Polar region transfer alignment method for coping with data loss

Abstract

The invention relates to a polar region transfer alignment method for coping with data loss, and belongs to the technical field of polar region navigation and transfer alignment. Comprising the following steps: 1) constructing a grid inertial navigation algorithm; according to the method, when the underwater vehicle is subjected to transfer alignment in a polar region and encounters measurement data loss, the alignment precision can still be stably guaranteed, and the method is used for improving and expanding the filtering estimation technology in the existing inertial navigation transfer alignment field.

Description

Technical Field

[0001] The invention relates to a polar region transfer alignment method for coping with data loss, belonging to the technical field of polar region navigation and transfer alignment. Background Art

[0002] In the current field of navigation and transfer alignment technology, ships, aircraft and other carriers can use GPS, Beidou and other satellite navigation systems to obtain accurate navigation information in polar regions. However, for underwater carriers 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 belong to high-latitude areas. As the latitude increases, the meridians converge quickly to a point, resulting in the inertial navigation system based on conventional mechanics being unable to define the heading angle and being unusable. Polar inertial navigation algorithms based on grid coordinate systems and lateral coordinate systems have received widespread attention, but the prerequisite for the application of lateral inertial navigation algorithms is to assume that the earth is a round sphere, which has a principle error. Therefore, the grid inertial navigation algorithm has gradually begun to be valued by scholars, and the polar transfer alignment technology based on the grid inertial navigation algorithm has gradually become a research hotspot.

[0003] In my country, research on polar region transfer alignment technology has begun to develop in the past decade. Some scholars have made improvements based on the grid inertial navigation algorithm, referring to the transfer alignment method of conventional inertial navigation algorithms. For example, the applicability of single parameter matching schemes (such as velocity matching) and combined parameter matching schemes (such as velocity plus attitude matching) in polar regions has gradually been verified by simulation or experiments. However, the main research directions today all assume that the measurement values ​​transmitted from the main inertial navigation system can reach the sub-inertial navigation system on time. However, in actual work applications, the measurement data is often delayed or even lost. Some scholars have used the delay time to By incorporating it into the state quantity, a delay state-based transfer alignment error compensation method was derived. Some scholars also proposed an adaptive filtering method with time delay compensation from the perspective of filtering estimation, which can adaptively adjust the robust factor according to the dynamic external environment and improve the accuracy of transfer 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 submersibles, the distance between the main and sub-INS is tens of meters or even hundreds of meters, and the electromagnetic environment is complex, resulting in delayed transmission of navigation data that cannot control the sub-INS solution in time. From the perspective of control theory, this significant data transmission delay can be regarded as data loss, and the polar hydrological environment is relatively harsh, which will also affect the transmission performance of the equipment to a certain extent. Therefore, studying the loss of measurement data is of great significance to the performance of the transfer alignment estimator. At present, the relevant research on solving the problem of measurement data loss in transfer alignment is carried out in low and medium latitudes based on conventional inertial navigation algorithms, and generally tends to be theoretical exploration. The coping methods in the polar environment need to be verified. As my country's development strategy gradually begins to extend to the Arctic region, how large submersibles can overcome the problem of measurement data loss caused by the harsh environment when performing transfer alignment in the polar region needs to be solved urgently. Summary of the invention

[0005] The purpose of the present invention is to solve the deficiencies of the above-mentioned prior art and to provide a polar transfer alignment method for coping with data loss. This method can enable a suboptimal estimation algorithm to stably guarantee the alignment accuracy when a submersible encounters measurement data loss during transfer alignment in the polar region, so as to improve and expand the existing filtering estimation technology in the field of inertial navigation transfer alignment.

