Polar delivery alignment method to combat data loss

Abstract

The application relates to a polar region transmission alignment method for coping with data loss, and belongs to the technical field of polar region navigation and transmission alignment. The method comprises the following steps: step 1) constructing a grid inertial navigation algorithm; step 2) establishing a grid system rapid transmission alignment model; and step 3) establishing a suboptimal estimator. The method can still guarantee the suboptimal estimation algorithm of alignment precision when the submarine encounters measurement data loss during transmission alignment in the polar region, and is used for improving and expanding the filtering estimation technology in the existing inertial navigation transmission alignment field.

Description

Technical Field

[0001] This invention relates to a polar region transfer alignment method for dealing with data loss, belonging to the field of polar navigation and transfer alignment technology. Background Technology

[0002] In the current field of navigation and alignment technology, ships and aircraft can use satellite navigation systems such as GPS and BeiDou to obtain accurate navigation information in polar regions. However, for underwater vehicles such as submersibles, since satellite navigation information cannot be effectively received underwater, inertial navigation systems are often used to achieve navigation functions. However, the polar regions are high-latitude areas, and as latitude increases, meridians converge rapidly to a single point, making conventional mechanics-based inertial navigation systems unusable due to the inability to define the heading angle. Polar inertial navigation algorithms based on grid coordinate systems and lateral coordinate systems have received widespread attention. However, the application of lateral inertial navigation algorithms relies on the assumption that the Earth is a sphere, which introduces a fundamental error. Therefore, grid inertial navigation algorithms are gradually gaining importance among scholars, and polar alignment technology based on grid inertial navigation algorithms is becoming a research hotspot.

[0003] In my country, research on polar region transfer alignment technology has begun to develop in the last decade. Some scholars have referenced conventional inertial navigation (INS) algorithms for transfer alignment, focusing on improvements to grid-based INS algorithms. For example, the applicability of single-parameter matching schemes (e.g., velocity matching) and combined-parameter matching schemes (e.g., velocity plus attitude matching) in polar regions has been gradually verified through simulation or experiments. However, current research mainly assumes that measurements transmitted from the main INS system can arrive at the sub-INS system on time. In practical applications, however, measurement data often experiences delays or even loss. Some scholars have addressed this by adjusting the delay time... By incorporating state variables, a method for compensating for transmission alignment errors based on delayed states was derived. Some scholars have also proposed an adaptive filtering method with time delay compensation from the perspective of filtering estimation. This method can adaptively adjust the robustness factor according to the dynamic external environment and improve the accuracy of transmission alignment.

[0004] From the perspective of practical engineering application, the above method is feasible for small carriers such as aircraft and vehicles, but for large ships and underwater vehicles, the distance between the master and the slave inertial navigation system is tens of meters or even hundreds of meters, and the electromagnetic environment is complex, resulting in that the delayed navigation data cannot control the calculation of the slave inertial navigation system in time. From the perspective of control theory, this significant data transmission delay can be regarded as data loss, and the hydrological environment in the polar region is relatively poor, which will also affect the transmission performance of the equipment to a certain extent, so it is of great significance to study the influence of measurement data loss on the performance of the transfer alignment estimator. At present, the related research on solving the problem of measurement data loss in transfer alignment is carried out in the middle and low latitude areas based on the conventional inertial navigation algorithm, and generally tends to explore in theory, and the response method in the polar region environment still needs to be verified. How to overcome the problem of measurement data loss caused by the harsh environment when the large underwater vehicle performs transfer alignment in the polar region needs to be solved. SUMMARY

[0005] The purpose of the present application is to solve the above-mentioned problems of the prior art, and to provide a polar region transfer alignment method for coping with data loss, which can still ensure the suboptimal estimation algorithm of alignment accuracy when the underwater vehicle encounters measurement data loss during polar region transfer alignment, so as to improve and expand the filtering estimation technology in the field of conventional inertial navigation transfer alignment.

