming that each target and sensor is based on a linear gaussian model;

f_k|k-1(x|ζ)＝N(x；F_k-1ζ,Q_k-1) (10)

g_k(z|x)＝N(z；H_kx,R_k) (11)

where N (·; m, P) -Gaussian distribution with mean m and covariance P;

F_k-1-a channel state transition matrix;

Q_k-1-a covariance matrix of the process noise;

H_k-measuring the matrix;

R_k-measuring a covariance matrix of the noise;

a2: the survival probability and the detection probability of the path are assumed to exist independently, namely:

p_S,k(x)＝p_S,k,P_D,k(x)＝P_D,k(12)

a3: assuming the new channel state also follows a gaussian pattern and assuming no derivation, the new channel strength function is as follows:

in the formula-the weight of the new channel;

-expectation of a new channel state;

-a covariance matrix;

J_γ,k-the total number of gaussian terms;

the filtering process of the PHD algorithm is mainly divided into two steps of prediction and updating:

1) prediction similarly, the posterior intensity function at time k-1 is also in the form of a weighted sum of gaussians:

the channel state prediction strength function at time k is

v_k|k-1(x)＝v_S,k|k-1(x)+γ_k(x) (15)

In the formula v_S,k|k-1(x) -a function of the strength of the surviving channel,

γ_k(x) -a new channel strength function, as shown in equation (13);

-the expectation of the multi-path state,a state estimating section in the predicting step;

-the covariance estimation part of the prediction step,

2) if the prediction strength function at the k time is written into a weighted sum form:

then, time k is updated to

In the formula-measuring an intensity function of the information;

-a posterior probability of the measurement information;

-multipath state expectation estimation;

-multipath covariance matrix estimation;

-gain factor calculation;

meanwhile, the PHD estimates the number of randomly varying targets, and is also divided into two steps of prediction and update:

however, when the number of targets is large, the accuracy of PHD estimation target number is greatly reduced, and a potential estimation Probability Hypothesis Density Filter (CPHD) is an improved method for PHD in target number estimation, which adds second-order information of target number and simultaneously transfers the PHD of target and potential estimation of target number in the filtering process; similarly, the CPHD filtering process is mainly prediction and update;

1) the prediction is the same as PHD, the posterior intensity at the k-1 moment is still the formula (14), the prediction intensity function of CPHD at the k moment is the same as PHD, and the prediction of potential estimation is shown in the formula (19);

in the formula p_,k(n-j) -the probability of n-j new paths occurring from time k-1 to k;

C-Combined calculation symbols;

2) the update step of updating the CPHD also includes updates of the potential distribution and intensity functions:

in the formula

The above are PHD and CPHD iterative formulas in a linear Gaussian mode, while a nonlinear system often exists in actual communication, and a nonlinear EK filter and a PHD/CPHD are combined to form an extended Kalman PHD and an extended Kalman CPHD;

writing the general form of a nonlinear system into

x_k＝f_k(x_k-1,v_k-1)，z_k＝h_k(x_k,_k) (22)

Then, in the nonlinear gaussian mode, the iterative formula of the prediction step is different from the linear mode as follows:

in the formula

The iterative formula difference from the linear mode in the update step is as follows:

in the formula

And finally, trimming and combining to obtain a final tracking result, wherein the trimming part removes channel information with lower posterior strength by using a threshold value, and combines similar paths by using a dragging ball threshold.

6. The method of claim 1, wherein the method comprises: the sub-path underwater acoustic channel tracking method is applied to a single carrier time domain system and an OFDM system, hyperbolic frequency modulation signals are adopted in the single carrier time domain system, pilot signals are adopted in the OFDM system, the sub-path measurement is respectively extracted, and the tracking sub-path information is utilized to reconstruct sending signals, so that the primary application of the tracking method in two typical underwater acoustic communication systems is realized.

Technical Field

The invention relates to a channel tracking method, in particular to a sub-path underwater sound channel tracking method.

Background

The traditional channel tracking method, such as the adaptive tracking method, can only roughly recover the whole information of the channel, and can not obtain the branch path information. However, as underwater communication is continuously developed, the importance of underwater acoustic channel parameters in deep understanding of underwater communication environment and in various researches is gradually highlighted, such as channel equalization, environment detection and the like.

