COMPUTATIONAL AIR DATA SYSTEM FOR ANGLE-OF-ATTACK AND ANGLE-OF-SIDESLIP

US 20050090947A1
Filed: 05/13/2003
Published: 04/28/2005
Est. Priority Date: 05/13/2003
Status: Active Grant

First Claim

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1. A method for estimating angle-of-attack and angle-of-sideslip of an aircraft, said method comprising the steps of:

modeling the full six degree-of-freedom dynamics, aerodynamics, and propulsion forces and moments of the aircraft in a nonlinear state space form;

utilizing extended Kalman filters with said modeling to estimate said angle-of-attack and angle-of-sideslip;

utilizing inertial measurement system measurements of the aircraft'"'"'s body rates and body accelerations in estimating said angle-of-attack and angle-of-sideslip; and

utilizing dynamic pressure measurements in estimating the angle-of-attack and angle-of-sideslip.

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Abstract

A computational air data method and system for estimating angle-of-attack and angle-of-sideslip of an aircraft utilizing a detailed aerodynamic model of the aircraft, extended Kalman filters, inertial system measurements of body rates and body accelerations, and computation of dynamic pressure.

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26 Claims

1. A method for estimating angle-of-attack and angle-of-sideslip of an aircraft, said method comprising the steps of:
- modeling the full six degree-of-freedom dynamics, aerodynamics, and propulsion forces and moments of the aircraft in a nonlinear state space form;
  
  utilizing extended Kalman filters with said modeling to estimate said angle-of-attack and angle-of-sideslip;
  
  utilizing inertial measurement system measurements of the aircraft'"'"'s body rates and body accelerations in estimating said angle-of-attack and angle-of-sideslip; and
  
  utilizing dynamic pressure measurements in estimating the angle-of-attack and angle-of-sideslip.
- View Dependent Claims (4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
- - 4. The method of claim 1 further comprising the step of utilizing said extended Kalman filters to estimate the dynamic state vector containing said angle-of-attack and angle-of-sideslip.
  - 5. The method of claim 1 wherein the dynamics of the aircraft are modeled in a nonlinear state space form as:
    - {dot over (x)}(t)=a(x(t),u(t),t)+Gw(t)
      z(t)=h(x(t),u(t),t)+v(t) where xε
      
      ⁿ^xis the state vector, uε
      
      ⁿ^uis the control input vector, wε
      
      ⁿ^wis the stochastic plant disturbance vector, zε
      
      ⁿ^zis the measurement vector, vε
      
      ⁿ^zis the stochastic measurement noise, Gε
      
      ⁿ^w^xn^wis the plant disturbance distribution matrix, and the vector fields a(●
      
      ) and h(●
      
      ) model said state dynamics and said inertial measurement system measurements.
  - 6. The method of claim 5 further comprising the step of partitioning said state vector into longitudinal and lateral-directional components in accordance with:
    - {circumflex over (x)}_lon=[{circumflex over (θ
      