[0006] The polar region transfer alignment method for coping with data loss of the present application has the special feature that it comprises the following steps:

[0007] Step 1) Constructing a grid inertial navigation algorithm

[0008] In order to solve the problem that the conventional inertial navigation algorithm cannot define the heading angle in the polar region, resulting in navigation failure, the geographic coordinate system is rotated to the grid coordinate system to obtain a newly defined grid heading angle, which is allowed to participate in the inertial navigation calculation. However, the inertial navigation system works normally in the polar region, providing a navigation information calculation platform for subsequent polar region transfer alignment work;

[0009] Step 2) Establishing a grid system fast transfer alignment model

[0010] Based on the real-time navigation information calculated by the master and slave inertial navigation systems in the grid system, the system state equation and the measurement state equation are constructed, and the lever effect error and the flexural deformation error are considered comprehensively to establish the polar region grid system fast transfer alignment equation;

[0011] Step 3) Establishing a suboptimal estimator

[0012] The measurement data loss is modeled as an independent and identically distributed Bernoulli process, and the state equation containing data loss is constructed. Based on the time stamp technology, a suboptimal estimator for polar region transfer alignment is derived to realize accurate estimation of the transfer alignment state.

[0013] Preferably, the specific steps of step 1 are as follows:

[0014] Firstly, a grid coordinate system (G system) is established, and the grid north direction is formed with a certain angle with the true north direction by rotating the conventional geographic coordinate system (T system) So that when the submarine moves near the pole, the problem that the heading angle cannot be defined by the conventional mechanics-based inertial navigation system does not occur, because Because of the existence of the angle, there is always a grid heading angle involved in the inertial navigation solution, so that the navigation system can work normally, and the conversion from the geographic system to the grid system is as shown in Figure 1 The conversion matrix is as follows:

[0015] .

[0016] At this time, the solution equation of the inertial navigation system in the grid coordinate system is as follows:

[0017]

[0018] Wherein is the differential form of the attitude matrix update of the grid inertial navigation system; is the projection of the rotation angular velocity of the carrier relative to the grid coordinate system in the carrier coordinate system; is the differential form of the velocity vector in the grid coordinate system; is the specific force measured by the accelerometer in the carrier coordinate system; is the projection of the rotation angular velocity of the earth relative to the inertial space in the earth coordinate system; is the projection of the rotation angular velocity of the grid coordinate system relative to the earth system in the grid coordinate system; is the projection of the gravitational acceleration of the point where the carrier is located in the grid coordinate system; is the differential form of the position vector of the point where the carrier is located, and by solving the above equations, the attitude, velocity and position of the carrier when moving in the polar region can be obtained.

[0019] Preferably, the specific steps of step 2 are as follows:

[0020] Firstly, the discrete system model and the measurement model are defined:

[0021] ;

[0022] Wherein is the state vector of the system at time is the system dynamic matrix, is the measurement vector, is the measurement matrix, and and are mutually independent zero-mean white noise processes, and the covariance matrix is and ;

[0023] The state variables are selected as follows:

[0024] ;

[0025] in They are the main and sub inertial navigation systems respectively. The velocity difference calculated on the three axes They are the main and sub inertial navigation systems respectively. Calculation of misalignment angles on three axes They are the main and sub inertial navigation systems respectively. The actual installation error angles on the three axes and the angular relationship of the single axis are as follows: Figure 2 As shown, where For flexural angle variation, The main inertial navigation carrier coordinate system For the sub-inertial navigation carrier coordinate system, Calculate the carrier coordinate system for the sub-inertial navigation system;

[0026] Considering gyroscope drift, acceleration bias, and deflection angle variation as process noise, and compensating for lever arm effect error in velocity error measurement, the state equation is as follows:

[0027] ;

[0028] In the formula For the drift of the inertial gyroscope, For the sub-inertial accelerometer to have zero bias, For flexural variable angular velocity;

[0029] Select the velocity error compensated for by the lever arm effect as the observation:

[0030]

[0031] Rigid lever speed The solution formula is as follows:

[0032]

[0033] in The transformation matrix from the main inertial navigation system to the lattice system of the underwater vehicle; This represents the angular velocity calculated by the main inertial navigation system of the submersible relative to the inertial frame. The length of the lever arm between the master and sub-inertial navigation systems;

[0034] Select speed error and measurement misalignment angle As an attitude observation, the following observation equations are formed:

[0035] ;

[0036] wherein, as follows:

[0037] .

