1. A TWS radar multi-target continuous tracking method is characterized by comprising the following steps:

selecting each observation received by the TWS radar to form a first preselected observation set by the observation obtained before the current time, wherein the interval between the receiving time of the observation in the first preselected observation set and the current time is 0.8T-1.2T, the observation is not utilized by the existing track, and T is the scanning period of the TWS radar; establishing a flight path according to the first preselected observation set, filtering by combining the state of the flight path, and calculating the predicted estimation of the next updated flight path and the corresponding gate time interval;

and (2) for each existing track, iteratively updating the estimate of the track and the corresponding gate time interval in the continuous tracking process in the following mode:

each time of updating, at the finishing moment of the wave gate time interval corresponding to the current flight path, determining an acquisition time interval according to the wave gate time interval, acquiring the observation in the acquisition time interval, and forming a second preselected observation set; and at the end time of the acquisition time interval, updating the state of the current flight path by using the second preselected observation set, filtering by combining the state of the flight path, and calculating the predicted estimation of the next updated flight path and the corresponding gate time interval.

2. The TWS radar multi-target continuous tracking method according to claim 1,

in step (1), when a flight path is established according to the first preselected observation set, each observation in the first preselected observation set is judged whether the following initialization conditions are met:

wherein z is_x ^reAnd z_y ^reRespectively representing the abscissa and ordinate positions, z, of the observations received at the current moment_x ⁱAnd z_y ⁱRespectively representing the abscissa and ordinate positions, T, of the ith observation in the first preselected observation set_rIs a time difference representing the current time and the time at which the ith observation in the first preselected set of observations was received; v. of_maxRepresenting the target maximum speed, v_errorError representing target velocity calculation;

and if the ith observation in the first preselected observation set meets the initialization condition, initializing the flight path according to the observation at the current moment and the ith observation in the first preselected observation set, and establishing the flight path to obtain the initial state of the flight path.

3. The TWS radar multi-target continuous tracking method according to claim 1,

in the step (2), determining the acquisition time interval according to the wave gate time interval, including:

if the wave gate time intervals corresponding to the current flight path and the rest of the existing flight paths are not crossed, the acquisition time interval is the same as the wave gate time interval corresponding to the current flight path;

if the current flight path is crossed with the gate time intervals corresponding to the rest of the existing flight paths, and the latest gate time interval ending time corresponding to the crossed flight path is equal to or earlier than the gate time interval ending time corresponding to the current flight path, the starting time of the earliest gate time interval corresponding to the crossed flight path and the current flight path is the starting time of the acquisition time interval, and the gate time interval ending time corresponding to the current flight path is the acquisition time interval ending time;

if the current flight path is crossed with the gate time intervals corresponding to the rest of the existing flight paths, and the latest gate time interval ending time corresponding to the crossed flight path is later than the gate time interval ending time corresponding to the current flight path, the starting time of the earliest gate time interval corresponding to the crossed flight path and the current flight path is the starting time of the acquisition time interval, and the latest gate time interval ending time corresponding to the crossed flight path is the ending time of the acquisition time interval.

4. The TWS radar multi-target continuous tracking method according to claim 1,

in the step (2), calculating the prediction estimation of the next updated track and the corresponding gate time interval, including:

calculating clutter densities corresponding to the observations in the second preselected observation set;

selecting the observation in the second preselected observation set according to the wave gate to obtain an observation set for updating;

calculating a likelihood function of each observation in the second preselected observation set and the current track;

modulating clutter density corresponding to the observation in the observation set for updating by combining a likelihood function;

carrying out data association on the observation set used for updating and the current flight path to obtain the posterior probability of the existence of the target and the data association posterior probability;

performing track component control;

updating the track state to obtain a target track state corresponding to the current track;

and calculating the predicted estimation of the next updated track of each track component and the corresponding gate time interval.

5. The TWS radar multi-target continuous tracking method according to claim 4,

in the step (2), calculating clutter densities corresponding to the observations in the second preselected observation set, including:

looking for an observation z_k(i) With said second preselected observation set Z_τ(k) Of the rest of the observations, and a small distance r of nth between the other observationsⁿ(i) N is an integer greater than 0, z_k(i)∈Z_τ(k) K represents the number of updates; if the second preselected observation set Z_τ(k) If the number of observations in (1) is less than (n +1), the observation set received from the beginning of the kth update scan cycle to the current time is defined asLooking for an observation z_k(i) In the observation setMiddle nth small distance rⁿ(i)；

Calculating an observation z_k(i) Corresponding sparsity, the expression is:

γ(z_k(i))＝V(rⁿ(i))/n；

wherein the content of the first and second substances,

Γ (·) is the gamma function, l is the dimension of the space;

calculating clutter density according to sparsity, wherein the expression is as follows:

6. the TWS radar multi-target continuous tracking method according to claim 5,

in the step (2), during the k-th updating, the second preselected observation set Z is updated according to the wave gate_τ(k) The observation of (1) is selected, comprising:

track component c for current track τ_k-1Die ofType σ, selected observation set y_k(c_k-1σ) satisfies:

wherein y is an observation set y_k(c_k-1The observation in (a), the observation in (c),represents the track component c of the current track tau at the kth update_k-1Predicted observation of model σ of (1), S_k(c_k-1σ) track component c at kth update of current track τ_k-1The innovation matrix of the model a of (a),is S_k(c_k-1σ), g is the gate size, the expression is:

chi2inv (·) is chi²Inverse function of the distribution function, P_GRepresenting the gate probability, l represents the dimension of observation y;

for models with different current flight paths tau, all selected observation sets are merged into an observation set for updating

7. The TWS radar multi-target continuous tracking method according to claim 6,

in the step (2), the track component control is carried out, and the method comprises the following steps:

observation set y to be used for updating_kEach observation y in (1)_k(i) With each track component c_k-1Associating to form a temporary track component;the number of temporary track components beingWherein C is_k-1Represents the number of track components after the k-1 th update, m_kRepresenting observation set y for updating_kThe number of observations in (1);

calculating the relative probability of each temporary track component, wherein the expression is as follows:

wherein the content of the first and second substances,representing temporal track componentsRelative probability of (a), beta_k(i) Representation for establishing temporal track componentObservation y of_k(i) Correlating posterior probability, p (c), with data of track τ_k-1) Represents the flight path component c after k-1 th update of the flight path tau_k-1The relative probability of (a) of (b),represents an observation z_k(i) Track component c of current track tau_k-1The likelihood function of (a) is,represents an observation z_k(i) A likelihood function with the current track τ;

performing the leaf clipping of the track component if a temporary track componentRelative to each otherProbability ofIf the value is less than the threshold value, removing the temporary track component