Therefore, how to acquire the branch path information is an urgent technical problem to be solved in channel tracking.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a method for tracking a sub-path underwater acoustic channel.

The invention provides a sub-path underwater acoustic channel tracking method, which comprises the following steps:

s1, giving time-varying state models of time delay and Doppler factors of the branch paths based on the relative motion between the transceivers;

and S2, performing multi-path parameter tracking by using a probability density hypothesis filter based on a random finite set to obtain branch path information.

As a further improvement of the present invention, in step S1, the relationship between the delay and doppler factor at each time and the previous time is calculated to obtain a state model of the underwater acoustic channel parameters.

As a further improvement of the present invention, in step S2, a random finite set of underwater acoustic channel state information under shallow sea underwater acoustic environment is established.

As a further improvement of the present invention, in step S1, the time delay and doppler of the path i at time k are obtained according to the properties of the right triangle:

time delayDoppler device

Finishing to obtain:

setting intermediate variable under the k time path i

Then the delay and doppler for path i at time k +1 are:

noting the state vector asThe equation of state is

The measurement equation is

Wherein the content of the first and second substances,

c is 1500m/s, and the propagation speed of sound in water is c;

D_i(k) the equivalent distance of the path i at the kth moment in the connecting line direction of the signal source S and the receiver R;

d_2ithe equivalent distance of the path i at the kth moment in the vertical direction of the connecting line of the signal source S and the receiver R;

is the included angle of the path i at the k moment in the moving direction of the receiver R;

the distance between the sea surface and the seabed is d meters;

t is tracking interval time;

the signal source S and the receiver R are always parallel to the sea surface and the seabed and are d1 meters away from the sea surface, and the initial distance is dsr meters; the receiver R is far away from the transmitter at v m/s.

As a further improvement of the present invention, in step S2, a random finite set of multipath channel state information is constructed based on RFS (random finite set) theory;

it is known that in underwater acoustic communication, the probability that a certain path continues to exist or disappear at the next time is random, and whether a new path is generated at the next time cannot be confirmed, wherein the randomness mainly represents the change of the number of multipaths and channel state information at a certain time, and the channel state information RFS at the time k is recorded as

In the formula x_k,iThe state vector of the ith multipath at time k,

N_k-the number of multipaths at time k is a random number;

X_k-1-channel state information RFS at time k;

_k-new emerging channel information RFS at time k;

-multipath channel state information RFS surviving at time k-1 to time k;

it is known that the measured values of the multipath channel state information are also random, because it is uncertain whether each channel generates an observed value or is missed to be detected at the receiving end, and whether the receiver is false alarm information, so the number of the measured values is random, and the change of the channel state information affected by the communication environment is also random, and the channel state information measurement RFS at the time k is represented as:

in the formula z_k,i-measurement vector of ith multipath at time k;

M_k-the number of multipaths at time k is a random number;

K_k-clutter information RFS at time k;

Θ_k(x) -measurement RFS of multipath channel at time k;

the most recursive formula based on the multi-target Bayesian filter of the formula (6) and the formula (7) is as follows:

p_k|k-1(X_k|Z_1:k-1)＝∫f_k|k-1(X_k|X)p_k-1(X|Z_1:k-1)μ_S(dX) (8)

in the formula p_k(·|Z_1:k) -multi-objective posterior probability;

f_k|k-1(. I.) -multi-target transition probability;

g_k(. I.) -multiple target likelihoods;

the Probability Hypothesis Density Filter (PHD) algorithm is adopted to transfer the posterior intensity to replace the multi-target posterior Probability, and the method is an approximation method based on the first-order statistical moment of the multi-target state;

basic assumptions for the PHD filtering algorithm include:

① the status and measurement of each target are not related to each other;

② the clutter is independent of the target measurement and obeys Poisson distribution;

③ the newborn target is independent of the surviving target;

the assumption of multi-target tracking PHD in linear gaussian mode becomes more rigid:

a1: assuming that each target and sensor is based on a linear gaussian model;

f_k|k-1(x|ζ)＝N(x；F_k-1ζ,Q_k-1) (10)

g_k(z|x)＝N(z；H_kx,R_k) (11)

where N (·; m, P) -Gaussian distribution with mean m and covariance P;