[0038] Preferably, the specific steps of step 3) are:

[0039] When there is loss of data, the measurement equation can be expressed as follows:

[0040] ;

[0041] In the above formula, the probability of the measurement vector containing the main inertial navigation state information is , and the probability of not containing is ;

[0042] Whether the measurement data is successfully delivered is considered as a Bernoulli process, and the system can be described as follows:

[0043] ;

[0044] In the above formula, is the system state vector is the measurement vector, is the system noise, is the measurement noise, both with mean 0 and covariance matrix , , wherein , are both greater than 0, is the Kronecker function, the initial state of the system is a random vector with mean and covariance , is a data arrival index with value 0 or 1, when is 0, it means that the measurement data is lost, and when is 1, it means that the measurement data is successfully delivered, has the following distribution:

[0045] ;

[0046] wherein ;

[0047] It is generally considered that all , , and the initial state are independent of each other, and the value of which can be obtained in real time through the timestamp technology;

[0048] Define the innovation sequence related to the measurement vector As follows:

[0049]

[0050] Where

[0051] ;

[0052] To obtain the state estimate , the value of can be obtained by minimizing the following formula:

[0053] ;

[0054] According to the given system, Write as:

[0055] ;

[0056] Where the estimator gain is:

[0057]

[0058]

[0059] The covariance matrix is expressed as follows:

[0060] .

[0061] The polar region transfer alignment method for coping with data loss of the application has the following beneficial effects:

[0062] (1) The traditional method generally uses standard Kalman filtering to estimate the transfer alignment error, and when the measurement data is lost, the accuracy will be greatly reduced. The application models the randomly lost measurement data as an independent and identically distributed Bernoulli random process, and sequentially establishes an estimator, which can adapt to different data loss probabilities and ensure high alignment accuracy.

[0063] (2) Compared with linear minimum variance estimation, the algorithm only needs to solve one Riccati equation, improves the stability of the system, and is more suitable for engineering use.

[0064] Through simulation, it is verified that the application can not only cope with the problem of accuracy reduction caused by data loss, but also has good accuracy under different data loss probabilities, and is suitable for transfer alignment of underwater vehicles under different dynamic conditions. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 is a schematic diagram of a grid coordinate system of the present application;

[0066] Figure 2 is a schematic diagram of a transfer misalignment angle;

[0067] Figure 3 is a flow chart of a transfer alignment process of the grid inertial navigation system;

[0068] Figure 4 is a diagram of measurement data arrival when the data loss probability is 0.8;

[0069] Figure 5 is a diagram of installation error angle estimation error under high dynamics when the data loss probability is 0.8; in the diagram, (a), (b), and (c) are, in sequence, a comparison diagram of installation error angle estimation error of the pitch angle, the roll angle, and the heading angle;

[0070] Figure 6 is a diagram of installation error angle estimation error under low dynamics when the data loss probability is 0.8; in the diagram, (a), (b), and (c) are, in sequence, a comparison diagram of installation error angle estimation error of the pitch angle, the roll angle, and the heading angle;

[0071] Figure 7 is a diagram of measurement data arrival when the data loss probability is 0.5;

[0072] Figure 8 is a diagram of installation error angle estimation error under high dynamics when the data loss probability is 0.5; in the diagram, (a), (b), and (c) are, in sequence, a comparison diagram of installation error angle estimation error of the pitch angle, the roll angle, and the heading angle;

[0073] Figure 9 is a diagram of installation error angle estimation error under low dynamics when the data loss probability is 0.5; in the diagram, (a), (b), and (c) are, in sequence, a comparison diagram of installation error angle estimation error of the pitch angle, the roll angle, and the heading angle.

[0074] Figure 5 , Figure 6 , Figure 8 , Figure 9 The image contents of the diagrams are similar, and the effects are different due to different parameters. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solutions and advantages of the present application more clear and understandable, the present application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application, and are not used to limit the present application.

[0076] Example 1

[0077] This embodiment provides a polar region transfer alignment method to address data loss, comprising the following steps:

[0078] Step 1) Constructing a grid inertial navigation algorithm

[0079] To address the issue of conventional inertial navigation algorithms failing to define heading angles in polar regions, resulting in navigation failure, a new grid heading angle was obtained by rotating the geographic coordinate system to a grid coordinate system. This new grid heading angle was then incorporated into the inertial navigation calculation, allowing the inertial navigation system to function normally in polar regions. This provides a platform for calculating navigation information for subsequent polar alignment transfer.

[0080] Step 2) Establish a grid system for rapid transfer alignment model

[0081] Based on the navigation information calculated in real time by the master and sub-inertial navigation systems in the grid system, the system state equation and measurement state equation are constructed. Taking into account the lever effect error and the flexural deformation error, the fast transfer alignment equation of the polar grid system is established.