Performing sub-tree cutting of the track component, tracing the track component of the previous update from the current k-th update, and keeping the relative probability p (c) for the k-th update_κ) A maximum track component; k-N, wherein N is subtree cutting depth;

after the track component leaves and the track component subtrees are cut, a temporary track component subset theta is reserved, and the complement set of theta is reservedThen it is deleted;

calculating a complement setIs expressed as:

the temporary track component in Θ is the confirmation track component, using c_kRepresenting, track component c_kThe expression for the relative probability is:

the posterior probability of the existence of the target is adjusted as follows:

p(χ_k|Y^k)＝p(χ_k|Y^k)(1-Δp)。

8. the TWS radar multi-target continuous tracking method according to claim 7,

in the step (2), calculating a gate time interval corresponding to the next updated track of each track component, including:

from the calculated track component c_kUpdating the information matrix obtained by the prediction estimation of the flight path next time, and aiming at the flight path component c of the current flight path tau_kCalculates the range [ theta ] of the corresponding gate azimuth angle_min，θ_max]；

The expression for the range of the wave gate azimuth angle is:

wherein g is the size of the wave gate, θ₀Is the center azimuth angle of the wave gate, S_ijI, j e {1, 2} is the track component c_kOf the model σ_k(c_kσ) of the elements;

calculating the track component c of the current track tau according to the range of the wave gate azimuth angles_kThe gate time range corresponding to the model σ of (a);

after the wave gate time range corresponding to each model of each track component of the current track tau is calculated, the earliest wave gate time interval starting time corresponding to all models of all track components is used as the wave gate time interval starting time of the current track, and the latest wave gate time interval ending time corresponding to all models of all track components is used as the wave gate time interval ending time of the current track.

9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor when executing the computer program implements the steps of the TWS radar multi-target continuous tracking method according to any one of claims 1 to 8.

10. A computer readable storage medium having stored thereon a computer program, wherein the computer program, when executed by a processor, implements the steps of the TWS radar multi-target continuous tracking method of any one of claims 1 to 8.

Background

Most scanning and tracking radar (TWS radar) are mechanically scanned radars that scan a surveillance area by mechanically rotating an antenna to change the direction of the antenna beam. After the target is scanned, the antenna returns an observation of the target to the radar, which tracks the target using the received observation. For a circular scanning TWS radar, when the target is at different azimuth positions in the monitored area, the time from which the antenna scans it is also different, but in the same scanning period, the status updates of these targets are performed simultaneously, which results in a certain delay between processing observations from the reception observations, i.e. a delay problem. In addition, when tracking a target, the conventional tracking method assumes that an antenna detects only one observation from the target in one scanning period, and updates the track state only once in one scanning period. However, in practice, this assumption is not always true. For the circular scanning TWS radar, when the target is near the scanning boundary (i.e. the position of the scanning start or end), the number of times it is detected in one scanning period may not be equal to 1, i.e. a boundary problem occurs, and the accuracy and reliability of tracking are affected.

Disclosure of Invention

Technical problem to be solved

The invention aims to solve the technical problems that the TWS radar low-delay tracking cannot be realized and the tracking stability when a target crosses a scanning boundary cannot be ensured in the prior art.

(II) technical scheme

In order to solve the technical problem, the invention provides a TWS radar multi-target continuous tracking method, which comprises the following steps:

selecting each observation received by the TWS radar to form a first preselected observation set by the observation obtained before the current time, wherein the interval between the receiving time of the observation in the first preselected observation set and the current time is 0.8T-1.2T, the observation is not utilized by the existing track, and T is the scanning period of the TWS radar; establishing a flight path according to the first preselected observation set, filtering by combining the state of the flight path, and calculating the predicted estimation of the next updated flight path and the corresponding gate time interval;

and (2) for each existing track, iteratively updating the estimate of the track and the corresponding gate time interval in the continuous tracking process in the following mode:

each time of updating, at the finishing moment of the wave gate time interval corresponding to the current flight path, determining an acquisition time interval according to the wave gate time interval, acquiring the observation in the acquisition time interval, and forming a second preselected observation set; and at the end time of the acquisition time interval, updating the state of the current flight path by using the second preselected observation set, filtering by combining the state of the flight path, and calculating the predicted estimation of the next updated flight path and the corresponding gate time interval.

Preferably, in step (1), when a flight path is established according to the first preselected observation set, it is determined whether the following initialization conditions are satisfied for each observation in the first preselected observation set:

wherein z is_x ^reAnd z_y ^reRespectively representing the abscissa and ordinate positions, z, of the observations received at the current moment_x ⁱAnd z_y ⁱRespectively representing the abscissa and ordinate positions, T, of the ith observation in the first preselected observation set_rIs a time difference representing the current time and the time at which the ith observation in the first preselected set of observations was received; v. of_maxRepresenting the target maximum speed, v_errorError representing target velocity calculation;

and if the ith observation in the first preselected observation set meets the initialization condition, initializing the flight path according to the observation at the current moment and the ith observation in the first preselected observation set, and establishing the flight path to obtain the initial state of the flight path.

Preferably, in the step (2), determining the acquisition time interval according to the gate time interval includes:

if the wave gate time intervals corresponding to the current flight path and the rest of the existing flight paths are not crossed, the acquisition time interval is the same as the wave gate time interval corresponding to the current flight path;

if the current flight path is crossed with the gate time intervals corresponding to the rest of the existing flight paths, and the latest gate time interval ending time corresponding to the crossed flight path is equal to or earlier than the gate time interval ending time corresponding to the current flight path, the starting time of the earliest gate time interval corresponding to the crossed flight path and the current flight path is the starting time of the acquisition time interval, and the gate time interval ending time corresponding to the current flight path is the acquisition time interval ending time;

if the current flight path is crossed with the gate time intervals corresponding to the rest of the existing flight paths, and the latest gate time interval ending time corresponding to the crossed flight path is later than the gate time interval ending time corresponding to the current flight path, the starting time of the earliest gate time interval corresponding to the crossed flight path and the current flight path is the starting time of the acquisition time interval, and the latest gate time interval ending time corresponding to the crossed flight path is the ending time of the acquisition time interval.