F_k-1-a channel state transition matrix;

Q_k-1-a covariance matrix of the process noise;

H_k-measuring the matrix;

R_k-measuring a covariance matrix of the noise;

a2: the survival probability and the detection probability of the path are assumed to exist independently, namely:

p_S,k(x)＝p_S,k,P_D,k(x)＝P_D,k(12)

a3: assuming the new channel state also follows a gaussian pattern and assuming no derivation, the new channel strength function is as follows:

in the formula-the weight of the new channel;

-expectation of a new channel state;

-a covariance matrix;

J_γ,k-the total number of gaussian terms;

the filtering process of the PHD algorithm is mainly divided into two steps of prediction and updating:

1) prediction similarly, the posterior intensity function at time k-1 is also in the form of a weighted sum of gaussians:

the channel state prediction strength function at time k is

v_k|k-1(x)＝v_S,k|k-1(x)+γ_k(x) (15)

In the formula v_S,k|k-1(x) -a function of the strength of the surviving channel,

γ_k(x) -a new channel strength function, as shown in equation (13);

-the expectation of the multi-path state,a state estimating section in the predicting step;

-the covariance estimation part of the prediction step,

2) if the prediction strength function at the k time is written into a weighted sum form:

then, time k is updated to

In the formula-measuring an intensity function of the information;

-a posterior probability of the measurement information;

-multipath state expectation estimation;

-multipath covariance matrix estimation;

-gain factor calculation;

meanwhile, the PHD estimates the number of randomly varying targets, and is also divided into two steps of prediction and update:

however, when the number of targets is large, the accuracy of PHD estimation target number is greatly reduced, and a potential estimation Probability Hypothesis Density Filter (CPHD) is an improved method for PHD in target number estimation, which adds second-order information of target number and simultaneously transfers the PHD of target and potential estimation of target number in the filtering process; similarly, the CPHD filtering process is mainly prediction and update;

1) the prediction is the same as PHD, the posterior intensity at the k-1 moment is still the formula (14), the prediction intensity function of CPHD at the k moment is the same as PHD, and the prediction of potential estimation is shown in the formula (19);

in the formula p_,k(n-j) -the probability of n-j new paths occurring from time k-1 to k;

C-Combined calculation symbols;

3) the update step of updating the CPHD also includes updates of the potential distribution and intensity functions:

in the formula

The above are PHD and CPHD iterative formulas in a linear Gaussian mode, while a nonlinear system often exists in actual communication, and a nonlinear EK filter and a PHD/CPHD are combined to form an extended Kalman PHD and an extended Kalman CPHD;

writing the general form of a nonlinear system into

x_k＝f_k(x_k-1,v_k-1)，z_k＝h_k(x_k,_k) (22)

Then, in the nonlinear gaussian mode, the iterative formula of the prediction step is different from the linear mode as follows:

in the formula

The iterative formula difference from the linear mode in the update step is as follows:

in the formula

And finally, trimming and combining to obtain a final tracking result, wherein the trimming part removes channel information with lower posterior strength by using a threshold value, and combines similar paths by using a dragging ball threshold.

As a further improvement of the invention, the sub-path underwater acoustic channel tracking method is applied to a single carrier time domain system and an OFDM system, hyperbolic frequency modulation signals are adopted in the single carrier time domain system, pilot signals are adopted in the OFDM system, the measurement of the sub-paths is respectively extracted, and the tracking sub-path information is utilized to reconstruct the sending signals, so that the primary application of the tracking method in two typical underwater acoustic communication systems is realized.

The invention has the beneficial effects that: the underwater acoustic multipath channel tracker under the random finite set frame is designed by combining the basic physical characteristics of the underwater acoustic channel and the multi-target tracking technology, and the path-splitting tracking of the multipath channel characteristic parameters is realized.

Drawings

Fig. 1 is a shallow sea simple sound ray propagation model diagram of the branching underwater acoustic channel tracking method of the present invention.