[0006] A polar region transfer alignment method for coping with data loss of the present invention is special in that it comprises the following steps: Step 1) Build a grid inertial navigation algorithm In order to solve the problem that conventional inertial navigation algorithms cannot define heading angles in polar regions, resulting in navigation failure, the geographic coordinate system is rotated to a grid coordinate system to obtain a newly defined grid heading angle, which is then used in the inertial navigation solution. This allows the inertial navigation system to work normally in polar regions, providing a navigation information solution platform for subsequent polar region transfer and alignment work. Step 2) Establishing a grid system fast transfer alignment model Based on the navigation information solved in real time by the main and sub-INS in the grid system, the system state equation and measurement state equation are constructed, and the rapid transfer alignment equation of the polar grid system is established by comprehensively considering the arm effect error and the flexural deformation error. Step 3) Build a suboptimal estimator The measurement data loss is modeled as an independent and identically distributed Bernoulli process, and a state equation including data loss is constructed. Based on the timestamp technology, a suboptimal estimator for polar transfer alignment is derived to achieve accurate estimation of the transfer alignment state.

[0007] Preferably, the specific steps of step 1 are: First, a grid coordinate system (G system) is established. By rotating the conventional geographic coordinate system (T system), the grid north direction forms an angle with the true north direction. , so that when the submersible moves to the vicinity of the pole, the inertial navigation system based on conventional mechanics will not be unable to define the heading angle. The existence of the angle means that there will always be a grid heading angle involved in the inertial navigation solution, so that the navigation system can work normally. The conversion from the geographic system to the grid system is as follows: Figure 1 As shown, the transformation matrix is ​​as follows: .

[0008] At this time, the solution equation of the inertial navigation system in the grid coordinate system is:

[0009] in It is the differential form of the attitude matrix update of the grid inertial navigation system; It is the projection of the 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; It is the specific force under the load system measured by the accelerometer; It is the projection of the Earth's rotational angular velocity relative to the inertial space in the Earth coordinate system; It is the projection of the angular velocity of the grid coordinate system relative to the earth system in the grid coordinate system; It is the projection of the gravity acceleration at the point where the carrier is located in the grid coordinate system; It is the differential form of the position vector of the carrier. By solving the above equations, we can get the attitude, velocity and position of the carrier when it moves in the polar region.

[0010] Preferably, the specific steps of step 2) are: First, define the discrete system model and measurement model: ; in yes The state vector of the system at time instant, is the system dynamic matrix, is the measurement vector, is the measurement matrix, and is an uncorrelated zero-mean white noise process, and its covariance matrix is and ; Select the state quantities as follows: ; in They are respectively the main and sub inertial navigation The speed difference calculated on the three axes, They are respectively the main and sub inertial navigation Calculate misalignment angle on three axes, They are respectively the main and sub inertial navigation The actual installation error angle on the three axes, the angle relationship of the single axis is as follows Figure 2 As shown, is the flexural deformation angle, is the main inertial navigation carrier coordinate system, is the coordinate system of the sub-INS carrier, Calculate the carrier coordinate system for the sub-INS; Considering gyro drift, acceleration bias and flexural deformation angle as process noise, and compensating the lever arm effect error in the velocity error measurement, the state equation is as follows: ; In the formula is the drift of the INS gyro, is the zero bias of the sub-inertial navigation accelerometer, is the angular velocity of the flexural deformation; The velocity error after lever arm effect compensation is selected as the observed quantity:

[0011] Rigid lever arm speed The solution formula is as follows:

[0012] in It is the transformation matrix from the main inertial navigation system of the submarine to the grid system; is the angular velocity of the main inertial navigation of the submarine relative to the inertial system; The length of the arm between the main and sub-INS; Select speed error and measuring misalignment angle As the attitude observation quantity, the following observation equation is formed: ; in, As shown below: .

[0013] Preferably, the specific steps of step 3) are: When data is missing, the measurement equation can be expressed as follows: ; In the above formula, the probability that the measurement vector contains the main inertial navigation state information is , the probability of not including is ; Measuring whether data is successfully transmitted is considered a Bernoulli process. The system can be described as follows: ; In the above formula is the system state vector are the measurement vector, is the system noise, is the measurement noise, the mean is 0, and the covariance matrix is , ,in , are greater than 0, is the Kronecker function, the initial state of the system is a mean value , the covariance is A random vector of is a data arrival index with a value of 0 or 1. When it is 0, it means the measurement data is lost. When it is 1, it indicates that the measurement data is successfully transmitted. The distribution of is: ; in ; It is generally believed that all , , And the initial state Independent of each other, and We can get the value of in real time through timestamp technology; Define the innovation sequence associated with the measurement vector as follows: in ; To obtain the state estimate The value of The value of can be obtained by minimizing the following formula: ; According to the given system, Written as: ; where the estimator gain for:

[0014] Covariance matrix It is expressed as follows: .