Preferably, in the step (2), calculating the predicted estimate of the next updated track and the corresponding gate time interval includes:

calculating clutter densities corresponding to the observations in the second preselected observation set;

selecting the observation in the second preselected observation set according to the wave gate to obtain an observation set for updating;

calculating a likelihood function of each observation in the second preselected observation set and the current track;

modulating clutter density corresponding to the observation in the observation set for updating by combining a likelihood function;

carrying out data association on the observation set used for updating and the current flight path to obtain the posterior probability of the existence of the target and the data association posterior probability;

performing track component control;

updating the track state to obtain a target track state corresponding to the current track;

and calculating the predicted estimation of the next updated track of each track component and the corresponding gate time interval.

Preferably, in step (2), calculating a clutter density corresponding to each observation in the second pre-selected observation set comprises:

looking for an observation z_k(i) With said second preselected observation set Z_τ(k) Of the rest of the observations, and a small distance r of nth between the other observationsⁿ(i) N is an integer greater than 0, z_k(i)∈Z_τ(k) K represents the number of updates; if the second preselected observation set Z_τ(k) If the number of observations in (1) is less than (n +1), the observation set received from the beginning of the kth update scan cycle to the current time is defined asLooking for an observation z_k(i) In the observation setMiddle nth small distance rⁿ(i)；

Calculating an observation z_k(i) Corresponding sparsity, the expression is:

γ(z_k(i))＝V(rⁿ(i))/n；

wherein the content of the first and second substances,

Γ (·) is a gamma function,is the dimension of the space;

calculating clutter density according to sparsity, wherein the expression is as follows:

preferably, in step (2), at the time of k-th update, the second preselected observation set Z is updated according to a wave gate_τ(k) The observation of (1) is selected, comprising:

track component c for current track τ_k-1Model σ of (c), selected observation set y_k(c_k-1σ) satisfies:

wherein y is an observation set y_k(c_k-1The observation in (a), the observation in (c),represents the track component c of the current track tau at the kth update_k-1Predicted observation of model σ of (1), S_k(c_k-1σ) track component c at kth update of current track τ_k-1The innovation matrix of the model a of (a),is S_k(c_k-1σ), g is the gate size, the expression is:

chi2inv (·) is chi²Inverse function of the distribution function, P_GRepresenting the gate probability, l represents the dimension of observation y;

for models with different current flight paths tau, all selected observation sets are merged into an observation set for updating

Preferably, in step (2), the track component control includes:

observation set y to be used for updating_kEach observation y in (1)_k(i) With each track component c_k-1Associating to form a temporary track component; the number of temporary track components beingWherein C is_k-1Represents the number of track components after the k-1 th update, m_kRepresenting observation set y for updating_kThe number of observations in (1);

calculating the relative probability of each temporary track component, wherein the expression is as follows:

wherein the content of the first and second substances,representing temporal track componentsRelative probability of (a), beta_k(i) Representation for establishing temporal track componentObservation y of_k(i) Correlating posterior probability, p (c), with data of track τ_k-1) Represents the flight path component c after k-1 th update of the flight path tau_k-1The relative probability of (a) of (b),represents an observation z_k(i) Track component c of current track tau_k-1The likelihood function of (a) is,represents an observation z_k(i) A likelihood function with the current track τ;

performing the leaf clipping of the track component if a temporary track componentRelative probability ofIf the value is less than the threshold value, removing the temporary track component

Performing sub-tree clipping on the track component, tracing the previously updated track component from the current k-th update onwards, and keeping the relative probability p (for the k-th update)c_κ) A maximum track component; k-N, wherein N is subtree cutting depth;

after the track component leaves and the track component subtrees are cut, a temporary track component subset theta is reserved, and the complement set of theta is reservedThen it is deleted;

calculating a complement setIs expressed as:

the temporary track component in Θ is the confirmation track component, using c_kRepresenting, track component c_kThe expression for the relative probability is:

the posterior probability of the existence of the target is adjusted as follows:

p(χ_k|Y^k)＝p(χ_k|Y^k)(1-Δp)。

preferably, in the step (2), calculating a gate time interval corresponding to the next updated track of each track component includes:

from the calculated track component c_kUpdating the information matrix obtained by the prediction estimation of the flight path next time, and aiming at the flight path component c of the current flight path tau_kCalculates the range [ theta ] of the corresponding gate azimuth angle_min，θ_max]；

The expression for the range of the wave gate azimuth angle is:

wherein g is the size of the wave gate, θ₀Is the center azimuth angle of the wave gate, S_ijI, j e {1, 2} is the track component c_kOf the model σ_k(c_kσ) of the elements;

calculating the track component c of the current track tau according to the range of the wave gate azimuth angles_kThe gate time range corresponding to the model σ of (a);

after the wave gate time range corresponding to each model of each track component of the current track tau is calculated, the earliest wave gate time interval starting time corresponding to all models of all track components is used as the wave gate time interval starting time of the current track, and the latest wave gate time interval ending time corresponding to all models of all track components is used as the wave gate time interval ending time of the current track.

The invention also provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the TWS radar multi-target continuous tracking method when executing the computer program.

The invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps of any one of the TWS radar multi-target continuous tracking methods described above.

(III) advantageous effects

The technical scheme of the invention has the following advantages: the invention provides a TWS radar multi-target continuous tracking method, computer equipment and a computer readable storage medium, in the multi-target continuous tracking process, a corresponding gate time interval is established through a target track, and the track state is timely updated according to the gate time interval, so that the tracking delay is reduced to the maximum extent, the TWS radar low-delay tracking is realized, and the tracking accuracy is improved.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.

