Aircraft airspeed state estimation method based on extended state Kalman filtering

Abstract

The invention provides an aircraft airspeed state estimation method based on extended state Kalman filtering. The aircraft airspeed state estimation method comprises the following steps: 1, carrying out equivalent unbiased conversion on a measured airspeed state; 2, constructing an estimation model and designing a filtering method; and 3, adjusting parameters of the estimation method. According to the method, an aircraft dynamics system can be converted into a linear time-varying system, and a covariance matrix of equivalent measurement noise is described; for an extended state model constructed by an aircraft airspeed model, an aircraft airspeed state estimation method based on an extended state Kalman filtering method is designed, and more accurate estimation is realized by introducing a compensation parameter matrix to disturbance in a dynamic model; depending on prior information of disturbance, an adjustment criterion of parameters in the estimation method is given. According to the parameter adjustment theory, the stability of the extended state Kalman filtering method can be ensured, and the cost for adjusting parameters in actual engineering can be reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft system state estimation, and specifically relates to a consistency filter design method and a parameter adjustment method for an aircraft system. Background Art

[0002] Kalman filtering is a recursive state estimation method in the time domain that uses a series of data observed over time, which contains noise and other inaccurate data, to more accurately estimate unknown variables. It was proposed by RE Kalman in 1960 and became a standard method for optimal estimation. KF is a linear optimal state estimation method and is known as one of the most famous Bayesian filtering theories. The classic Kalman filtering method is applied to linear systems, but in reality, nonlinearity and uncertain dynamics of the system are widely present. In the face of uncertain dynamics in the system, reference [1] proposed a method to optimize the worst-case bound for estimation. In reference [2], a KF based on extended state is proposed, the idea of ​​which is to estimate unknown dynamics in a timely manner to achieve better robustness and higher estimation accuracy. The concept of extended state is derived from active disturbance rejection control (ADRC), which is an effective method for dealing with internal and external uncertainties in the system, see references [3], [4] and [5], and is widely used in the aerospace field, see references [6] and [7] and the robotics field, see reference [8].

[0003] In the aircraft system, the change of wind field will bring uncertainty to the system, see reference [9]. Therefore, the airspeed state estimation problem in this case is difficult to estimate using the classic Kalman filter. It is necessary to use a filtering technology that can effectively deal with the uncertainty in the system to accurately and real-time estimate the airspeed state. Although there are many methods for estimating the airspeed state of aircraft, due to the diversity of actual flight scenarios and the inevitable interference of aircraft with complex wind fields, the difficulty of parameter design, stability and robustness of the above methods still face great challenges.

[0004] References

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[0008] [4]Zhang X,Zhang X,Xue W,et al.An overview on recent progress ofextended state observers for uncertain systems:Methods,theory,andapplications[J].Advanced Control for Applications:Engineering and IndustrialSystems,2021,3(2):89-97.

[0009] [5]Tang G,Xue W,Peng H,et al.Parallel multiple extended stateobservers based adrc with application to high-speed precision motion stage[J].IEEE Transactions on Industrial Electronics,2023,99:1-10.

[0010] [6]Huang Y,Xu K,Han J,et al.Flight control design using extendedstate observer and nonsmooth feedback[C] / / Proceedings of the 40th IEEEconference on decision and control.IEEE,2001:223-228.

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[0012] [8]Su J, Ma H, Qiu W, et al.Task-independent robotic uncalibrated hand-eye coordination based on the extended state observer[J]. IEEE Transactions onSystems,Man,and Cybernetics,Part B(Cybernetics),2004,34(4):1917-1922.

[0013] [9]Sonneveldt L.Nonlinear f-16model description[M].Delft University of Technology,2006. Summary of the invention

[0014] The technical problem solved by the present invention is: to design an aircraft airspeed state estimation method based on an extended state Kalman filter to realize effective real-time estimation of the aircraft's angle of attack, sideslip angle and airspeed rate, and to realize real-time estimation of system uncertainty, thereby enhancing the estimation accuracy of the airspeed state.