      )} {circumflex over (q)} {circumflex over (α
      
      )} {circumflex over (V)}]^T{circumflex over (x)}_lat-dir=[{circumflex over (φ
      
      )} {circumflex over (p)} {circumflex over (r)} {circumflex over (β
      
      )}]^T.
  - 7. The method of claim 5 comprising the steps of modeling the aircraft'"'"'s dynamics for use in estimating said angle-of-attack and angle-of-sideslip as:
    - $\begin{matrix} \dot{θ} = q \cos ϕ - r \sin ϕ \\ \dot{ϕ} = p + q \sin ϕ \tan θ + r \cos ϕ \tan θ \\ [\begin{matrix} \dot{p} \\ \dot{q} \\ \dot{r} \end{matrix}] = I^{- 1} ([\begin{matrix} L \\ M \\ N \end{matrix}] - [\begin{matrix} p \\ q \\ r \end{matrix}] \times I [\begin{matrix} p \\ q \\ r \end{matrix}]) \\ \dot{α} = \frac{1}{Vm \cos β} [- L_{IFT} + Z_{T} \cos α - X_{T} \sin α + \\ m g (\cos α \cos ϕ \cos θ + \sin α \sin θ)] + \\ q - \tan β (p \cos α + r \sin α) \\ \dot{β} = \frac{1}{m V} [D_{RAG} \sin β + Y \cos β - X_{T} \cos α \sin β + Y_{T} \cos β - \\ Z_{T} \sin α \sin β + m g (\cos α \sin β \sin θ + \cos β \sin ϕ \cos θ - \\ \sin α \sin β \cos ϕ \cos θ)] + p \sin α - r \cos α \\ \dot{V} = \frac{1}{m} [- D_{RAG} \cos β + Y \sin β + X_{T} \cos α \cos β + \\ Y_{T} \sin β + Z_{T} \sin α \cos β - m g (\cos α \cos β \sin θ - \\ \sin β \sin ϕ \cos θ - \sin α \cos β \cos ϕ \cos θ)] \end{matrix}$
  - 8. The method of claim 7 further comprising the steps of evaluating the right side of said equations wherein the dynamics of the aircraft are modeled in a nonlinear state space form and wherein the aircraft'"'"'s dynamics for use in estimating said angle-of-attack and angle-of-sideslip are modeled using a posteriori state estimate for use in a time update of the state vector, and time propagating an error covariance matrix using a linear model formed from the Jacobian of said equations.
  - 9. The method of claim 5 further comprising the step of processing Jacobians of a(●
    - ) and h(●
      
      ) with respect to the state vector x in the extended Kalman filter.
  - 10. The method of claim 9 wherein the Jacobians are expressed by:
    - $\begin{matrix} A (x (t), u (t), t) = \frac{\partial a (x (t), u (t), t)}{\partial x} |_{x = \hat{x}} \\ H (x (t), u (t), t) = \frac{\partial h (x (t), u (t), t)}{\partial x} |_{x = \hat{x}} \end{matrix} .$ Where a(x(t),u(t),t) is described by the right side of the following equations;
      
      $\begin{matrix} \dot{θ} = q \cos ϕ - r \sin ϕ \\ \dot{ϕ} = p + q \sin ϕ \tan θ + r \cos ϕ \tan θ \\ [\begin{matrix} \dot{p} \\ \dot{q} \\ \dot{r} \end{matrix}] = I^{- 1} ([\begin{matrix} L \\ M \\ N \end{matrix}] - [\begin{matrix} p \\ q \\ r \end{matrix}] \times I [\begin{matrix} p \\ q \\ r \end{matrix}]) \\ \dot{α} = \frac{1}{Vm \cos β} [- L_{IFT} + Z_{T} \cos α - X_{T} \sin α + \\ m g (\cos α \cos ϕ \cos θ + \sin α \sin θ)] + \\ q - \tan β (p \cos α + r \sin α) \\ \dot{β} = \frac{1}{m V} [D_{RAG} \sin β + Y \cos β - X_{T} \cos α \sin β + Y_{T} \cos β - \\ Z_{T} \sin α \sin β + m g (\cos α \sin β \sin θ + \cos β \sin ϕ \cos θ - \\ \sin α \sin β \cos ϕ \cos θ)] + p \sin α - r \cos α \\ \dot{V} = \frac{1}{m} [- D_{RAG} \cos β + Y \sin β + X_{T} \cos α \cos β + \\ Y_{T} \sin β + Z_{T} \sin α \cos β - m g (\cos α \cos β \sin θ - \\ \sin β \sin ϕ \cos θ - \sin α \cos β \cos ϕ \cos θ)] \end{matrix}$ and where h(x(t),u(t),t) is described by the right side of the following equations;
      
