CN112152954B - Method for suppressing coordinate data networking transmission distortion of flight simulator - Google Patents

Method for suppressing coordinate data networking transmission distortion of flight simulator Download PDF

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CN112152954B
CN112152954B CN202011001030.6A CN202011001030A CN112152954B CN 112152954 B CN112152954 B CN 112152954B CN 202011001030 A CN202011001030 A CN 202011001030A CN 112152954 B CN112152954 B CN 112152954B
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孙文柱
曹建平
孙忠云
王志乐
周秀芝
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Qingdao Campus of Naval Aviation University of PLA
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Abstract

The invention discloses a method for suppressing the distortion of coordinate data networking transmission of a flight simulator, which comprises the steps of firstly establishing a Kalman filtering model, inputting airplane coordinates after network transmission into the Kalman filtering model, acquiring an airplane position predicted value, and then outputting the airplane position predicted value to a visual scene of the flight simulator; according to the method, the estimated value of the flight dynamics data at the next moment is estimated by adopting a Kalman filtering method, the data delay is reduced, the root mean square error of distortion data is greatly reduced, when the flight dynamics data transmitted by a network are abnormal, the optimal estimation of the coordinate data of the flight simulator can be more accurately given, the distortion of the coordinate data of the simulator caused by networking transmission is effectively inhibited, the problem of jitter in the visual scene of the flight simulator is prevented, the training benefit of the simulator is improved, and the use experience of training personnel is improved.

Description

Method for suppressing coordinate data networking transmission distortion of flight simulator
Technical Field
The invention relates to the technical field of flight simulation training, in particular to a method for suppressing networking transmission distortion of coordinate data of a flight simulator.
Background
Flight simulation training is as an efficient, safe, low-cost auxiliary training mode, can provide the training environment that is close to the real flight condition for flight operating personnel, promotes training quality benefit by a wide margin. With the development of science and technology, the complexity of the aircraft is continuously improved, and the flight simulation training equipment is developed into a large-scale networking type simulation training style after the stages of simple mechanical simulation, electromechanical simulation, computer simulation and the like. However, the problem of distortion of network transmission coordinate values commonly exists in the process of training the networking of the simulator, and the distortion phenomenon occurs after coordinate values of entities (such as airplanes, satellites and the like) with higher speed in the simulator are transmitted through a network, so that the visual images of the simulator are severely jittered. When the viewpoint is close to the entity, the jitter is more obvious, the use experience of training personnel is seriously influenced, and the training benefit of the simulator is reduced.
Aiming at the problem of distortion of the transmission coordinate values of the simulator network, a plurality of documents carry out targeted research and provide a solution. Setting the visual simulation coordinate to be consistent with the dynamic coordinate system of the manned aircraft in order to eliminate the visual simulation jitter phenomenon of the manned aircraft; the Wangwei and the like perform interpolation smoothing on the flying parameter data to eliminate jitter in the flying playback process; the method provides a 7-point moving average method based on frame synchronization and smoothing algorithms for the brave wave and the like, effectively relieves the shaking phenomenon when an adjacent airplane is observed in networking flight simulation training, and improves and provides a visual shaking elimination method based on a weighted moving average filtering algorithm for the Caojiaping and the like on the basis. The above methods can reduce the degree of numerical distortion to some extent, but still have jitter phenomenon in severe cases and bring about the negative effect of data delay.
Disclosure of Invention
The invention aims to provide a method for suppressing the networking transmission distortion of coordinate data of a flight simulator, which can greatly reduce the root mean square error of the distortion data, reduce the true value of the coordinate data of the flight simulator to a greater extent and effectively solve the problem of entity jitter in a visual system of the flight simulator.
The technical scheme adopted by the invention is as follows:
a method for suppressing the networking transmission distortion of coordinate data of a flight simulator comprises the following steps:
s1, transmitting the aircraft coordinates output by the flight dynamics model to a receiving port through a network;
s2, establishing a Kalman filtering model, inputting the aircraft coordinates transmitted through the network into the Kalman filtering model, and acquiring an aircraft position estimated value;
s3, outputting the estimated value of the airplane position to the view of the flight simulator and updating the system covariance;
s4, updating the system covariance according to the estimated value of the airplane position to judge whether the network transmission is finished, if so, finishing the filtering process, otherwise, taking the updated covariance as the system prediction covariance and returning to the step S1; the covariance update formula is:
Figure BDA0002694318180000021
in the formula (1), the first and second groups of the compound,
Figure BDA0002694318180000022
represents the predicted covariance update, K k Representing the kalman gain, H representing the observation matrix,
Figure BDA0002694318180000023
representing the prediction covariance.