[0015] Consider the dynamic equations satisfied by the aircraft airspeed:

[0016]

[0017] in, is the airspeed of the aircraft, θ is the pitch angle, φ is the roll angle, p is the roll rate, q is the pitch rate, r is the yaw rate, is the overload of the aircraft, g is the acceleration of gravity, is the transformation matrix from the ground coordinate system to the body coordinate system, is the derivative of wind speed in the ground coordinate system.

[0018] Considering that the airspeed state of the aircraft (i.e., angle of attack, sideslip angle, and airspeed) can be measured, the design goal is to use the aircraft's airspeed state measurement to design an estimation method, so as to quickly and accurately estimate the aircraft's angle of attack, sideslip angle, and airspeed, and reduce the sensitivity to noise.

[0019] The technical solution of the present invention comprises the following three steps:

[0020] Step (1): Perform an equivalent unbiased transformation on the measured airspeed state:

[0021] The true values ​​of airspeed, angle of attack, and sideslip angle are recorded as V, α, and β respectively, and their measured values ​​are recorded as V m ,α m ,β m , and the relationship satisfies:

[0022]

[0023] Among them, the measurement noise U represents uniform distribution, a1, a2, a3>0.

[0024] Next, we use the airspeed, angle of attack, and sideslip angle measurements to get the airspeed The equivalent measurement value of is:

[0025]

[0026] in, To satisfy The parameters designed for unbiased measurement, the covariance of the noise in equation (1.3) is set to:

[0027]

[0028] Among them, R ij,k =R ji,k (i≠j)(For simplicity, the following formula omits the subscript k)

[0029]

[0030] Step 2: Estimation model construction and filtering method design:

[0031] Consider the model without measurement noise where the airspeed satisfies:

[0032]

[0033] in, is the airspeed of the aircraft, θ is the pitch angle, φ is the roll angle, p is the roll rate, q is the pitch rate, r is the yaw rate, is the overload of the aircraft, g is the acceleration of gravity, is the transformation matrix from the ground coordinate system to the body coordinate system, is the derivative of wind speed in the ground coordinate system.

[0034] Based on the above model, an airspeed estimation method based on Kalman filtering can be constructed. First, since Kalman filtering is used in discrete environments, the airspeed model needs to be discretized:

[0035]

[0036] in, t k The airspeed of the aircraft at time t k ) is the pitch angle, φ(t k ) is the roll angle, p(t k ) is the rolling angular rate, q(t k ) is the pitch angular rate, r(t k ) is the yaw rate, is the overload of the aircraft, g is the acceleration of gravity, is the transformation matrix from the ground coordinate system to the body coordinate system, is the derivative of wind speed in the ground coordinate system, t s is the sampling step of the system, t k+1 -t k =t s ,

[0037] The original discrete model (1.7) is set as:

[0038]

[0039] Among them, ω k and η k are process noise and measurement noise respectively;

[0040]

[0041] The purpose of this invention is to design an extended state Kalman filter (ESKF) method to estimate the disturbance and airspeed X k . First, construct a discrete system model with an extended state:

[0042]

[0043] The above model is equivalent to model (1.8). The above model can be organized as follows:

[0044]

[0045] in,

[0046]

[0047] η k The covariance of is the R designed in formula (1.4) in step (1). k .

[0048] Constructing ESKF method:

[0049]

[0050] in, Represents Z k+1 The estimated value of Q k Parameters to be designed, R k is the equivalent measurement noise η k The covariance of and disturbance The estimated value of is then defined by the angle of attack, sideslip angle and airspeed:

[0051]

[0052] Angle of attack, sideslip angle, and airspeed estimates are calculated.

[0053] Step (III): Parameter adjustment of estimation method:

[0054] The parameters that need to be adjusted in the aircraft airspeed state estimation method based on the extended state Kalman filter designed by the present invention are the matrix Q k and the matrix R k , where the matrix Q k The design principle is: Design Q k is the diagonal coefficient matrix:

[0055]

[0056] Among them, Q 1,k represents the covariance of the process noise, is the coefficient matrix to be designed to compensate for system disturbances, Given by the prior information of the disturbance, ζ = 0.5. k Follow the design of formula (1.4).