FIG. 1 is a schematic diagram of TWS radar tracking delay;

FIG. 2(a) is a schematic diagram of a boundary problem for TWS radar;

FIG. 2(b) is a schematic diagram of another boundary problem for TWS radar;

FIG. 3 is a schematic diagram illustrating steps of a TWS radar multi-target continuous tracking method according to an embodiment of the present invention;

FIG. 4 is a diagram of a target motion trajectory;

FIG. 5(a) is a graph of the IMM-LMITS method versus the target tracking results of FIG. 4;

FIG. 5(b) is a diagram of a target tracking result of the TWS radar multi-target continuous tracking method in the embodiment of the present invention with respect to FIG. 4;

FIG. 6(a) shows the tracking delay of target 1 by the IMM-LMITS method;

FIG. 6(b) shows the tracking delay of a target 1 by a TWS radar multi-target continuous tracking method in the embodiment of the present invention;

FIG. 7(a) shows the tracking delay of target 2 by the IMM-LMITS method;

FIG. 7(b) shows the tracking delay of a target 2 by a TWS radar multi-target continuous tracking method in the embodiment of the present invention;

FIG. 8(a) shows the IMM-LMITS method and the position RMSE of the tracking target 1 by the TWS radar multi-target continuous tracking method in the embodiment of the present invention;

FIG. 8(b) shows the position RMSE of the tracking target 2 by the IMM-LMITS method and one TWS radar multi-target continuous tracking method in the embodiment of the present invention;

FIG. 9(a) shows the velocity RMSE of a tracking target 1 by the IMM-LMITS method and one TWS radar multi-target continuous tracking method in the embodiment of the present invention;

FIG. 9(b) shows the velocity RMSE of the tracking target 2 by the IMM-LMITS method and one TWS radar multi-target continuous tracking method in the embodiment of the present invention;

FIG. 10 shows a comparison of true track rate for an IMM-LMITS method and a TWS radar multi-target continuous tracking method in an embodiment of the invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer and more complete, the technical solutions in the embodiments of the present invention will be described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention, and based on the embodiments of the present invention, all other embodiments obtained by a person of ordinary skill in the art without creative efforts belong to the scope of the present invention.

As mentioned above, referring to FIG. 1, the TWS radar is used for tracking, the radar antenna is set to rotate counterclockwise, two targets are in the space, and the track for tracking the two targets is T₁(k₁) And T₂(k₂) If the two tracks are at t respectively₁And t₂The time instants are scanned by the antennas. The antenna then continues to scan, at t_endAt that time, the antenna ends the scanning of this scanning period. Target update at t_endThe time goes on, then two tracks T₁(k₁)，T₂(k₂) Respectively, is t_delay1＝t_end-t₁，t_delay2＝t_end-t₂. The closer the target is to the position where the scanning period starts, i.e. the smaller the antenna azimuth angle corresponding to the target position, the greater the tracking delay.

In addition, the conventional tracking method also causes a boundary problem when the target crosses the boundary. As shown in figure 2(a) of the drawings,the antenna rotating in an anti-clockwise direction, if track T₁(k₁) Kth of tracked object₁The sub-scanning takes place at t₁Time of day, kth₁+1 scans occur at t₂Time of day, and target at t₁And t₂Crossing the boundary clockwise between moments, t₂The moment is earlier than the end moment t of the scanning period_endThus, in the same scanning cycle, the target is detected twice by the antenna, returning two observations. As shown in fig. 2(b), the antenna rotates counterclockwise at the k-1 th scanning period, if the antenna is at t₁Scanning to track state T at all times₁(k₁) The tracked target, and the antenna end the k-1 th scanning period thereafter, and enter the k-th scanning period. During this time, the target crosses the scan boundary counterclockwise, resulting in the antenna not scanning the target at the kth scan cycle. In the k +1 th scanning period t₂The antenna scans the target again at the moment, and the corresponding track state is T₁(k₁+1). As such, the antenna returns zero observations during the kth scan cycle, i.e., the antenna is not scanning the target during the kth scan cycle. For the conventional method, the k-1 th scanning period observes z for the k-th scanning period target_kActually occurs at the (k +1) th scan cycle. Thus, the predicted observations of the tracking method are misaligned with the actually received observations. At the end of the kth scan cycle, conventional methods use predicted observations to make an observation selection of all observations received during the kth scan cycle to select observations from the target. But in practice it is the desired observation z from the target_kThere is an observation set for the (k +1) th scan cycle. Thus, the conventional method considers that the k-th scanning period has a false alarm, updates and estimates the track state under the premise of lacking observation, and predicts the next observation again. At the end of the k +1 th scan cycle, the conventional method continues with the update. This observation z expected by the conventional method_k+1In practice, it is scanned only during the (k + 2) th scanning period. As a result, the conventional method cannot correctly obtain the observation from the target after the boundary problem occurs. This time may beThere are two consequences: (1) the flight path wave gate is large enough to correlate to the target observation z in the k +1 th scanning period_k. This is a false correlation that can result in reduced accuracy of the tracking system and possibly also in track breaking. (2) The track wave gate is small and cannot be correlated to the observation from the target all the time. This can lead to track breaks. But this track break does not last too long. A new flight path will be initiated to track the current target after a few scan cycles.

To minimize tracking delay, it is preferable to update the state of the track as the antenna sweeps to the end of the gate of the track. The specific implementation method of the scheme relies on the observation selection technology based on the wave gate. In the observation selection technique, the gate is a range of observations that contains, with a probability close to 1, an observation from a target tracked by the current track. Thus, when the antenna is swept across the gate, there is a very small probability that no observation from the target is scanned. Updating at this time achieves a minimum of tracking delay theoretically. The invention researches the shape of the wave gate and uses the geometrical relation to calculate the azimuth angle when the antenna sweeps over the tail end of the wave gate so as to obtain the corresponding time, therefore, the updated time can be determined when the wave gate is built. When the time of the TWS radar reaches the time corresponding to the tail end of the wave gate, the corresponding track is updated, so that the tracking delay is reduced to the maximum extent, and the delay problem is solved. The root cause of the boundary problem is that the number of detections and the number of updates to the target within one scanning period do not match. Therefore, the invention replaces the original thinking of updating according to the scanning period, and updates according to the time instead, and updates once every detection, thereby thoroughly solving the boundary problem. The invention combines a linear multi-target method (LM) and an interactive multi-model method (IMM) to realize the tracking of a plurality of targets, and the continuous tracking method provided by the invention can be called as an IMM-LMCITS method for short.

Specific implementations of the above concepts are described below.