[0082] Step 3) Establish a suboptimal estimator

[0083] The measurement data loss is modeled as an independent and identically distributed Bernoulli process. A state equation incorporating the data loss is constructed. Based on timestamp technology, a suboptimal estimator for polar region transfer alignment is derived, achieving accurate estimation of the transfer alignment state.

[0084] The specific steps of step 1 are as follows:

[0085] First, establish a grid coordinate system (G system). Then, by rotating the conventional geographic coordinate system (T system), make the grid's north direction form an angle with the true north direction. This prevents the inertial navigation system, based on conventional mechanics, from being unable to define the heading angle when the submersible approaches its extreme point. The existence of an angle ensures that a grid heading angle will always participate in the inertial navigation calculation, enabling the navigation system to function properly. The conversion from geographic frame to grid frame is as follows: Figure 1 As shown, the transformation matrix is ​​as follows:

[0086] .

[0087] The solution equations for the inertial navigation system in the grid coordinate system are as follows:

[0088]

[0089] in It is the differential form of the attitude matrix update of the grid inertial navigation system; It is the projection of the rotational angular velocity of the carrier relative to the grid coordinate system onto the carrier coordinate system; It is the differential form of the velocity vector in the grid coordinate system; is the specific force measured by the accelerometer under the carrier system; is the projection of the earth's angular velocity in the inertial space in the earth coordinate system; is the projection of the rotation angular velocity of the grid coordinate system relative to the earth coordinate system in the grid coordinate system; is the projection of the gravity acceleration of the point where the carrier is located in the grid coordinate system; is the differential form of the position vector of the point where the carrier is located, and by solving the above equations, the attitude, velocity and position of the carrier during the movement in the polar region can be obtained.

[0090] The specific steps of step 2) are as follows:

[0091] First, define the discrete system model and the measurement model:

[0092]

[0093] wherein is the state vector of the system at the moment, is the system dynamic matrix, is the measurement vector, is the measurement matrix, and are mutually independent zero-mean white noise processes, and the covariance matrix is and ;

[0094] The state quantity is selected as follows:

[0095]

[0096] wherein are the velocity difference values calculated on the three axes between the main and sub inertial navigation systems, are the calculated misalignment angles on the three axes between the main and sub inertial navigation systems, are the actual installation error angles on the three axes between the main and sub inertial navigation systems, and the angle relationship of the single-axis is shown in , wherein is the flexure deformation angle, is the carrier coordinate system of the main inertial navigation system, Figure 2 is the carrier coordinate system of the sub inertial navigation system, is the carrier coordinate system calculated by the sub inertial navigation system; The gyro drift, acceleration zero offset and flexure deformation angle are considered as process noise, and the rod arm effect error is compensated in the velocity error measurement, and the state equation is as follows:

[0097]

[0098] ​​​​​​​

[0099] where is the drift of the sub-inertial gyro, is the bias of the sub-inertial accelerometer, is the angular velocity of the flexure deformation;

[0100] The velocity error compensated by the lever arm effect is selected as the observation:

[0101]

[0102] The rigid lever velocity is solved by the following formula:

[0103]

[0104] where is the transformation matrix from the main inertial system of the underwater vehicle to the grid system; is the angular velocity calculated by the main inertial system of the underwater vehicle relative to the inertial system; is the lever length between the main and sub-inertial systems;

[0105] The velocity error and the measurement misalignment angle are selected as the attitude observations, and the following observation equations are constructed:

[0106] ;

[0107] where, is as follows:

[0108] .

[0109] The specific steps of step 3) are as follows:

[0110] When data loss exists, the measurement equation can be expressed as follows:

[0111] ;

[0112] In the above formula, the probability that the main inertial state information is contained in the measurement vector is , and the probability that it is not contained is ;

[0113] Whether the measurement data is successfully transmitted is regarded as a Bernoulli process, and the system can be described as follows:

[0114] ;

[0115] In the above formula, is the system state vector is the measurement vector, is the system noise, are the measurement noises, with mean value 0 and covariance matrix , where , are all greater than 0, is the Kronecker function, and the initial state is a random vector with mean value and covariance , is a data arrival index with value 0 or 1, where 0 means that the measurement data is lost, and 1 means that the measurement data is successfully transmitted, has the following distribution:

[0116] ;

[0117] where ;

[0118] It is generally believed that all , , and the initial state are mutually independent, and the value of can be obtained in real time through the time stamping technique;

[0119] The innovation sequence related to the measurement vector is defined as as follows:

[0120]

[0121] where

[0122] ;

[0123] To obtain the value of the state estimation , the value of can be obtained by minimizing the following equation:

[0124] ;

[0125] According to the given system, it can be written as:

[0126] ;

[0127] where the estimator gain is:

[0128]

[0129] ​

[0130] covariance matrix is expressed as follows:

[0131] .