[0057] The flowchart of the aircraft airspeed state estimation method based on the extended state Kalman filter is shown in Figure 1 .

[0058] The advantages of the present invention compared with the prior art are:

[0059] 1. The system targeted is a common fixed-wing aircraft system in practice. The model has strong universality and takes into account the presence of wind interference in the aircraft system.

[0060] 2. The present invention proposes an aircraft airspeed state estimation method based on an extended state Kalman filter, which can estimate the state of the aircraft system (i.e., airspeed), calculate the aircraft's angle of attack, sideslip angle, and airspeed rate from the estimated value of the airspeed, and simultaneously estimate the disturbance of the aircraft system (derivative of wind speed);

[0061] 3. The parameter adjustment criteria in the estimation method are given quantitatively and explicitly. This parameter adjustment theory can ensure the stability of the ESKF and reduce the cost of adjusting parameters in practical engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A diagram showing the steps of the method of the present invention.

[0063] Figure 2 This is the estimated and true value curve of airspeed.

[0064] Figure 3 This is the estimated and true value curve of the empty rate.

[0065] Figure 4 This is the estimated value and true value curve of wind speed.

[0066] Figure 5 It is the curve of estimated and true value of angle of attack.

[0067] Figure 6 It is the estimated value and true value curve of the sideslip angle.

[0068] Figure 7 are the true and estimated values ​​of the disturbance.

[0069] Explanation of symbols

[0070] t: operating time of the aircraft system; Airspeed of the aircraft in the aircraft system; α: angle of attack;

[0071] β: sideslip angle; V: airspeed; θ: pitch angle; ψ: yaw angle; φ: roll angle;

[0072] p: roll angular rate; q: pitch angular rate; r: yaw angular rate;

[0073] t s : Sampling interval of aircraft system; Overload of the aircraft; g: gravitational acceleration; W: wind speed in the ground coordinate system; The derivative of wind speed in ground coordinates. DETAILED DESCRIPTION

[0074] In view of the situation where there is wind interference in a fixed-wing aircraft system, the present invention invents an aircraft airspeed state estimation method based on an extended state Kalman filter. The present invention solves the following technical problems in the field of aircraft state estimation:

[0075] 1. In view of the complex and changeable environment and working conditions faced by aircraft during flight, nonlinear systems can better describe the dynamic behavior under these complex conditions, so the dynamic systems of aircraft are mostly nonlinear systems. The present invention can transform the dynamic model of the aircraft into a linear system, greatly reducing the difficulty of estimating its state.

[0076] 2. The airspeed of an aircraft is affected by wind, but due to the limitations of physical equipment, it is almost impossible to estimate the speed and direction of the wind in real time in a complex flight scenario. The present invention can estimate the impact of wind on the airspeed state of an aircraft in real time and minimize this impact to help design the feedback control law in the subsequent aircraft control method. This problem is of great significance and great challenge.

[0077] In order to verify the practicality of the method of the present invention, we adopted two forms of aircraft system disturbance, namely constant disturbance and time-varying disturbance, to test the effect of the method respectively. The following are the specific implementation steps of the method of the present invention:

[0078] Specific implementation step 1: Set up the algorithm environment and measure unbiased transformation.

[0079] The wind speed and noise in the algorithm environment are as follows: Wind speed setting: The derivative (i.e., disturbance) of the wind speed from 0 to 50 seconds is (10, 10, 10) / 50 respectively; Noise parameter setting: The airspeed, angle of attack, and sideslip angle measurement noises satisfy the Gaussian distribution with a mean of 0, a standard deviation of 1, a mean of 0, a standard deviation of 0.02, and a mean of 0, a standard deviation of 0.02 respectively.

[0080] The unbiased conversion of the measurement is implemented as follows: the measured airspeed, angle of attack, and sideslip angle are converted to equivalent measured airspeed according to formula (1.3), and the covariance of the airspeed measurement noise in formula (1.3) is calculated according to formula (1.4).

[0081] Specific implementation step 2: Construction of system model and calculation of filtering method.