As shown in fig. 3, a TWS radar multi-target continuous tracking method provided by the embodiment of the present invention includes:

step 301, for each observation z received by TWS radar_reChoosing to obtain observation z_reConstitute a first preselected observation setFirst set of preselected observationsThe interval between the TWS radar receiving time corresponding to the internal observation and the current time is 0.8T-1.2T, and a first preselected observation setThe internal observation is not utilized by the existing track, T is the scanning period of one rotation of the TWS radar, and a first preselected observation set is setIncluding the number of observations ofk represents the updating times, k is greater than or equal to 2, and k is equal to 1 and corresponds to the first scanning period;

according to a first preselected observation setAnd establishing a flight path, filtering by combining the state of the flight path, and calculating the prediction estimation of the next updated flight path (namely the k +1 th updated flight path) and the corresponding gate time interval.

In the method provided by the invention, every time an observation is received, the operation of track initialization is carried out, and the track is tried to be established. In order to improve the reliability of the new track, a speed wave gate can be used as a condition for establishing the new track, if the condition is met, the new track is established, and if the condition is not met, the received observation is stored for subsequent use. Obviously, if the first set of preselected observations isFor empty gathers, it is considered that no track can be established。

Preferably, in step 301, when a track is created according to the first pre-selected observation set, a velocity wave gate is created with each observation in the first pre-selected observation set as a center, and it is determined whether a new track can be created, that is, for each observation in the first pre-selected observation set, it is determined whether the observation satisfies the following initialization conditions:

wherein z is_x ^reAnd z_y ^reRespectively representing observations z received by the TWS radar at the current time_reThe abscissa and ordinate positions of (a), z_x ⁱAnd z_y ⁱRespectively representing a first set of preselected observationsThe abscissa and ordinate positions of the ith observation,T_rto indicate the current time of day and the reception of the first set of preselected observations by the TWS radarTime difference of the ith observed time; v. of_maxRepresenting the target maximum speed, v_errorThe error of the target speed calculation can be set according to actual conditions;

if the first preselected observation setIf the ith observation meets the initialization condition, the first pre-selected observation set is selected according to the observation received by the TWS radar at the current momentAnd initializing the flight path by the ith observation, and establishing the flight path to obtain the initial state of the flight path.

When a new track is established, according to the current observation z_reCan determine the position of the new track, and then combines the current observation z_reThe difference between the time stamp of the previous observation in the track and the time stamp of the previous observation in the track can calculate the speed of the new track, and further determine the initial state of the track. The covariance of the initial state of the track is:

wherein R is_cRepresenting the observed noise covariance matrix observed in a rectangular coordinate system.

Step 302, for each existing track, iteratively updating the estimate of the track and the corresponding gate time interval in the continuous tracking process in the following way:

each time of updating, determining an acquisition time interval according to the wave gate time interval at the finishing time of the wave gate time interval corresponding to the current flight path, and acquiring the observation received by the TWS radar in the acquisition time interval to form a second preselected observation set;

and at the end time of the acquisition time interval, updating the state of the current flight path by using a second preselected observation set, filtering by combining the state of the flight path, and calculating the predicted estimation of the next updated flight path and the corresponding gate time interval.

The method of the invention utilizes a second preselected observation set Z during continuous tracking_τ(k) And updating the state of the current track tau, predicting the next updated state of the current track tau after the updating is finished, and obtaining the estimation of the next updated track tau so as to realize filtering. By the method, when the time of the TWS radar reaches the corresponding moment of the end of the wave gate (namely the end moment of the wave gate time interval), the corresponding track is updated, so that the delay is effectively reduced.

Considering that there may be multiple tracks in the continuous tracking process, and the gates of each track may have intersections, that is, there is an intersection in the corresponding gate time interval, in step 302, to further optimize the time of track update, the determining the acquisition time interval according to the gate time interval includes:

if the current flight path tau and the wave gate time intervals corresponding to the rest of the existing flight paths are not crossed, the acquisition time interval is the same as the wave gate time interval corresponding to the current flight path;

if the current track tau is crossed with the gate time intervals corresponding to the rest of the existing tracks, and the latest gate time interval ending time corresponding to all the tracks crossed with the current track tau is equal to or earlier than the gate time interval ending time corresponding to the current track, the starting time of all the tracks crossed with the current track tau and the earliest gate time interval corresponding to the current track are set as the starting time of the acquisition time interval, and the gate time interval ending time corresponding to the current track is set as the acquisition time interval ending time;

if the current track tau is crossed with the gate time intervals corresponding to the rest of the existing tracks, and the latest gate time interval ending time corresponding to all the tracks crossed with the current track tau is later than the gate time interval ending time corresponding to the current track, the starting time of the earliest gate time interval corresponding to all the tracks crossed with the current track tau and the current track is the starting time of the acquisition time interval, and the latest gate time interval ending time corresponding to all the tracks crossed with the current track tau is the ending time of the acquisition time interval. Where "early" means earlier in time and the corresponding value is smaller, and "late" means later in time and the corresponding value is larger.

Further, when the foregoing manner is implemented, the foregoing manner may be distinguished by determining whether the current track τ is delayed from being updated, if the track τ is not marked as a track delayed from being updated, the track τ is updated according to the end time of the gate time interval corresponding to the track τ, and if the track τ is marked as a track delayed from being updated, the time for updating needs to be adjusted, specifically, step 302 includes:

step 302-1, during the k-th updating, in the gate time interval [ t ] corresponding to the current track tau_s(k),t_d(k)]End time t of_d(k) Judging whether the current track tau is marked as a track for delaying updating or not, if so, skipping to execute the step302-7, otherwise, executing step 302-2;

step 302-2, judging whether the current track tau is crossed with other tracks by gates, if so, executing step 302-4, otherwise, executing step 302-3;

step 302-3, making the acquisition time interval the same as the gate time interval corresponding to the current track, namely, taking the gate time interval [ t ] of the current track tau_s(k),t_d(k)]Inner observations, constituting a second preselected observation set Z_τ(k)；

Using a second preselected observation set Z_τ(k) Updating and predicting the current track tau, and calculating the next updated gate time interval [ t ] of the current track tau_s(k+1),t_d(k+1)]；