Fig. 2 is an equivalent diagram of a sound ray propagation model of the method for tracking a sub-path underwater acoustic channel according to the present invention.

Fig. 3 is a diagram of CPHD demodulation process of a method for tracking a split-path underwater acoustic channel according to the present invention.

Detailed Description

The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.

A sub-path underwater acoustic channel tracking method combines the physical characteristics of shallow sea underwater acoustic channels, and is a channel tracking method for directly tracking underwater acoustic multi-path parameters. The multipath channel tracking method based on the random finite set can be applied to an underwater sound single carrier communication system and an OFDM (orthogonal Frequency Division multiplexing) system.

For a random finite set-based multipath channel tracking method, a time delay and Doppler factor time-varying state model of a branch path is given based on relative motion between transceivers. Then, conventional multi-target tracking is converted into multi-path parameter tracking by using a Probability Density Hypothesis Filter (PHD) based on a random finite set and an improved method thereof, and relevant parameters of each path can be obtained.

In addition, the channel tracking techniques described above may be applied in single carrier time domain systems and OFDM systems. The difficulty of the application is in tracking the acquisition of the measurements. In contrast, hyperbolic frequency modulation signals are adopted in a single carrier time domain system, pilot signals are adopted in an OFDM system, and measurement of the sub-paths is extracted respectively. And the tracking sub-path information is utilized to reconstruct the sending signal, thereby realizing the primary application of the tracking method in two typical underwater acoustic communication systems.

The underwater acoustic multipath channel tracker under the random finite set frame is designed by combining the basic physical characteristics of the underwater acoustic channel and the multi-target tracking technology, the sub-path tracking of the multipath channel characteristic parameters is realized, and the method is preliminarily applied to a single carrier system and an OFDM system.

(one) State model

In a shallow sea area, the sound velocity can be approximated to be a constant (c is 1500m/s, which is the propagation velocity of sound in water), and the propagation route of sound waves can be approximated to be a straight line. A simplified ray model of shallow sea channel acoustic transmission is shown in fig. 1. Wherein the upper and lower blue bold lines respectively represent the sea surface and the seabed at a distance of d meters; s and R respectively represent a signal source and a receiver, the signal source and the receiver are always parallel to the sea surface and the sea bottom and are d1 meters away from the sea surface, and the initial distance is dsr meters; the receiver is far away from the transmitter at v m/s.

Numbering according to the position of the first reflection of the sound wave after the sound wave starts from the signal source and the total number of reflection before the sound wave reaches a receiving end: path 1 is a direct path; the paths 2-6 are paths of the first reflection points on the seabed; the path 7-11 is the path of the first reflection point at the sea surface, as noted as path 8 in fig. 1. On the basis, according to the reflection principle and the geometric knowledge of the triangle, the trajectory line can be made into a symmetrical line of the reflection surface by keeping the reflection point still, and finally the trajectory line is equivalent to a triangle, as shown in fig. 2, the trajectory equivalent diagram of the ith path at the kth moment is shown. And calculating the relation between the time delay and the Doppler factor of each moment and the previous moment so as to obtain a state model of the underwater acoustic channel parameters.

The time delay and the Doppler of the path i at the moment k are obtained according to the properties of the right triangle:

time delayDoppler device

After finishing, the following can be obtained:

setting intermediate variable under the k time path i

(2)

Then the delay and doppler for path i at time k +1 are:

noting the state vector asThe equation of state is

The measurement equation is

D_i(k) The equivalent distance of the path i at the kth moment in the connecting line direction of the signal source S and the receiver R;

d_2ithe equivalent distance of the path i at the kth moment in the vertical direction of the connecting line of the signal source S and the receiver R;

is the included angle of the path i at the k moment in the moving direction of the receiver R;

the distance between the sea surface and the seabed is d meters;

t is tracking interval time;

the signal source S and the receiver R are always parallel to the sea surface and the seabed and are d1 meters away from the sea surface, and the initial distance is dsr meters; the receiver R is far away from the transmitter at v m/s.