[0015] The present invention provides a polar region transfer alignment method for coping with data loss, and the beneficial effects are as follows: (1) Traditional methods generally use standard Kalman filtering to estimate the transfer alignment error. When measurement data is lost, the accuracy will drop significantly. The present invention models the randomly lost measurement data as an independent and identically distributed Bernoulli random process, and establishes an estimator in turn, which can adapt to different data loss probabilities and ensure high alignment accuracy.

[0016] (2) Compared with the linear minimum variance estimation, this algorithm only needs to solve one Riccati equation, which improves the stability of the system and is more suitable for engineering use.

[0017] Through simulation, it is verified that the present invention can not only deal with the problem of reduced accuracy caused by data loss, but also has good accuracy at different data loss probabilities, and is suitable for transfer alignment under different dynamic conditions of the submersible. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the grid coordinate system of the present invention; Figure 2 It is a schematic diagram of the transfer alignment misalignment angle; Figure 3 It is the flow chart of grid inertial navigation system transfer alignment; Figure 4 This is the measurement data arrival diagram when the data loss probability is 0.8; Figure 5 It is the installation error angle estimation error diagram under high dynamic conditions when the data loss probability is 0.8; in the figure, (a), (b), and (c) are the installation error angle estimation error comparison diagrams of the pitch angle, roll angle, and heading angle respectively; Figure 6 It is the installation error angle estimation error diagram under low dynamic conditions when the data loss probability is 0.8; in the figure, (a), (b), and (c) are the installation error angle estimation error comparison diagrams of the pitch angle, roll angle, and heading angle respectively; Figure 7 This is the measurement data arrival diagram when the data loss probability is 0.5; Figure 8 It is the installation error angle estimation error diagram under high dynamic conditions when the data loss probability is 0.5; in the figure, (a), (b), and (c) are the installation error angle estimation error comparison diagrams of the pitch angle, roll angle, and heading angle respectively; Fig. 9It is the installation error angle estimation error diagram under low dynamic conditions when the data loss probability is 0.5; in the figure, (a), (b), and (c) are the installation error angle estimation error comparison diagrams of the pitch angle, roll angle, and heading angle, respectively.

[0019] Figure 5 , Figure 6 , Figure 8 , Fig. 9 The image contents are similar, but different parameters produce different effects. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0021] Example 1 A polar region transfer alignment method for coping with data loss in this embodiment includes the following steps: Step 1) Build a grid inertial navigation algorithm In order to solve the problem that conventional inertial navigation algorithms cannot define heading angles in polar regions, resulting in navigation failure, the geographic coordinate system is rotated to a grid coordinate system to obtain a newly defined grid heading angle, which is then used in the inertial navigation solution. This allows the inertial navigation system to work normally in polar regions, providing a navigation information solution platform for subsequent polar region transfer and alignment work. Step 2) Establishing a grid system fast transfer alignment model Based on the navigation information solved in real time by the main and sub-INS in the grid system, the system state equation and measurement state equation are constructed, and the rapid transfer alignment equation of the polar grid system is established by comprehensively considering the arm effect error and the flexural deformation error. Step 3) Build a suboptimal estimator The measurement data loss is modeled as an independent and identically distributed Bernoulli process, and a state equation including data loss is constructed. Based on the timestamp technology, a suboptimal estimator for polar transfer alignment is derived to achieve accurate estimation of the transfer alignment state.