Further, the step S2 specifically includes:
2.1: receiving aircraft coordinates ((P) over a network x (k),P y (k),P z (k));
2.2: calculating the first derivative (V) of the aircraft coordinates x (k),V y (k),V z (k));
2.3: calculating the second derivative of the aircraft coordinates ((a) x (k),a y (k),a z (k));
2.4: a distortion corrected estimated aircraft position is obtained.
Further, the step 2.4 specifically includes:
the aircraft flight dynamics model containing the disturbances can be represented by the following formula:
Figure BDA0002694318180000024
in the formula (2), x k And x k+1 The aircraft state at time k and at time k +1, respectively, y k Is the system output, u k The motion parameters of the airplane at the moment k;
x k =[P x (k) V x (k) P y (k) V y (k) P z (k) V z (k)] T (3)
Figure BDA0002694318180000025
a is a state transition matrix:
Figure BDA0002694318180000031
b is a control matrix:
B=diag[Δt 2 /2,Δt,Δt 2 /2,Δt,Δt 2 /2,Δt] (6)
h is an observation matrix:
Figure BDA0002694318180000032
w k and v k For system disturbance noise, a normal distribution is followed:
w k ~N(0,Q) (8)
v k ~N(0,R) (9)
g is an identity matrix;
the prediction estimation equation of the current state of the system is as follows:
Figure BDA0002694318180000033
in the formula (10), the first and second groups,
Figure BDA0002694318180000034
an estimate representing a current state;
the prediction covariance is:
Figure BDA0002694318180000035
in the formula (11), the reaction mixture,
Figure BDA0002694318180000036
representing the prediction covariance, P k Representing covariance, a representing a state transition matrix, and Q representing a system noise covariance matrix;
the kalman gain is:
Figure BDA0002694318180000037
in formula (12), H represents an observation matrix, and R represents an observation noise covariance matrix;
the filtering estimate is:
Figure BDA0002694318180000041
in the formula (13), the first and second groups,
Figure BDA0002694318180000042
representing the state estimate at time k +1,
Figure BDA0002694318180000043
expressed as state estimates at time K, K k Representing a Kalman gain, H representing an observation matrix;
and (4) calculating and obtaining an estimated value of the position of the airplane according to the formulas (10) to (13).
Further, the network transmission process in the step S1 includes suppression of three factors; the three factors are: truncation error factors, access cycle inconsistency factors, network transmission packet loss and disorder factors.
Further, the principle followed for truncation error factor suppression is:
(1.1) avoiding converting longitude and latitude coordinate values into single-precision floating point numbers in the network transmission and resampling processes;
and (1.2) if only a single-precision type is provided in the network transmission tool, extending a network protocol, decomposing the coordinate data into two single-precision values, and respectively transmitting the two single-precision values according to high and low bits.
Further, the principle followed for inconsistent factor suppression for access cycles is:
(2.1) setting the access periods of the sending end and the receiving end to be the same or in a multiple relation;
(2.2) the network transmission adopts a real-time operating system;
(2.3) time synchronization;
and (2.4) adopting an event trigger mechanism for data transceiving.
Further, the principle followed to suppress the network transmission packet loss and the out-of-order factor is as follows:
(3.1) the data transmission frequency does not exceed a set value;
(3.2) the packet length is not greater than the defined length;
and (3.3) optimizing a sending and receiving algorithm.
The invention has the following beneficial effects:
(1) the method has the advantages that the estimated value of the flight dynamics data at the next moment is estimated by adopting a Kalman filtering method, data delay is reduced, the root mean square error of distortion data is greatly reduced, when the flight dynamics data transmitted by a network are abnormal, the optimal estimation of the coordinate data of the flight simulator can be more accurately given, the distortion of the coordinate data of the simulator caused by networking transmission is effectively inhibited, the jitter problem in the visual scene of the flight simulator is prevented, the training benefit of the simulator is improved, and the use experience of training personnel is improved;
(2) the problem of position coordinate value distortion generated in the networking transmission process can be effectively solved by inhibiting three factors, namely a truncation error factor, an access cycle inconsistency factor and a network transmission packet loss and disorder factor in the network transmission process.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of longitude versus time for an experimental aircraft;
FIG. 3 is a graph of range error for the data processing results of experiment one;
FIG. 4 is a graph of acceleration values of data processing results in experiment one.