Design of tracker

Before the underwater acoustic channel tracker based on the random finite set is realized, a random finite set about the underwater acoustic channel state information in the shallow sea underwater acoustic environment needs to be established. In the underwater acoustic channel tracking scenario, a random finite set can be understood as an aggregation space of underwater acoustic state information. The random finite set has two important features: the number of elements in the random finite set is random; and the elements themselves are random, disordered. The method is just consistent with the random change of the number of the multipath channels and the random change of the multipath channel state information in underwater acoustic communication, so that a random finite set of the multipath channel state information is constructed based on an RFS (random finite set) theory.

It is known that in underwater acoustic communication, the probability that a certain path continues to exist or disappear at the next time is random, and whether a new path is generated at the next time cannot be confirmed, and the randomness is mainly represented by the change of the number of multipaths and channel state information at a certain time. Let us note the channel state information RFS at time k

In the formula x_k,iThe state vector of the ith multipath at time k,

N_k-the number of multipaths at time k is a random number;

X_k-1-channel state information RFS at time k;

_k-new emerging channel information RFS at time k;

-multipath channel state information RFS surviving at time k-1 to time k.

It is known that the measured values of the multipath channel state information are also random, because it is uncertain whether each channel generates an observed value or is missed, and whether the receiver has false alarm information, the number of the measured values is random. And the change of the channel state information affected by the communication environment also has a certain randomness. We express the csi measurement RFS at time k as:

in the formula z_k,i-measurement vector of ith multipath at time k;

M_k-the number of multipaths at time k is a random number;

K_k-clutter information RFS at time k;

Θ_k(x) -measurement RFS of multipath channel at time k.

The most recursive formula based on the multi-target Bayesian filter of the formula (6) and the formula (7) is as follows:

p_k|k-1(X_k|Z_1:k-1)＝∫f_k|k-1(X_k|X)p_k-1(X|Z_1:k-1)μ_S(dX) (8)

in the formula p_k(·|Z_1:k) -multi-objective posterior probability;

f_k|k-1(. I.) -multi-target transition probability;

g_k(. I.) -multiple target likelihoods.

The upper form comprises a spaceThe calculation of these integrals is difficult, which undoubtedly increases the computational complexity and complexity of the filter. On the basis, the Probability hypothesis density filtering (PHD) algorithm transfers posterior intensity to replace multi-purposeThe standard posterior probability is an approximate method based on the first-order statistical moment of the multi-target state, and the difficulty of multi-time integral calculation in the multi-target Bayes is effectively reduced.

Basic assumptions for the PHD filtering algorithm include:

① the status and measurement of each target are not related to each other;

② the clutter is independent of the target measurement and obeys Poisson distribution;

③ the newborn target is independent of the surviving target;

the assumption of multi-target tracking PHD in linear gaussian mode becomes more rigid:

a1: assuming that each target and sensor is based on a linear gaussian model;

f_k|k-1(x|ζ)＝N(x；F_k-1ζ,Q_k-1) (10)

g_k(z|x)＝N(z；H_kx,R_k) (11)

where N (·; m, P) -Gaussian distribution with mean m and covariance P;

F_k-1-a channel state transition matrix;

Q_k-1-a covariance matrix of the process noise;

H_k-measuring the matrix;

R_k-measuring the covariance matrix of the noise.

A2: the survival probability and the detection probability of the path are assumed to exist independently, namely:

p_S,k(x)＝p_S,k,P_D,k(x)＝P_D,k(12)

a3: the new channel state is assumed to follow a gaussian pattern as well and no derivation is assumed. The new channel strength function is as follows:

in the formula-the weight of the new channel;

-expectation of a new channel state;

-a covariance matrix;

J_γ,k-total number of gaussian terms.

The filtering process of the PHD algorithm is mainly divided into two steps of prediction and updating:

1. prediction similarly, the posterior intensity function at time k-1 is also in the form of a weighted sum of gaussians:

the channel state prediction strength function at time k is

v_k|k-1(x)＝v_S,k|k-1(x)+γ_k(x) (15)

In the formula v_S,k|k-1(x) -a function of the strength of the surviving channel,

γ_k(x) -a new channel strength function, as shown in equation (13);

-the expectation of the multi-path state,a state estimating section in the predicting step;

-the covariance estimation part of the prediction step,

2. if the prediction strength function at the k time is written into a weighted sum form:

then, time k is updated to

In the formula-measuring an intensity function of the information;

-a posterior probability of the measurement information;

-multipath state expectation estimation;

-multipath covariance matrix estimation;

-gain factor calculation.