[0022] The specific steps of step 1 are: First, a grid coordinate system (G system) is established. By rotating the conventional geographic coordinate system (T system), the grid north direction forms an angle with the true north direction. , so that when the submersible moves to the vicinity of the pole, the inertial navigation system based on conventional mechanics will not be unable to define the heading angle. The existence of the angle means that there will always be a grid heading angle involved in the inertial navigation solution, so that the navigation system can work normally. The conversion from the geographic system to the grid system is as follows: Figure 1 As shown, the transformation matrix is ​​as follows: .

[0023] At this time, the solution equation of the inertial navigation system in the grid coordinate system is:

[0024] in It is the differential form of the attitude matrix update of the grid inertial navigation system; It is the projection of the 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; It is the specific force under the load system measured by the accelerometer; It is the projection of the Earth's rotational angular velocity relative to the inertial space in the Earth coordinate system; It is the projection of the angular velocity of the grid coordinate system relative to the earth system in the grid coordinate system; It is the projection of the gravity acceleration at the point where the carrier is located in the grid coordinate system; It is the differential form of the position vector of the carrier. By solving the above equations, we can get the attitude, velocity and position of the carrier when it moves in the polar region.

[0025] The specific steps of step 2) are: First, define the discrete system model and measurement model: ; in yes The state vector of the system at time instant, is the system dynamic matrix, is the measurement vector, is the measurement matrix, and is an uncorrelated zero-mean white noise process, and its covariance matrix is and ; Select the state quantities as follows: ; in They are respectively the main and sub inertial navigation The speed difference calculated on the three axes, They are respectively the main and sub inertial navigation Calculate misalignment angle on three axes, They are respectively the main and sub inertial navigation The actual installation error angle on the three axes, the angle relationship of the single axis is as follows Figure 2 As shown, is the flexural deformation angle, is the main inertial navigation carrier coordinate system, is the coordinate system of the sub-INS carrier, Calculate the carrier coordinate system for the sub-INS; Considering gyro drift, acceleration bias and flexural deformation angle as process noise, and compensating the lever arm effect error in the velocity error measurement, the state equation is as follows: ; In the formula is the drift of the INS gyro, is the zero bias of the sub-inertial navigation accelerometer, is the angular velocity of the flexural deformation; The velocity error after lever arm effect compensation is selected as the observed quantity:

[0026] Rigid lever arm speed The solution formula is as follows:

[0027] in It is the transformation matrix from the main inertial navigation system of the submarine to the grid system; is the angular velocity of the main inertial navigation of the submarine relative to the inertial system; The length of the arm between the main and sub-INS; Select speed error and measuring misalignment angle As the attitude observation quantity, the following observation equation is formed: ; in, As shown below: .

[0028] The specific steps of step 3) are: When data is missing, the measurement equation can be expressed as follows: ; In the above formula, the probability that the measurement vector contains the main inertial navigation state information is , the probability of not including is ; Measuring whether data is successfully transmitted is considered a Bernoulli process. The system can be described as follows: ; In the above formula is the system state vector are the measurement vector, is the system noise, is the measurement noise, the mean is 0, and the covariance matrix is , ,in , are greater than 0, is the Kronecker function, the initial state of the system is a mean value , the covariance is A random vector of is a data arrival index with a value of 0 or 1. When it is 0, it means the measurement data is lost. When it is 1, it indicates that the measurement data is successfully transmitted. The distribution of is: ; in ; It is generally believed that all , , And the initial state Independent of each other, and We can get the value of in real time through timestamp technology; Define the innovation sequence associated with the measurement vector as follows: in ; To obtain the state estimate The value of The value of can be obtained by minimizing the following formula: ; According to the given system, Written as: ; where the estimator gain for:

[0029] Covariance matrix It is expressed as follows: .

[0030] Example 2 This embodiment is a performance simulation of different data loss probabilities and different dynamic next-best estimators. This embodiment is a polar region transfer alignment method for coping with data loss. The flowchart is referenced Figure 3 ,The following will simulate the navigation environment of the submersible under different data loss probabilities and ,different dynamic situations, verify the performance of the suboptimal estimator through simulation and ,compared with the ordinary Kalman filtering method.