Detailed Description
The invention discloses a method for suppressing the networking transmission distortion of coordinate data of a flight simulator, which comprises the following steps as shown in figure 1:
s1, transmitting the aircraft coordinates output by the flight dynamics model to a receiving port through a network;
s2, establishing a Kalman filtering model, inputting the aircraft coordinates transmitted by the network into the Kalman filtering model, and acquiring an aircraft position estimated value;
s3, outputting the estimated value of the airplane position to the view of the flight simulator and updating the system covariance;
s4, updating the system covariance according to the estimated value of the airplane position to judge whether the network transmission is finished, if so, finishing the filtering process, otherwise, taking the updated covariance as the system prediction covariance and returning to the step S1; the covariance update formula is:
Figure BDA0002694318180000051
in the formula (1), the first and second groups,
Figure BDA0002694318180000052
represents the predicted covariance update, K k Representing the kalman gain, H representing the observation matrix,
Figure BDA0002694318180000053
the prediction covariance is indicated.
The technical solution of the present invention is further described with reference to the following specific embodiments.
A method for suppressing networking transmission distortion of coordinate data of a flight simulator comprises the following steps:
and S1, transmitting the aircraft coordinates output by the flight dynamics model to a receiving port through a network.
The flight simulators trained in the networking generally carry out data interaction through a 'concentration-distribution' mode, each flight simulator collects the position coordinates of the flight entities output by the flight dynamics model into a data pool through operations such as sampling, network transmission and the like, and all the position coordinates of the flight entities are distributed to each view after collection is finished.
In different networking flight simulators, the network technology, the sampling mode and the network transmission frequency and step length adopted by the position coordinate value are different. Therefore, the distortion of the position coordinate values caused by the whole transmission process is generally generated by coupling three factors, including: truncation errors, inconsistent access periods, and network transmission packet loss and misordering.
In the process of transmitting and resampling the flight simulator coordinate data network, in order to avoid generating truncation errors, the following principles are followed:
(1.1) avoiding converting longitude and latitude coordinate values into single-precision floating point numbers in the network transmission and resampling processes;
and (1.2) if only a single-precision type is provided in the network transmission tool, extending a network protocol, decomposing the coordinate data into two single-precision values, and respectively transmitting the two single-precision values according to high and low bits.
In order to avoid errors caused by asynchronous data access cycles and inconsistent step sizes, the following principles should be followed for data transmission and reception:
(2.1) setting the access periods of the sending end and the receiving end to be the same or in a multiple relation;
(2.2) the network transmission adopts a real-time operating system;
(2.3) time synchronization;
and (2.4) adopting an event triggering mechanism for data transceiving.
In order to avoid the occurrence of network transmission packet loss and disorder, the following principles should be followed:
(3.1) the data transmission frequency does not exceed a set value;
(3.2) the packet length is not greater than the defined length;
and (3.3) optimizing a sending and receiving algorithm.
S2, establishing a Kalman filtering model, inputting the aircraft coordinates transmitted by the network into the Kalman filtering model, and obtaining the estimated value of the aircraft position.
The specific process is as follows:
2.1: receiving aircraft coordinates ((P) over a network x (k),P y (k),P z (k));
2.2: determining the first derivative (V) of the aircraft coordinates x (k),V y (k),V z (k));
2.3: second derivative of aircraft coordinates ((a) x (k),a y (k),a z (k));
2.4: a distortion corrected estimated aircraft position is obtained.
The aircraft flight dynamics model containing the disturbances can be represented by the following formula:
Figure BDA0002694318180000071
in the formula (2), x k And x k+1 The aircraft state at time k and at time k +1, y k As system output, u k The motion parameters of the airplane at the moment k;
x k =[P x (k) V x (k) P y (k) V y (k) P z (k) V z (k)] T (3)
Figure BDA0002694318180000072
a is a state transition matrix:
Figure BDA0002694318180000073
b is a control matrix:
B=diag[Δt 2 /2,Δt,Δt 2 /2,Δt,Δt 2 /2,Δt] (6)
h is an observation matrix:
Figure BDA0002694318180000074
w k and v k For system disturbance noise, a normal distribution is followed:
w k ~N(0,Q) (8)
v k ~N(0,R) (9)
g is an identity matrix.