Meanwhile, the PHD can also estimate the number of randomly varying targets, which is also divided into two steps of prediction and update:

however, when the number of targets is large, the accuracy of PHD estimation target number is greatly reduced, and a potential estimation Probability Hypothesis Density Filter (CPHD) is an improved method for PHD in target number estimation, which adds second-order information of target number and simultaneously transfers PHD of target and potential estimation of target number in the filtering process. Also, the CPHD filtering process is mainly prediction and update.

1. The prediction is the same as PHD, here the posterior intensity at time k-1 is still equation (14), the prediction intensity function of CPHD at time k is the same as PHD, and the prediction of potential estimation is shown in equation (19).

In the formula p_,k(n-j) -the probability of n-j new paths occurring from time k-1 to k;

C-Combined calculation symbol.

2. The update step of updating the CPHD also includes updates of the potential distribution and intensity functions:

in the formula

The above are PHD and CPHD iterative formulas in the linear gaussian mode, and a nonlinear system often exists in actual communication. For example, the shallow sea water multipath channel state model is a nonlinear model established based on the simple propagation rule of sound waves. In this case, we combine the nonlinear EK filter with PHD/CPHD to form extended Kalman PHD (EK-PHD) and extended Kalman CPHD (EK-CPHD).

Writing the general form of a nonlinear system into

x_k＝f_k(x_k-1,v_k-1)，z_k＝h_k(x_k,_k) (22)

Then, in the nonlinear gaussian mode, the iterative formula of the prediction step is different from the linear mode as follows:

in the formula

The iterative formula difference from the linear mode in the update step is as follows:

in the formula

And finally, trimming and combining to obtain a final tracking result, wherein the trimming part removes channel information with lower posterior strength by using a threshold value, and combines similar paths by using a dragging ball threshold.

Applications of tracker

1. Application in single carrier time domain system

(1) Acquisition of measurement information

In a single carrier time domain system, an estimation method based on hyperbolic frequency modulation signals is selected to obtain a measurement value: inserting a blank information between two sections of HFM signals to construct UMD-HFM signal, obtaining the amplitude and the correlation peak of time delay search HFM signal, and then using the variation of time delay difference of two HFM signals at the transmitting and receiving ends to carry out Doppler estimation.

The UMD-HFM signal is inserted at the head with a swept-up HFM signal, denoted HFM +, and at the tail with a swept-down HFM signal, denoted HFM-. Next we derive in detail how to use the HFM signal delay difference for doppler estimation.

The HFM signal after a path is expressed as:

the instantaneous frequency can be calculated as:

in the formula, b is a constant,

f₁-the starting frequency of the HFM signal;

f₂-the cut-off frequency of the HFM signal;

t-duration of HFM + and HFM-signals;

α -Doppler factor as described previously.

From the above formula, the Doppler time delays of HFM + and HFM-can be obtained respectively as

According to the UMD-HFM and the simulation conditions, the following can be obtained:after the arrangement, an estimation formula of the Doppler factor can be finally obtained:

where B is bandwidth, B ═ f₂-f₁；

f_c-the frequency of the center of the frequency,

so far, the unknown parameters in equation (30) are only the delay difference of the receiving endCan be divided by a matched filterObtaining the difference after obtaining the correlation peak of the up-and-down scanning HFM signal, wherein the specific estimation method comprises the following steps:

① cross-correlating the received signal with HFM +, extracting the correlation peak information to get tau⁺And (6) estimating the value.

② cross-correlating the received signal with HFM-, extracting the information of the correlation peak to get tau^-And (6) estimating the value.

③ are in accordance withAnd finally obtaining an estimated value of the time delay difference of the receiving end.