[0132] Example 2

[0133] This embodiment is the performance simulation of the suboptimal estimator under different data loss probabilities and different dynamics. This embodiment is an extreme region transfer alignment method for dealing with data loss, and the flowchart is referred to Figure 3 The submarine navigation environment under different data loss probabilities and different dynamics will be simulated, the performance of the suboptimal estimator will be verified through simulation, and the ordinary Kalman filtering method will be compared.

[0134] (1) When the data loss probability is 0.8, the effectiveness of error estimation under different dynamics is verified.

[0135] This embodiment simulates the transfer alignment of the submarine under two motion states when the data loss probability is 0.8 through simulation. Since the submarine is impacted by the sea current during navigation, it inevitably produces three-axis periodic rocking motion. High dynamic: simulate the rocking state of the ship sailing on the water, the roll angle amplitude is 5°, the period is 5s; the pitch angle amplitude is 6°, the period is 8s; the heading angle amplitude is 3°, the period is 6s; low dynamic: the submarine is in a small angle rocking state when sailing underwater, the roll angle amplitude is 1.5°, the period is 8s; the pitch angle amplitude is 2°, the period is 12s; the heading angle amplitude is , the period is 10s. The true value of the three-axis fixed installation error angle is ; the arm length is meters; the initial position of the submarine is set to be north latitude 89.999 degrees, east longitude 120 degrees, and the speed is 20kn towards true north, the three-axis gyro drift of the SINS is , and the three-axis accelerometer bias is . The SINS data solving period is 10ms, the transfer alignment filter period is 50ms, and the initial misalignment angle and velocity error are all set to 0.

[0136] The arrival of the measurement data, the simulation results of state 1 and state 2 are shown in Figure 4~Figure 6 , and the alignment numerical accuracy at the end of the simulation is shown in Table 1.

[0137]

[0138] (2) When the data loss probability is 0.5, the effectiveness of error estimation under different dynamics is verified.

[0139] This embodiment simulates the transfer alignment of the submarine in two motion states when the data loss probability is 0.5 by simulation, the relevant parameter settings are the same as in (1), the arrival of the measurement data, the simulation results of state 1 and state 2 are shown in Figure 7~Figure 9 The alignment numerical accuracy at the end of the simulation is shown in Table 2.

[0140]

[0141] When the submarine sails in the polar region, in order to deal with the situation of measurement data loss caused by the special hydrological environment in the polar region, this embodiment proposes a suboptimal estimator method applied to the transfer alignment in the polar region, by simulating two measurement data arrival probabilities and simulating the two different dynamic conditions of the submarine on water and underwater, it can be seen from the simulation results that if there is measurement data loss, even if the probability of successful data transmission is as high as 0.8, the accuracy of the standard Kalman filter will still be greatly reduced, if the submarine encounters special weather or ocean environment in the polar region, with the decrease of the transmission success probability, the accuracy of the standard Kalman filter will be further reduced, and the greater the angular motion and the higher the swing frequency, the lower the accuracy. In contrast, the estimation accuracy of the suboptimal estimator is almost not affected by the transmission arrival probability and the dynamic condition of the submarine, no matter what environment and motion condition the submarine is in, it can ensure that the transfer alignment has high accuracy. In summary, the three-axis transfer alignment accuracy of the suboptimal estimator compared with the standard Kalman filter is increased by 95.3%, 98.8% and 91.5% respectively. It can be seen from this that the research results not only have more advantages in alignment accuracy, but also have wider application range, when the submarine encounters various abnormal situations, the estimation system can be stable and convergent, and has certain engineering application value.