Kalman filtering is an algorithm for performing optimal estimation on the system state by using a linear system state equation and inputting and outputting observation data through the system. The prediction estimation equation of the current state of the system is as follows:
Figure BDA0002694318180000075
in the formula (10), the first and second groups,
Figure BDA0002694318180000081
an estimate representing a current state;
the prediction covariance is:
Figure BDA0002694318180000082
in the formula (11), the reaction mixture,
Figure BDA0002694318180000083
representing the prediction covariance, P k Representing covariance, a representing a state transition matrix, and Q representing a system noise covariance matrix;
the kalman gain is:
Figure BDA0002694318180000084
in formula (12), H represents an observation matrix, and R represents an observation noise covariance matrix;
the filtering is estimated as:
Figure BDA0002694318180000085
in the formula (13), the first and second groups,
Figure BDA0002694318180000086
representing the state estimate at time k +1,
Figure BDA0002694318180000087
when denoted by kEstimation of the state of the moment, K k Representing a Kalman gain, and H representing an observation matrix;
and (4) calculating and obtaining an estimated value of the position of the airplane according to the formulas (10) to (13).
As can be seen from equation (11), the larger Q the larger the prediction covariance, which results in K in equation (12) k The larger the value is, the larger the new observed value weight is in filtering estimation, and the smaller the predicted value weight is. The larger Q is, the larger K k The easier it is to converge. From the formula (12), it can be seen that the larger R is, the larger K is k The smaller the value, the smaller the new observed value weight and the larger the predicted value weight in the filtering estimation. The smaller R is, the lower K k The easier it is to converge. R can be derived from a statistical method,
Figure BDA0002694318180000088
and outputting the aircraft position after Kalman filtering. It should be noted that, if the speed vector and the acceleration vector of the aircraft are provided in the flight dynamics model of the simulator, the speed vector and the acceleration vector of the aircraft solved by the dynamics model can be directly used as the input of the kalman filter model, so that the model estimation result can be more accurate.
The Kalman filtering is an algorithm for optimally estimating system state parameters through system input and output observation data based on a linear system state equation, can effectively filter the influence of interference and noise in a system, and is widely applied to the fields of sensing signal fusion and flight navigation. The problem of distortion of network transmission coordinate values can be attributed to interference caused by delay randomness in real-time simulation, and an aircraft motion equation can be regarded as linear under a smaller time scale, so that the method is suitable for Kalman filtering to estimate the motion state of the aircraft.
S3, outputting the estimated value of the airplane position to the view of the flight simulator and updating the system covariance;
s4, judging whether the network transmission is finished, if so, finishing the filtering process, otherwise, taking the updated covariance as the system prediction covariance and returning to the step S1; the covariance update formula is:
Figure BDA0002694318180000091
in the formula (1), the first and second groups,
Figure BDA0002694318180000092
represents the prediction covariance update, K k Representing the kalman gain, H representing the observation matrix,
Figure BDA0002694318180000093
representing the prediction covariance.
The effect of the present invention is further verified by combining specific experiments.
Experiment one:
a section of linear flight coordinate data recorded by a dynamic model of a certain type of fighter simulator is selected as a true value, a singular value simulation observation value with 5% of total sampling points is added manually, and the flight data with the singular value are processed by using a 7-point moving average method and the method provided by the invention respectively. Fig. 2 shows the real longitude values of the airplane, the time-varying observed values, and the processing results of the two processing methods. In the observed value, a singular value is at 6.17 seconds, a large deviation is generated between the observed value and the real value, and the observed value is the same as the real value at other positions. The results of both data processing methods are shifted from the true values as a whole, since the flight data are delayed after being processed by the algorithm. It can be seen from the figure that the data processed by the 7-point moving average method has larger deviation compared with the true value, and the result delay of the kalman filtering method is smaller. After a singular value appears in the observed value, the data processing result is influenced, the data processed by the Kalman filtering method generates small fluctuation, the data processed by the 7-point moving average method has large fluctuation, and the data is recovered to be normal after 7 sampling points.