      $\begin{matrix} \begin{matrix} θ = θ, & ϕ = ϕ, & p = p, & q = q, & r = r \end{matrix} \\ A_{x} = \frac{1}{gm} [X_{T} - D_{RAG} \cos α + L_{IFT} \sin α] \\ A_{y} = \frac{1}{gm} [Y_{T} + Y] \\ A_{Z} = \frac{1}{gm} [Z_{T} - D_{RAG} \sin α - L_{IFT} \cos α] \end{matrix}$
  - 11. The method of claim 5 wherein the plant disturbance vector w and measurement noise vector v have covariance matrices Q and R, respectively.
  - 12. The method of claim 5 further comprising the step of estimating the stochastic state vector x by processing stochastic measurements z.
  - 13. The method of claim 12 further comprising the step of processing an error covariance matrix in accordance with the expression E{(x-{circumflex over (x)})(x-{circumflex over (x)})^T}=Pε
    - ⁿ^x^xn^x, propagated in time in accordance with the expression {dot over (P)}(t)=A^T(t)P(t)+P(t)A(t)+GQ(t)G^T, wherein A is said Jacobian described by $A (x (t), u (t), t) = \frac{\partial a (x (t), u (t), t)}{\partial x} |_{x = \hat{x}}$ and Q is said plant process disturbance vector covariance matrix.
  - 14. The method of claim 4 further comprising the steps of:
    - time propagating dynamic state vectors and error covariance matrices between dynamic pressure measurements, and updating the state vector and error covariance based upon said dynamic pressure measurements.

2. (canceled)

3. (canceled)

15. A system for estimating angle-of-attack and angle-of-sideslip of an aircraft, said system comprising:
- inertial system sensors for measuring body rates and body accelerations of the aircraft, an air data system, said air data system providing measurement of dynamic pressure to be used in forming aerodynamic and propulsive forces and moments used to model the aircraft'"'"'s dynamics, a nonlinear model of the aircraft'"'"'s equations of motion including models of the aerodynamic and propulsive forces and moments, and an extended Kalman filter to be used in estimating said angle-of-attack and angle-of-sideslip in response to said measurements and an aerodynamic model of said aircraft.
- View Dependent Claims (16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26)
- - 16. The system of claim 15 further comprising temperature and pressure sensors for measuring the dynamic pressure of the aircraft during flight to be used in developing the aerodynamic forces and moments during flight for estimating said angle-of-attack and angle-of-sideslip in response to said measurements.
  - 17. The system of claim 16 wherein said extended Kalman filter estimates the dynamic state vectors associated with said aircraft'"'"'s flight through the atmosphere.
  - 18. The system of claim 16 wherein the dynamics of the aircraft are modeled in a nonlinear state space form as:
    - {dot over (x)}(t)=a(x(t),u(t),t)+Gw(t)
      z(t)=h(x(t),u(t),t)+v(t) where xε
      
      ⁿ^xis the state vector, uε
      
      ⁿ^u^{the control input vector, wε}ⁿ^wis the stochastic plant disturbance vector, zε
      
      ⁿ^xis the measurement vector, and vε
      
      ⁿ^xis the stochastic measurement noise vector, and the vector fields a(●
      
      ) and h(●
      
      ) model said state dynamics and said inertial system measurements.
  - 19. The system of claim 18 wherein said state vector is partitioned into longitudinal and lateral-directional components in accordance with:
    - {circumflex over (x)}_lon=[{circumflex over (θ
      