[0031] (1) Verification of the validity of error estimation under different dynamics when the data loss probability is 0.8.

[0032] This embodiment uses simulation to simulate the transfer alignment of the submersible in two motion states when the data loss probability is 0.8. Since the submersible is impacted by the ocean current during navigation, it will inevitably produce three-axis periodic swaying motion. High dynamics: simulates the ship sailing on the water in a swaying state, with a roll angle amplitude of 5° and a period of 5s; a pitch angle amplitude of 6° and a period of 8s; a heading angle amplitude of 3° and a period of 6s; low dynamics: the submersible is in a small-angle swaying state when sailing underwater, with a roll angle amplitude of 1.5° and a period of 8s; a pitch angle amplitude of 2° and a period of 12s; a heading angle amplitude of , with a cycle of 10s. The true value of the three-axis fixed installation error angle is The length of the lever arm is meters; Assume that the initial position of the submersible is 89.999 degrees north latitude and 120 degrees east longitude, and it is sailing at a constant speed of 20 kn towards the true north direction. The drift of the three-axis gyro of the sub-inertial navigation is , the zero bias of the three-axis accelerometer is The inertial navigation data solution cycle is 10 ms, the transfer alignment filter cycle is 50 ms, and the initial misalignment angle and velocity error are set to 0.

[0033] The arrival of measured data and the simulation results of state 1 and state 2 are shown in Figure 4~Figure 6 The alignment numerical accuracy at the end of the simulation is shown in Table 1.

[0034]

[0035] (2) Verification of the effectiveness of error estimation under different dynamics when the data loss probability is 0.5.

[0036] This embodiment uses simulation to simulate the transfer alignment of the submersible in two motion states when the data loss probability is 0.5. The relevant parameter settings are the same as those in (1). The arrival of the measured data and the simulation results of state 1 and state 2 are as follows: Figure 7~Figure 9 The alignment numerical accuracy at the end of the simulation is shown in Table 2.

[0037]

[0038] When the submersible is navigating in the polar regions, in order to cope with the loss of measurement data caused by the special hydrological environment in the polar regions, this embodiment proposes a suboptimal estimator method for polar transfer alignment. By simulating the arrival probability of two measurement data and simulating the two different dynamic conditions of the submersible above and below the water, it can be seen from the simulation results that if there is a loss of measurement data, even if the probability of successful data transmission is as high as 0.8, the accuracy of the standard Kalman filter will still drop significantly. If the submersible encounters special weather or ocean environment in the polar regions, as the probability of successful transmission decreases, the accuracy of the standard Kalman filter will be further reduced, and the greater its own angular motion and the higher the swing frequency, the lower its accuracy will be. In contrast, the estimation accuracy of the suboptimal estimator is almost unaffected by the transmission arrival probability and the dynamic situation of the submersible. Regardless of the environment and motion conditions of the submersible, it can ensure that the transmission alignment has a high accuracy. Considering the arrival probability of the two measurement data and the two states, the three-axis transmission alignment accuracy of the suboptimal estimator is improved by 95.3%, 98.8%, and 91.5% respectively compared with the standard Kalman filter. It can be seen that the research results not only have advantages in alignment accuracy, but also have a wider range of adaptability. When the submersible encounters various abnormal situations, the estimation system can converge stably and has certain engineering application value.

Claims

1. A polar region transfer alignment method for coping with data loss, characterized in that The following steps are involved: Step 1) Build a grid inertial navigation algorithm In order to solve the problem that conventional inertial navigation algorithms cannot define heading angles in polar regions, resulting in navigation failure, the geographic coordinate system is rotated to a grid coordinate system to obtain a newly defined grid heading angle, which is then used in the inertial navigation solution. This allows the inertial navigation system to work normally in polar regions, providing a navigation information solution platform for subsequent polar region transfer and alignment work. Step 2) Establishing a grid system fast transfer alignment model Based on the navigation information solved in real time by the main and sub-INS in the grid system, the system state equation and measurement state equation are constructed, and the rapid transfer alignment equation of the polar grid system is established by comprehensively considering the arm effect error and the flexural deformation error. Step 3) Build a suboptimal estimator The measurement data loss is modeled as an independent and identically distributed Bernoulli process, and a state equation including data loss is constructed. Based on the timestamp technology, a suboptimal estimator for polar transfer alignment is derived to achieve accurate estimation of the transfer alignment state.