Fig. 3 shows the range error of the observed values and the results of the two data processing methods. It can be seen from the figure that before the singular value appears, the data processed by the two methods have different degrees of distance errors, the distance error of the data processed by the kalman filtering method is smaller and is 0.56m, and the distance error of the data processed by the 7-point moving average method is larger and is 10.58 m. Singular values with an amplitude of 20m have an effect on the results of both data processing methods, with the data processed by kalman filtering increasing by 0.42m deviation and the data processed by 7-point moving average generating a 2.86m deviation.
FIG. 4 shows the observed values and the acceleration values of the results of the two data processing methods, after the singular value appears, the observed values have great acceleration fluctuation of 10 4 (m/s 2 ) Magnitude, and the simulator frame will appear to shake dramatically at this time. The acceleration fluctuation is reduced to 10 after the treatment of 7-point moving average method 3 Magnitude order, at this time, the simulator still has obvious jitter, and 10 samples appear after 7 sampling points 3 Fluctuations of an order of magnitude. The acceleration fluctuation is reduced to 10 after the treatment of the Kalman filtering method 2 Magnitude and ripple only occurs once and then converges rapidly, where simulator frame jitter is not noticeable.
Experiment two:
selecting 3 sections of coordinate data of 3 states of linear flight, vertical fight and horizontal hover recorded by a dynamic model of a certain type of fighter simulator, wherein each section of data comprises 1000 sampling points, manually adding 50 singular values into the coordinate sampled data for the first time to serve as a simulation observation value, and adding white noise with the power of 20Dbw for the second time to serve as the simulation observation value. The flight data with singular values are processed using a 7-point moving average method and a kalman filtering method, respectively. And comparing the root mean square error of the processing results. The root mean square error E is calculated as:
Figure BDA0002694318180000101
in the formula (14), n is the number of samples,
Figure BDA0002694318180000103
estimated flight data for the ith sample, P i The flight data true value of the ith sample is obtained.
The root mean square error of the observation value added with the singular value and the results of the two data processing methods are shown in the table 1.
TABLE 1
Figure BDA0002694318180000102
As can be seen from table 1, the root mean square error of the 3 motion observations is between 2.5 and 2.8 when singular values are added. The root mean square error processed by the 7-point moving average method is not reduced, but is obviously increased, and particularly the increase is more obvious when the aircraft flies in a straight line. This is because this method produces a large delay that can produce a root mean square error. When the airplane horizontally spirals, the airplane circularly moves, the projection of the circular motion in one direction is reciprocating motion, and a part of root mean square error can be compensated in the reciprocating process, so that the root mean square error of a 7-point sliding average method is slightly smaller when the airplane horizontally spirals; the situation of a vertical bucket is between straight flight and horizontal hover. The root mean square error of the data can be obviously reduced after the data is processed by the Kalman filtering method, and the root mean square error of the data is reduced to below 0.5 from 2.5 to 2.8.
Table 2 shows the observed values of the added white noise and the root mean square error of the results of the two data processing methods.
TABLE 2
Figure BDA0002694318180000111
As can be seen from Table 2, when white noise is added, the root mean square error of the observed values of 3 actions is large, and the error value is within 10 + -0.15. The root mean square error value of the straight line flight and the vertical somersault after the 7-point sliding average method treatment is slightly increased, and the root mean square error value of the horizontal circle is slightly reduced. The root mean square error of the data can be obviously reduced after the data is processed by a Kalman filtering method, and the root mean square error of the data is reduced to below 2.5 from 10 +/-0.15.
The experiment proves that the method has the advantages of being small in delay, capable of greatly reducing the root mean square error of the distortion data and capable of reducing the real value of the coordinate data of the flight simulator to the maximum extent, and is an effective method for solving the problem of entity jitter in a view system in the flight simulator.