(2) Signal reconstruction method

It is known that the tracking result directly obtained by the CPHD filter is a parameter estimation value of a multipath channel, and obviously, the received signal cannot be directly equalized, and then demodulation cannot be performed according to a conventional coherent demodulation method. A method for reconstructing a signal directly using discrete channel parameter information is proposed: as shown in FIG. 3, the result is tracked using CPHDAnd constructing a reference signal, recovering the transmitted information by calculating the minimum mean square error and matching the minimum mean square error with the received signal, and finally carrying out BPSK demodulation to obtain the transmitted information.

Firstly, the variables and initial values involved in the method are briefly explained:

1) k is a time counting value, the initial value k is 1, and N times are total;

2) the method comprises the following steps that a data segment index divided according to the influence of a time-varying multipath channel is marked as i, an initial value is that i is equal to 1, each received signal contains n _ data segment data, the influence of the channel received in each segment is the same, and different data segments are affected differently by the channel;

3) j is a code element counting value contained in each section of data, the initial value is j equals to 1, and each section of data information contains n _ bits of code element information;

4) s1 and s0 are symbol sequences with initial values of all 1 s and all 0 s, respectively, and have a length of n _ bits.

And recovering the jth code element in the ith section of data at the time k, wherein the algorithm steps are as follows:

① BPSK modulates s1 and s0, X respectively¹And X⁰：

Wherein x is_jAnd (t) is a modulation signal corresponding to the jth character.

② in modulating signal X¹And X⁰The CPHD tracking information is superposed to obtain a 'reference signal' Y¹And Y²：

Wherein the content of the first and second substances,respectively representing the amplitude, doppler and delay parameter tracking values of the path p tracked by CPHD at time k.

③ the received signal is matched with the reference signal, the criterion is MSE:

if MSE0> MSE1, then updates s1 and s0 are: s1(j) 1; s0(j) 1; otherwise, s1(j) is 0; s0(j) is 0.

④, repeating steps ① - ③ until all code elements are updated, and obtaining the demodulated sequence.

The method is a process for recovering the transmitted signal by directly utilizing the parameter values of the underwater acoustic multipath channel, and the method successfully applies the discrete multipath channel parameter values to channel equalization and signal reconstruction. Under the condition that the structure of the transmitted signal is simpler, the method can accurately demodulate the received signal to obtain the transmitted information, and is less influenced by the strength of the time-varying property of the channel.

Application under OFDM system

(1) Acquisition of measurement information

In the OFDM system, since the correlation peak of the HFM signal is not obvious, the measurement acquisition is different from that of the single carrier system, and the measurement value of the underwater acoustic multipath channel tracker is mainly obtained by the pilot-based channel estimation: firstly, realizing inverse Fourier transform from channel frequency domain impulse response to time domain response; the time delay and the amplitude are obtained by searching the relevant peak of the impulse response of the channel time domain; the estimation method of the doppler factor is shown in equation (30), where the delay difference is given by the channel estimation result of different data blocks.

(2) Signal reconstruction method

As is known in OFDM systems, the measurement information is derived from the frequency-domain impulse response obtained from channel estimation, where the channel impulse response is constructed from empirical formula (35) using the tracked channel parameters to indirectly reconstruct the transmitted signal.

The general expression of the frequency domain impulse response of the underwater acoustic multipath channel, namely the mixing matrix, is as follows:

in the formula N_p-the number of multipath channels;

ξ_p-a gain of the complex path,

Λ_p-a diagonal matrix, the diagonal elements being

_pThe (m, k) element is

b_p-the Doppler factor after the re-sampling,

τ′_p-the multi-path delay after resampling,

-the re-sampling factor is a function of,

the unknown parameters in the above formula include three main characteristic parameters of amplitude, delay and Doppler factor of the multipath channel, and are also direct results of our channel tracking. Record the multipath parameter tracking value asObtaining multipath channel impulse response estimation value by substituting formula (35)The transmitted signal is then estimated using a Minimum Mean Square Error (MMSE) receiver, as shown in equation (36):

in the formula, I is an identity matrix, and the dimension is the same as that of H;

N₀-a noise energy coefficient;

z-receive signal;

-sending the signal estimate.

The steps of the method for reconstructing the transmitted signal using the multipath channel parameters in the OFDM system are shown in table 1.

TABLE 1 channel parametersCalculating bit error rate

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.