2. A polar region transfer alignment method for coping with data loss according to claim 1, characterized in that The specific steps of step 1) are: First, the grid coordinate system G is established, and the grid north and true north form an angle by rotating the conventional geographic coordinate system T. ,because With the existence of the angle, there will always be 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 solution equation of the inertial navigation system in the grid coordinate system is: ； in It is the differential form of the attitude matrix update of the grid inertial navigation system; It is the projection of the 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; It is the specific force under the load system measured by the accelerometer; It is the projection of the Earth's rotational angular velocity relative to the inertial space in the Earth coordinate system; It is the projection of the angular velocity of the grid coordinate system relative to the earth system in the grid coordinate system; It is the projection of the gravity acceleration at the point where the carrier is located in the grid coordinate system; It is the differential form of the position vector of the carrier. By solving the above equations, we can get the attitude, velocity and position of the carrier when it moves in the polar region.

3. A polar region transfer alignment method for coping with data loss according to claim 1, characterized in that The specific steps of step 2) are: First, define the discrete system model and measurement model: ； in yes The state vector of the system at time instant, is the system dynamic matrix, is the measurement vector, is the measurement matrix, and is an uncorrelated zero-mean white noise process, and its covariance matrix is and ; Select the state quantities as follows: ； in They are respectively the main and sub inertial navigation The speed difference calculated on the three axes, They are respectively the main and sub inertial navigation Calculate misalignment angle on three axes, They are respectively the main and sub inertial navigation The actual installation error angle on the three axes, is the flexural deformation angle, is the main inertial navigation carrier coordinate system, is the coordinate system of the sub-INS carrier, Calculate the carrier coordinate system for the sub-INS; Considering gyro drift, acceleration bias and flexural deformation angle as process noise, and compensating the lever arm effect error in the velocity error measurement, the state equation is as follows: ； In the formula is the drift of the INS gyro, is the zero bias of the sub-inertial navigation accelerometer, is the angular velocity of the flexural deformation; The velocity error after lever arm effect compensation is selected as the observed quantity: ； Rigid lever arm speed The solution formula is as follows: ； in It is the transformation matrix from the main inertial navigation system of the submarine to the grid system; is the angular velocity of the main inertial navigation of the submarine relative to the inertial system; The length of the lever arm between the main and sub-INS; Select speed error and measuring misalignment angle As the attitude observation quantity, the following observation equation is formed: ； in, As shown below: 。 4. A polar region transfer alignment method for coping with data loss according to claim 1, characterized in that The specific steps of step 3) are: When data is missing, the measurement equation is expressed as follows: ； In the above formula, the probability that the measurement vector contains the main inertial navigation state information is , the probability of not including is ; Measuring whether data is successfully delivered is considered a Bernoulli process, and the system is described as follows: ； In the above formula is the system state vector are the measurement vector, is the system noise, is the measurement noise, the mean is 0, and the covariance matrix is , ,in , are greater than 0, is the Kronecker function, the initial state of the system is a mean value , the covariance is A random vector of is a data arrival index with a value of 0 or 1. When it is 0, it means the measurement data is lost. When it is 1, it indicates that the measurement data is successfully transmitted. The distribution of is: ； in ; All , , And the initial state Independent of each other, and The value of is obtained in real time through the timestamp technology; Define the innovation sequence associated with the measurement vector as follows: in: ； To obtain the state estimate The value of The value of can be obtained by minimizing the following formula: ； According to the given system, Written as: ； where the estimator gain for: ； ； Covariance matrix It is expressed as follows: 。

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