Claims (5)

1. A method for suppressing the networking transmission distortion of coordinate data of a flight simulator is characterized by comprising the following steps: the method comprises the following steps:
s1, transmitting the aircraft coordinates output by the flight dynamics model to a receiving port through a network;
s2, establishing a Kalman filtering model, inputting the aircraft coordinates transmitted by the network into the Kalman filtering model, and acquiring an aircraft position estimated value; the specific process of step S2 is:
2.1: receiving aircraft coordinates ((P) over a network x (k),P y (k),P z (k));
2.2: calculating the first derivative (V) of the aircraft coordinates x (k),V y (k),V z (k));
2.3: calculating the second derivative of the aircraft coordinates ((a) x (k),a y (k),a z (k));
2.4: obtaining a distortion corrected aircraft position estimated value; the step 2.4 specifically comprises the following steps:
the aircraft flight dynamics model containing the disturbances can be represented by the following formula:
Figure FDA0003733336190000011
in the formula (2), x k And x k+1 The aircraft state at time k and at time k +1, y k Is the system output, u k The motion parameters of the airplane at the moment k;
x k =[P x (k) V x (k) P y (k) V y (k) P z (k) V z (k)] T (3)
Figure FDA0003733336190000012
a is a state transition matrix:
Figure FDA0003733336190000013
b is a control matrix:
B=diag[Δt 2 /2,Δt,Δt 2 /2,Δt,Δt 2 /2,Δt] (6)
h is an observation matrix:
Figure FDA0003733336190000021
w k and v k For system disturbance noise, a normal distribution is followed:
w k ~N(0,Q) (8)
v k ~N(0,R) (9)
g is an identity matrix;
the prediction estimation equation of the current state of the system is as follows:
Figure FDA0003733336190000022
in the formula (10), the first and second groups of the chemical reaction are shown in the formula,
Figure FDA0003733336190000023
an estimate representing a current state;
the prediction covariance is:
Figure FDA0003733336190000024
in the formula (11), the reaction mixture,
Figure FDA0003733336190000025
representing the prediction covariance, P k Representing covariance, a representing a state transition matrix, and Q representing a system noise covariance matrix;
the kalman gain is:
Figure FDA0003733336190000026
in formula (12), H represents an observation matrix, and R represents an observation noise covariance matrix;
the filtering estimate is:
Figure FDA0003733336190000027
in the formula (13), the first and second groups of the compound,
Figure FDA0003733336190000028
representing the state estimate at time k +1,
Figure FDA0003733336190000029
expressed as state estimates at time K, K k Representing a Kalman gain, and H representing an observation matrix;
calculating and obtaining an aircraft position estimated value according to the formulas (10) to (13);
s3, outputting the estimated value of the airplane position to the view of the flight simulator and updating the system covariance;
s4, updating the system covariance according to the estimated value of the airplane position to judge whether the network transmission is finished, if so, finishing the filtering process, otherwise, taking the updated covariance as the system prediction covariance and returning to the step S1; the covariance update formula is:
Figure FDA00037333361900000210
in the formula (1), the first and second groups,
Figure FDA0003733336190000031
represents the predicted covariance update, K k Representing the kalman gain, H representing the observation matrix,
Figure FDA0003733336190000032
representing the prediction covariance.
2. The method for suppressing distortion in networked transmission of flight simulator coordinate data according to claim 1, wherein: the network transmission process in the step S1 includes suppression of three factors; the three factors are: truncation error factors, access cycle inconsistency factors, network transmission packet loss and disorder factors.
3. The method for suppressing distortion in networking flight simulator coordinate data transmissions of claim 2, wherein: the principle followed for truncation error factor suppression is:
(1.1) avoiding converting longitude and latitude coordinate values into single-precision floating point numbers in the network transmission and resampling processes;
and (1.2) if only a single-precision type is provided in the network transmission tool, extending a network protocol, decomposing the coordinate data into two single-precision values, and respectively transmitting the two single-precision values according to high and low bits.
4. The method for suppressing distortion in networking flight simulator coordinate data transmissions of claim 2, wherein: the principle followed for inconsistent factor suppression for access cycles is:
(2.1) setting the access periods of the sending end and the receiving end to be the same or in a multiple relation;
(2.2) the network transmission adopts a real-time operating system;
(2.3) time synchronization;
and (2.4) adopting an event triggering mechanism for data transceiving.
5. The method for suppressing distortion in networking flight simulator coordinate data transmissions of claim 2, wherein: the principle followed to suppress the network transmission packet loss and the disorder factor is as follows:
(3.1) the data transmission frequency does not exceed a set value;
(3.2) the packet length is not greater than the defined length;
and (3.3) optimizing a sending and receiving algorithm.
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