Patent ID: 11912433
Assignee: SOUTHEAST UNIVERSITY
Field: Transport (Mechanical engineering)
Classification: CPC B  G | IPC B  G

Claim 3:
4. The dual-filter-based transfer alignment method under dynamic deformation according to claim 2, wherein the expression of speed error and the expression of angular speed error are derived in step (3) as follows:
the expression of angular speed error is as follows:, Δ
    ⁢
    
     ω
     →
    
   
   =
   
    
     
      (
      
       
        
         ω
         →
        
        im
        m
       
       ×
      
      )
     
     ⁢
     
      φ
      →
     
    
    +
    
     
      (
      
       
        
         ω
         →
        
        im
        m
       
       ×
      
      )
     
     ⁢
     Δ
     ⁢
     
      ϕ
      →
     
    
    +
    
     
      A
      ⁡
      (
      
       
        ω
        →
       
       θ
      
      )
     
     ⁢
     
      
       u
       →
      
      is
      s
     
    
    -
    
     
      
       A
       ⁡
       (
       
        
         ω
         →
        
        θ
       
       )
      
      [
      
       
        (
        
         
          
           π
           2
          
          ⁢
          U
         
         -
         
          Δ
          ⁢
          
           ϕ
           →
          
         
        
        )
       
       ×
      
      ]
     
     ⁢
     
      
       u
       →
      
      is
      s
     
    
   
  
  ,
 

wherein, {right arrow over (ω)}imm represents the angular speed of the main system in the coordinate system of the main system, {right arrow over (φ)} represents the ideal error angle between the main system and the subsystem, A({right arrow over (ω)}θ) represent an amplitude matrix, {right arrow over (u)}iss represents the identity matrix in the direction of {right arrow over (ω)}iss, and {right arrow over (ω)}iss represents the angular speed of the subsystem under the coordinate system of the subsystem, U=[1 1 1]T;
the expression of speed error is as follows:, δ
    ⁢
    
     v
     
      →
      ·
     
    
   
   =
   
    
     
      -
      
       (
       
        
         2
         ⁢
         
          
           ω
           →
          
          ie
          n
         
        
        +
        
         
          ω
          →
         
         en
         n
        
       
       )
      
     
     ×
     δ
     ⁢
     
      v
      →
     
    
    +
    
     
      R
      0
     
     ⁢
     
      B
      2
     
     ⁢
     
      θ
      →
     
    
    +
    
     
      (
      
       
        2
        ⁢
        
         (
         
          
           
            ω
            →
           
           im
           n
          
          ×
         
         )
        
        ⁢
        
         R
         0
        
       
       +
       
        
         R
         0
        
        ⁢
        
         B
         1
        
       
      
      )
     
     ⁢
     
      
       θ
       →
      
      .
     
    
    +
    
     
      C
      s
      n
     
     ⁢
     
      
       
        ∇
        →
       
       s
      
      
       +
       
        R
        0
       
      
     
     ⁢
     Δ
     ⁢
     
      
       ϕ
       →
      
      ¨
     
    
    +
    
     
      [
      
       
        
         (
         
          
           
            ω
            →
           
           im
           n
          
          ×
         
         )
        
        ⁢
        
         (
         
          
           
            ω
            →
           
           im
           n
          
          ×
         
         )
        
       
       +
       
        (
        
         
          
           
            ω
            →
           
           .
          
          im
          n
         
         ×
        
        )
       
      
      ]
     
     ⁢
     δ
     ⁢
     
      r
      →
     
    
    +
    
     
      (
      
       
        f
        s
        n
       
       ×
      
      )
     
     ⁢
     Δ
     ⁢
     
      ϕ
      →
     
    
    +
    
     
      [
      
       
        
         (
         
          
           
            ω
            →
           
           im
           n
          
          ×
         
         )
        
        ⁢
        
         (
         
          
           
            ω
            →
           
           im
           n
          
          ×
         
         )
        
       
       +
       
        (
        
         
          
           
            ω
            →
           
           .
          
          im
          n
         
         ×
        
        )
       
      
      ]
     
     ⁢
     
      
       r
       →
      
      0
     
    
   
  
  ,
 

wherein, {right arrow over (ω)}ien represents the rotation of the navigation system caused by the rotation of the earth, {right arrow over (ω)}enn represents the rotation of the navigation system caused by the curvature of the surface of the earth as the subsystem moves on the surface of the earth, δ{right arrow over (v)}={right arrow over (v)}sn−{right arrow over (v)}mn, {right arrow over (v)}mn and {right arrow over (v)}sn represent the speed vectors of the main system and the subsystem in the navigation coordinate system, {right arrow over (θ)} represents the flexural deformation angle between the main inertial navigation system and the inertial navigation subsystem, Δ{right arrow over (ϕ)} represents the coupling angle between the main inertial navigation system and the inertial navigation subsystem, {right arrow over (ω)}imn represents the angular speed of the main system in the navigation system, Csn represents the transformation matrix between the subsystem and the navigation coordinate system, {right arrow over (∇)}s represents the zero drift of accelerometer measurement of the subsystem, fsn represents the specific force of the subsystem in the navigation coordinate system, δ{right arrow over (r)} represents dynamic lever arm, {right arrow over (r)}0=[x0 y0 z0]T represents static lever arm, x0 y0 z0 represent static lever arms in east, north, and sky directions respectively, and R0 can be expressed as:, R
   0
  
  =
  
   
    [
    
     
      
       0
      
      
       
        z
        0
       
      
      
       0
      
     
     
      
       0
      
      
       0
      
      
       
        x
        0
       
      
     
     
      
       
        y
        0
       
      
      
       0
      
      
       0
      
     
    
    ]
   
   .