Step 302-4, if the current track tau is crossed with the wave gates of the rest tracks, but the wave gate end time t of the rest tracks is the latest_{d_max}At the end of the gate time t not later than track tau_d(k) I.e. t_{d_max}≤t_d(k) Then go to step 302-5;

if the current track T is crossed with the rest wave gates, but the latest wave gate end time t of the rest tracks_{d_max}Wave gate end time t later than track tau_d(k) I.e. t_{d_max}＞t_d(k) Then go to step 302-6; t is t_{d_max}The latest wave gate time interval end time corresponding to the current flight path and each flight path crossed with the current flight path is taken as the time;

step 302-5, the starting time of the earliest wave gate time interval corresponding to the crossed flight path and the current flight path is the starting time of the acquisition time interval, the ending time of the wave gate time interval corresponding to the current flight path is the ending time of the acquisition time interval, namely, the time interval [ t ] is taken out_{s_min},t_d(k)]The observations in constitute a second preselected observation set Z_τ(k)，t_{s_min}The current flight path and the earliest starting time of the wave gate time interval corresponding to each flight path crossed with the current flight path;

using a second preselected observation set Z_τ(k) Updating and predicting the current track tau, and calculating the next updated gate time interval [ t ] of the current track tau_s(k+1),t_d(k+1)]；

Step 302-6, let the earliest gate time interval start time corresponding to the crossed track and the current track be the acquisition time interval start time, and the latest gate time interval end time corresponding to the crossed track be the acquisition time interval end time, i.e. t_d(k)'＝t_{d_max}＝max(t_d1,...,t_dn,t_d(k) In which t) is_d1,...,t_dnN number of gate end times, t, crossing the track T_s(k)'＝t_{s_min}＝min(t_s1,...,t_sn,t_s(k) In which t) is_s1,...,t_snN wave gate starting moments crossed with the flight path tau, and the collection time interval is [ t ]_s(k)',t_d(k)']Marking the track tau as a track delayed from updating, and executing the step 302-7;

step 302-7, at the end time t of the acquisition time interval_d(k) ', taking out the time interval [ t ]_s(k)',t_d(k)']Inner observations, constituting a second preselected observation set Z_τ(k)；

Using a second preselected observation set Z_τ(k) Updating and predicting the current track tau, and calculating the next updated gate time interval [ t ] of the current track tau_s(k+1),t_d(k+1)]。

In this preferred embodiment, step 302 may implement the multi-target update procedure through pseudo code as shown in table 1 below:

TABLE 1 Multi-target update Process pseudo code

Preferably, in step 302, calculating the predicted estimate of the next updated track and the corresponding gate time interval includes:

step 302-A, calculating a second preselected observation set Z_τ(k) All observations inThe corresponding clutter density.

Further, step 302-A includes:

first, look for observation z_k(i) And a second preselected observation set Z_τ(k) Of the rest of the observations, and a small distance r of nth between the other observationsⁿ(i) N is an integer greater than 0, preferably n is 2, z_k(i)∈Z_τ(k) I has a value from 1 to a second preselected observation set Z_τ(k) K represents the number of updates; if the second preselected observation set Z_τ(k) If the number of observations in (1) is less than (n +1), the observation set received from the beginning of the kth updated corresponding scanning period to the current time is set asLooking for an observation z_k(i) In the observation setMiddle nth small distance rⁿ(i) In order to calculate the clutter density.

Second, the observation z is calculated_k(i) Corresponding sparsity, the expression is:

γ(z_k(i))＝V(rⁿ(i))/n；

wherein the content of the first and second substances,

Γ (·) is a gamma function,is a spatial dimension, preferably

And finally, calculating clutter density according to sparsity, wherein the expression is as follows:

ρ_k(i) representing a second set of preselected observations Z_τ(k) Middle observation z_k(i) Corresponding clutter density, for a second preselected observation set Z_τ(k) Each of which performs the calculation process described above.

Step 302-B, pair the second preselected observation set Z according to the wave gate_τ(k) To obtain an observation set y for updating_k。

One track may correspond to multiple track components, and each track component may correspond to multiple models, and preferably, in step 302-B, the kth update is performed on the second preselected observation set Z according to the gate_τ(k) The observation of (1) is selected, comprising:

track component c for current track τ_k-1Model σ of (c), selected observation set y_k(c_k-1σ) satisfies:

wherein y is an observation set y_k(c_k-1The observation in (a), the observation in (c),represents the track component c of the current track tau at the kth update_k-1Predicted observation of model σ of (1), S_k(c_k-1σ) track component c at kth update of current track τ_k-1The innovation matrix of the model a of (a),is S_k(c_k-1σ), superscript "T" denotes transpose, g is the size of the gate, and the expression is:

chi2inv (·) is chi²Inverse function of the distribution function, P_GRepresenting the gate probability, l representing the observation vectory, typically the observation vector y has a dimension of 2;

for models with different current tracks tau, all selected observation sets are combined into one observation set y for updating_kThe expression is:

step 302-C, computing a second preselected observation set Z_τ(k) The likelihood function of each observation with the current track.

Preferably, the second preselected observation set Z_τ(k) Observation z in_k(i) Track component c of current track tau_k-1The likelihood function expression of model σ of (2) is:

wherein z is_k(i)∈V_k(c_k-1σ) represents observation z_k(i) The track component c of the current track τ_k-1In the model σ of (1), V_k(c_k-1σ) a track component c representing the current track τ_k-1I ranges from 1 to a second preselected observation set Z_τ(k) N (-) is a probability density function of the gaussian distribution;

obtaining an observation z_k(i) Track component c of current track tau_k-1The likelihood function expression of (1) is:

obtaining an observation z_k(i) The likelihood function expression with the current track tau is:

wherein, mu_k|k-1(c_k-1σ) represents the track component c at kth update of the track τ_k-1Model prediction probability of model σ of (1), p (c)_k-1) Represents the flight path component c after k-1 th update of the flight path tau_k-1Relative probability of (c).

Step 302-D, combining likelihood function, for updated observation set y_kObservation y in (1)_k(i) The corresponding clutter density is modulated.