      )} {circumflex over (q)} {circumflex over (α
      
      )} {circumflex over (V)}]^T{circumflex over (x)}_lat-dir=[{circumflex over (φ
      
      )} {circumflex over (p)} {circumflex over (r)} {circumflex over (β
      
      )}]^T.
  - 20. The system of claim 19 wherein said state vector is modeled as:
    - $\begin{matrix} \dot{θ} = q \cos ϕ - r \sin ϕ \\ \dot{ϕ} = p + q \sin ϕ \tan θ + r \cos ϕ \tan θ \\ [\begin{matrix} \dot{p} \\ \dot{q} \\ \dot{r} \end{matrix}] = I^{- 1} ([\begin{matrix} L \\ M \\ N \end{matrix}] - [\begin{matrix} p \\ q \\ r \end{matrix}] \times I [\begin{matrix} p \\ q \\ r \end{matrix}]) \\ \dot{α} = \frac{1}{Vm \cos β} [- L_{IFT} + Z_{T} \cos α - X_{T} \sin α + \\ m g (\cos α \cos ϕ \cos θ + \sin α \sin θ)] + \\ q - \tan β (p \cos α + r \sin α) \\ \dot{β} = \frac{1}{m V} [D_{RAG} \sin β + Y \cos β - X_{T} \cos α \sin β + Y_{T} \cos β - \\ Z_{T} \sin α \sin β + m g (\cos α \sin β \sin θ + \cos β \sin ϕ \cos θ - \\ \sin α \sin β \cos ϕ \cos θ)] + p \sin α - r \cos α \\ \dot{V} = \frac{1}{m} [- D_{RAG} \cos β + Y \sin β + X_{T} \cos α \cos β + \\ Y_{T} \sin β + Z_{T} \sin α \cos β - m g (\cos α \cos β \sin θ - \\ \sin β \sin ϕ \cos θ - \sin α \cos β \cos ϕ \cos θ)] \end{matrix}$ the right side of said equations wherein the dynamics of the aircraft are modeled in a nonlinear state space form, wherein said state vector is partitioned into longitudinal and lateral-directional components, and wherein said state vector is modeled being evaluated using the a posteriori state estimate for use in a time update of the state vector, and an error covariance matrix being propagated using a linear model formed from the Jacobian of said equations.
  - 21. The system of claim 18 wherein Jacobians of a(●
    - ) and h(●
      
      ) are processed with respect to the state vector x in the extended Kalman filter.
  - 22. The system of claim 21 wherein the Jacobians are expressed by:
    - $\begin{matrix} A (x (t), u (t), t) = \frac{\partial a (x (t), u (t), t)}{\partial x} ❘_{x = \hat{x}} \\ H (x (t), u (t), t) = \frac{\partial h (x (t), u (t), t)}{\partial x} ❘_{x = \hat{x}} \end{matrix} .$
  - 23. The system of claim 18 wherein the plant disturbance vector w and measurement noise vector v have covariance matrices Q and R, respectively.
  - 24. The system of claim 18 wherein the stochastic state vector x is estimated by processing stochastic measurements z using an extended Kalman filter.
  - 25. The system of claim 24 wherein an error covariance matrix is processed in accordance with the expression E{(x-{circumflex over (x)})(x-{circumflex over (x)})^T}=Pε
    - ⁿ^x^xn^xpropagated in time in accordance with the expression {dot over (P)}(t)=A^T(t)P(t)+P(t)A(t)+GQ(t)G^T, wherein A is said Jacobian of $\begin{matrix} A (x (t), u (t), t) = \frac{\partial a (x (t), u (t), t)}{\partial x} ❘_{x = \hat{x}} \\ H (x (t), u (t), t) = \frac{\partial h (x (t), u (t), t)}{\partial x} ❘_{x = \hat{x}} \end{matrix} .$ and Q is said plant process disturbance vector covariance matrix.
  - 26. The system of claim 17 wherein:
    - dynamic state vectors and error covariance matrices are time propagated between measurements, and said state vector and error covariance are updated based upon said measurements.

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Current Assignee
The Boeing Co.
Original Assignee
The Boeing Co.
Inventors
Wise, Kevin A.

Granted Patent

US 6,928,341 B2
Time in Patent Office

Days
Field of Search
US Class Current

701/6
CPC Class Codes

G01P 13/025 indicating air data, i.e. f...

COMPUTATIONAL AIR DATA SYSTEM FOR ANGLE-OF-ATTACK AND ANGLE-OF-SIDESLIP

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COMPUTATIONAL AIR DATA SYSTEM FOR ANGLE-OF-ATTACK AND ANGLE-OF-SIDESLIP

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