Claims

1. A polar delivery alignment method to cope with data loss, characterized in that The method comprises the following steps: Step 1) constructing a grid inertial navigation algorithm In order to solve the problem that the conventional inertial navigation algorithm cannot define a heading angle in the polar region, a new defined grid heading angle is obtained by rotating a geographic coordinate system into a grid coordinate system, so that the inertial navigation system can work normally in the polar region, and navigation information calculation platform is provided for subsequent polar region transfer alignment work; Step 2) establishing a grid system fast transfer alignment model Based on the navigation information calculated by the master and sub-inertial navigation systems in the grid system, the system state equation and the measurement state equation are constructed, and the arm effect error and the flexural deformation error are considered, and the polar region grid system fast transfer alignment equation is established; Step 3) establishing a suboptimal estimator The measurement data loss is modeled as an independent and identically distributed Bernoulli process, the state equation containing data loss is constructed, and based on the timestamp technology, a suboptimal estimator for polar region transfer alignment is derived to realize accurate estimation of the transfer alignment state.

2. The polar delivery alignment method for coping with data loss according to claim 1, characterized in that The specific steps of step 1) are: Firstly, the grid coordinate system G is established, and the grid north is made to form an angle with the true north by rotating the conventional geographic coordinate system T Because Because of the existence of the angle, there is always a grid heading angle involved in the inertial navigation solution, so that the navigation system can work normally. The conversion matrix is as follows: ； At this time, the calculation equation of the inertial navigation system in the grid coordinate system is: ； wherein is the differential form of the grid-INS attitude matrix update; is the projection of the carrier's rotation angular velocity relative to the grid coordinate system in the carrier coordinate system; is the differential form of the velocity vector in the grid coordinate system; is the specific force measured by the accelerometer in the carrier coordinate system; is the projection of the earth's rotation angular velocity relative to the inertial space in the earth coordinate system; is the projection of the grid coordinate system's rotation angular velocity relative to the earth coordinate system in the grid coordinate system; is the projection of the gravity acceleration at the carrier's point in the grid coordinate system; is the differential form of the carrier's point position vector, and by solving the above equations, the attitude, velocity and position of the carrier during the polar region movement can be obtained.

3. The polar delivery alignment method for coping with data loss according to claim 1, wherein The specific steps of step 2) are: First, define the discrete system model and measurement model: ； wherein is the state vector of the system at time instant is the system dynamic matrix, is the measurement vector, is the measurement matrix, and are mutually uncorrelated zero-mean white noise processes with covariance matrix and ; The state quantity is selected as follows: ； wherein are the master and slave inertial navigation systems, respectively is the calculated misalignment angle on the three axes, are the master and slave inertial navigation systems, respectively is the actual installation error angle on the three axes, are the master and slave inertial navigation systems, respectively is the actual installation error angle on the three axes, is the deflection angle, is the master inertial navigation system carrier coordinate system, is the slave inertial navigation system carrier coordinate system, is the slave inertial navigation system carrier coordinate system; The gyro drift, acceleration zero offset and flexural deformation angle are considered as process noise, and the arm effect error is compensated in the velocity error measurement, and the state equation is as follows: ； wherein is the drift of the child inertial navigation gyroscope, is the bias of the child inertial navigation accelerometer, is the flexure deformation angular velocity; The velocity error compensated by the arm effect is selected as the observation: ； Rigid bar arm velocity The solution formula is as follows: ； wherein is the transformation matrix from the main INS system of the submarine to the grid system; is the angular velocity calculated by the main INS of the submarine relative to the inertial system; is the length of the lever arm between the main and the sub-INS. selecting velocity errors and misalignment angles As attitude observations, the following observation equations are constituted: ； wherein As shown below: 。 4. The polar delivery alignment method for coping with data loss according to claim 1, wherein The specific steps of step 3) are: When data loss exists, the measurement equation is as follows: ； In the above formula, the probability that the measurement vector contains the primary inertial navigation state information is , and the probability that it does not contain is ; Whether the measurement data is successfully transferred is regarded as a Bernoulli process, and the system is described as follows: ； In the above formula is the system state vector is the measurement vector, is the system noise, is the measurement noise, both with mean 0 and covariance matrix , where , are both greater than 0, is the Kronecker function, the initial state of the system is a random vector with mean and covariance , is a data arrival index with value 0 or 1, when is 0, it means that the measurement data is lost, when is 1, it means that the measurement data is successfully transmitted, has the following distribution: ； wherein ; All of , , and the initial state are independent of each other, and the values are obtained in real time by timestamp technology; Defining innovation sequences related to measurement vectors As follows: wherein: ; To find the value of the state estimate The value of the state estimate can be found by minimizing​ ； According to the given system, written as: ； where the estimator gain is: ； covariance matrix is represented as follows: 。

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