Preferably, in step 302-D, the k-th update includes:

calculating the observation y in combination with the likelihood function_k(i) Is the prior probability P of the observation result of the k-th update of the target corresponding to the track tau^τ(i) The expression is:

wherein, theta_k(i) I > 0 denotes observation y_k(i) Is an event derived from object detection, θ_k(0) Event indicating that none of the observations is target detection, Y^k-1Representing the collection of all observations received by the TWS radar from the initial to the k-1 th update,representing the prior probability of the presence of the target at the kth update of the track tau,event, P, indicating the presence of a target corresponding to track τ_DRepresenting the probability of discovery of a target by a TWS radar, P_GRepresents the wave gate probability, m_kRepresenting observation set y for updating_kI is from 1 to m_k；

Obtain an observation y for track τ_k(i) The corresponding clutter density after modulation is:

and the flight path eta is the rest existing flight paths except the current flight path tau.

If y_k(i) If the clutter density is not selected by other tracks, the corresponding clutter density is not changed.

Step 302-E, Observation set y to be used for updating_kCarrying out data association with the current track tau to obtain the posterior probability of the existence of the targetAnd data associated posterior probabilityi＝0，…，m_k，Y^kRepresenting the collection of all observations received by the TWS radar from the initial time to the kth update.

Preferably, step 302-E comprises:

calculate the kth update, observe y_k(i) Likelihood ratio of_kThe expression is:

obtaining the posterior probability of the existence of the target after the kth update of the track tauThe expression is as follows:

wherein the content of the first and second substances,representing the prior probability of the existence of the target when the kth time of the track tau is updated;

obtain observation y_k(i) The posterior probability expression associated with the data of the flight path tau is as follows:

and step 302-F, performing track component control.

Preferably, step 302-F includes:

observation set y to be used for updating_kEach observation y in (1)_k(i) With each track component c_k-1Associating to form a temporary track component; the number of temporary track components beingWherein C is_k-1Represents the number of track components after the k-1 th update, m_kRepresenting observation set y for updating_kThe number of observations in (1);

calculating the relative probability of each temporary track component, wherein the expression is as follows:

wherein the content of the first and second substances,representing temporal track componentsRelative probability of (a), beta_k(i) Representation for establishing temporal track componentObservation y of_k(i) Correlating posterior probability, p (c), with data of track τ_k-1) Represents the flight path component c after k-1 th update of the flight path tau_k-1The relative probability of (a) of (b),represents an observation z_k(i) Track component c of current track tau_k-1The likelihood function of (a) is,represents an observation z_k(i) A likelihood function with the current track τ;

performing the leaf clipping of the track component if a temporary track componentRelative probability ofIf the temporary track component is less than the set threshold value, the temporary track component is removed

Performing sub-tree cutting on the track components, tracing the previously updated track components from the current k-th update to the previous k-th update, and updating every track component c for the k-th update_κThe comparison is carried out, preserving the relative probability p (c)_κ) The maximum track component, k-N, N is the subtree clipping depth, and N is generally 3; i.e. if the track component c_κRelative probability p (c) corresponding to the k layer_κ) Maximum, then reserve; the remaining track component is recorded asThus, all updates at the k-th time are not made byAll derived track components are deleted, after the track component leaves are cut and the track component subtrees are cut, a temporary track component subset theta is reserved, and the complement of the temporary track component subset theta is reservedThen it is deleted;

calculating a complement setIs expressed as:

the temporary track component in the subset theta is the confirmed track component, using c_kRepresenting, track component c_kThe expression for the relative probability is:

the posterior probability of the existence of the target is adjusted as follows:

p(χ_k|Y^k)＝p(χ_k|Y^k)(1-Δp)；

the left side of the equation above is the posterior probability of the presence of an adjusted target and the right side of the equation is the posterior probability of the presence of an unadjusted target.

And step 302-G, updating the track state to obtain a target track state corresponding to the current track tau.

Preferably, step 302-G comprises:

calculating the state estimation value and covariance of each track component of the current track tau, wherein the expression is as follows:

wherein, c_k-1Is to identify the track component c_kThe corresponding last updated track component,a track component c representing the current track τ_kState estimate of model σ of (1), P_k|k(c_kσ) a track component c representing the current track τ_kThe state covariance of the model a of (a),representing the track component c at the kth update of the track τ_k-1State prediction value of model σ of (2)，P_k|k-1(c_k-1σ) represents the track component c at kth update of the track τ_k-1The predicted covariance of the model a of (a),representing a Kalman filtering estimation, H representing an observation matrix, and R representing an observation noise covariance matrix.

The posterior model probabilities for each model are:

wherein, mu_k|k-1(c_k-1σ) represents the track component c at kth update of the track τ_k-1The model prediction probability of the model σ of (a);

the target track state corresponding to the current track tau is obtained by combining the track components, and the expression is as follows:

wherein the content of the first and second substances,represents the kth updated track state of track tau, P_k|kRepresents the flight path state covariance after the kth update of the flight path tau.

And step 302-H, calculating the predicted estimation of the next updated track of each track component and the corresponding gate time interval.

Preferably, in step 302-H, the state prediction, the predicted observation, the prior probability of the existence of the target and the track wave gate time when each model of each track component of the track is updated next time are calculated, specifically:

assuming a track component c_kA total of M models, the firstThe mean value of the track states corresponding to the sigma models isTrack state covariance of P_k|k(σ)。

Firstly, calculating the model prediction probability of each model, wherein the expression is as follows:

wherein r_σmDenotes the probability, μ, of the target switching to the m-th model at the k + 1-th update under the condition that the k-th update follows the a-th model_k+1|k(m) represents the model prediction probability of model m.

And then solving the probability and the mixing state of the mixing model, wherein the expression is as follows:

wherein the content of the first and second substances,the prior probability that the k-th update is the sigma model under the condition that the k + 1-th update is the m model, is called the mixed model probability for short,representing the state of the hybrid model of the model m,represents the hybrid model state covariance of model m.

For track component c_kThe expression of the state prediction is:

wherein the content of the first and second substances,represents the track component c of the k +1 th update of the track tau_kModel m State prediction value of, P_k+1|k(c_kM) represents the track component c at kth +1 update of the track τ_kThe prediction covariance matrix of model m. F denotes a state transition matrix, F^TQ represents the process noise matrix as a transpose of F.

The predicted observation expression is obtained as:

S_k(c_k，m)＝HP_k+1|k(c_k，m)H^T+Q；

wherein the content of the first and second substances,represents the track component c of the current track at the k +1 th update_kPredicted observation of model m, S_k(c_kM) represents the current track component c at the kth update_kThe innovation matrix of model m.

The prior probability expression of the existence of the target is as follows:

wherein the content of the first and second substances,the prior probability of the existence of the target when the track tau is updated for the k +1 th time is represented, and gamma is the conversion probability of the existence of the target and can be set according to the actual situation.

Preferably, in step 302, calculating a gate time interval corresponding to the next updated track of each track component includes:

from the calculated track component c_kUpdating the information matrix obtained by the prediction estimation of the flight path next time, and aiming at the flight path component c of the current flight path tau_kCalculates the range [ theta ] of the corresponding gate azimuth angle_min，θ_max]；

The expression for the range of the wave gate azimuth angle is:

wherein g is the size of the wave gate, θ₀Is the center azimuth angle of the wave gate, S_ijI, j e {1, 2} is the track component c_kOf the model σ_k(c_kσ) of the elements;

calculating the track component c of the current track tau according to the range of the wave gate azimuth angles_kThe gate time range corresponding to the model σ of (a);

track component c to track τ_kThe model σ of (c), the expression of the gate time range is:

wherein the content of the first and second substances,for scanning an antennaSpeed, t₀For the time of the center of the wave gate, the track component c_kThe gate time range of the model σ is noted asWherein a is a serial number, and if the track component of the track tau is C and the number of the models is M, the value range of a is [1, CM]。

At this step the time range of each model for each track component needs to be calculated. After calculating the wave gate time range corresponding to each model of each track component of the current track tau, taking the initial time of the earliest wave gate time interval corresponding to all models of all track components as the initial time t of the wave gate time interval of the current track_s＝min{t_s ¹，...,t_s ^CMAnd taking the latest wave gate time interval end time corresponding to all models of all track components as the wave gate time interval end time t of the current track_d＝max{t_d ¹,...,t_d ^CM}。

In step 301, a flight path is established according to the first preselected observation set, filtering is performed in combination with the state of the flight path, and the prediction estimation of the next updated flight path and the corresponding gate time interval are calculated, which may be referred to above step 302 for specific implementation and will not be further described herein.

Referring to fig. 4 to 9(b), the present invention also performs simulation verification on the proposed TWS radar multi-target continuous tracking method, where the radar is located at the origin (0m,0m) of the cartesian coordinate system. Two targets (namely target 1 and target 2) are subjected to the motion process of uniform velocity-uniform acceleration-uniform velocity-turning-uniform velocity-uniform deceleration-turning-uniform velocity. The initial states of the two targets are shown in table 2, x represents the abscissa of the target position,representing the velocity of the target on the abscissa,representing the acceleration of the target on the abscissa, y represents the ordinate of the target position,representing the velocity of the object on the ordinate,representing the acceleration of the object on the ordinate.

TABLE 2 initial states of two targets

The accelerations of the two target acceleration phases are respectively [ -0.1m/s ]²，-0.2m/s²]And [ -0.3m/s²,0.15m/s²]The acceleration at the deceleration stage is [0.1m/s ] respectively²，0.2m/s²]And [0.3m/s²，-0.15m/s²]. During the turning phase, their angular velocities are each π/20. The experiment was run with 100 Monte Carlo simulations, each simulating 80 updates. Clutter density in the surveillance area is 2.0 x 10^-6/scan/m²Here, the clutter density is also uniformly distributed, and the target discovery probability P is_D0.9. The scanning period T of the antenna is 1s, scanning in the counterclockwise direction. The process noise is set to ds 0.01m/s²The standard deviation of the observation noise of the distance and the azimuth angle is respectively sigma_r＝5m，σ_θ＝0.01deg。

The obtained motion trajectories of the two targets are shown in fig. 4, and the traditional integrated track splitting tracking method (abbreviated as IMM-LMITS for short for ITS) in the prior art is compared with the TWS radar multi-target continuous tracking method (abbreviated as IMM-lmCITS for short for CITS) provided by the invention. Referring to fig. 5(a) to 10, it can be seen from fig. 5(a) and 5(b) that both methods successfully track the target, but as can be seen from the local enlargement of the track identified in fig. 5(a) and 5(b), when the target 1 crosses the scanning boundary, the track tracked by the conventional IMM-LMITS method is broken, whereas the track tracked by the continuous tracking IMM-LMCITS method of the present invention is not broken. This shows that the conventional IMM-LMITS method is affected by the boundary problem when crossing the boundary, resulting in track break, and the method provided by the present invention solves the boundary problem well. As can be seen from fig. 6(a) to 7(b), the tracking delay of the IMM-LMCITS method provided by the present invention is much smaller than that of the IMM-LMITS method. As can be seen from fig. 8(a) and 8(b), for target 1, the RMSE of the IMM-LMITS method is much greater after the target crosses the boundary (during the 24 th to 58 th updates), and for target 2, the RMSE of the two is very close because it does not cross the boundary, and no boundary problem occurs. As can be seen from fig. 9(a) and 9(b), the tracking accuracy of the target velocity is very close to that of the two methods. As can be seen from fig. 10, after the tracking is stable, the IMM-LMCITS method keeps the real track rate higher, while the IMM-LMCITS method has a substantial decrease in the real track rate around the 24 th and 58 th updates, because the target is affected by the boundary problem and the track is broken. The TWS radar multi-target continuous tracking method greatly reduces tracking delay, the tracking accuracy rate is not reduced due to the reduction of the tracking delay, and when the target crosses a boundary, the target can be continuously tracked by the continuous tracking method provided by the invention, and the situation of track breakage is avoided.

In particular, in some preferred embodiments of the present invention, there is further provided a computer device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the TWS radar multi-target continuous tracking method in any one of the above embodiments when executing the computer program.

In other preferred embodiments of the present invention, a computer-readable storage medium is further provided, on which a computer program is stored, and the computer program is executed by a processor to implement the steps of the TWS radar multi-target continuous tracking method in any one of the above embodiments.

It will be understood by those skilled in the art that all or part of the processes of the methods according to the above embodiments may be implemented by a computer program, which may be stored in a non-volatile computer-readable storage medium, and when executed, the computer program may include the processes of the embodiments of the TWS radar multi-target continuous tracking method, and will not be described repeatedly herein.

Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.