[0082] Based on the measured pitch angle, roll angle, roll angular rate, pitch angular rate, yaw angular rate, and overload of the aircraft, a system for estimation is built according to formulas (1.8) and (1.9), and a filtering estimation method is designed according to formula (1.11).

[0083] Specific implementation step three: Setting the parameters of the extended state Kalman filter estimation method.

[0084] The parameters of the extended state Kalman filter method are as follows: Satisfy the parameter adjustment criteria in step (iii), R k The design of the covariance matrix of the unbiased estimation of the quantity measurement in formula (1.4) is satisfied. Substituting the above parameter design into formula (1.11), the estimated value of the airspeed can be obtained, and then the estimated value of the above physical quantity is calculated from the angle of attack, sideslip angle and airspeed, that is, the result of this method is obtained.

[0085] Figure 2 is the estimated value and true value curve of airspeed, Figure 3 is the estimated value and true value curve of the empty rate, Figure 4 is the estimated value and true value curve of wind speed, Figure 5 is the estimated and true value curve of angle of attack, Figure 6 is the estimated value and true value curve of the sideslip angle, Figure 7 are the true and estimated values ​​of the disturbance.

[0086] Figure 2 The performance of the ESKF method for estimating airspeed is demonstrated. It can be seen that the results of airspeed estimation are satisfactory. Since the angle of attack and sideslip angle are defined by airspeed, this result provides a guarantee for accurate estimation of the angle of attack and sideslip angle (see the next section for the simulation results of the angle of attack and sideslip angle). Figure 3 The estimation results of the empty velocity are presented, which shows that the ESKF can better estimate the original measured physical quantity disturbed by noise.

[0087] In order to better illustrate the effectiveness of the aircraft airspeed state estimation method based on the extended state Kalman filter in the present invention, this method is compared with the airspeed state estimation method based on the traditional linear Kalman filter method, and the estimation effects of these two methods on the airspeed state are compared.

[0088] Figure 4 The estimated wind speed is given. Figure 5 and Figure 6 The estimation results of angle of attack and sideslip angle are given. The estimated results of wind speed converge to the true value after 5 seconds. The estimation results of angle of attack and sideslip angle by ESKF are better than those by KF. Figure 7Given the disturbance estimation results, it is worth noting that due to the lack of a dynamic model for disturbance estimation, its estimated value requires sufficient measurement data to be close to the true value, which will produce a certain time delay. The above results demonstrate the effectiveness of the method proposed in the present invention.

Claims

1. An aircraft airspeed state estimation method based on extended state Kalman filtering needs to consider the dynamic equation satisfied by the aircraft airspeed: in, is the airspeed of the aircraft, θ is the pitch angle, φ is the roll angle, p is the roll rate, q is the pitch rate, r is the yaw rate, is the overload of the aircraft, g is the acceleration of gravity, is the transformation matrix from the ground coordinate system to the body coordinate system, is the derivative of wind speed in the ground coordinate system; It is characterized in that it includes the following steps: Step (1): Perform an equivalent unbiased transformation on the measured airspeed state: The true values ​​of airspeed, angle of attack, and sideslip angle are recorded as V, α, and β respectively, and their measured values ​​are recorded as V m ,α m ,β m , and the relationship satisfies: Among them, the measurement noise U represents uniform distribution, a1, a2, a3>0; Using the airspeed, angle of attack, and sideslip angle measurements, we can get the airspeed The equivalent measurement value of is: Step 2: Estimation model construction and filtering method design: Consider the model without measurement noise where the airspeed satisfies: in, is the airspeed of the aircraft, θ is the pitch angle, φ is the roll angle, p is the roll rate, q is the pitch rate, r is the yaw rate, is the overload of the aircraft, g is the acceleration of gravity, is the transformation matrix from the ground coordinate system to the body coordinate system, is the derivative of wind speed in the ground coordinate system; Based on the above model, an airspeed estimation method based on Kalman filtering can be constructed; Step (III): Parameter adjustment of estimation method: The parameters that need to be adjusted in the aircraft airspeed state estimation method based on the extended state Kalman filter designed by the present invention are the matrix Q k and the matrix R k , where the matrix Q k The design principle is: Design Q k is the diagonal coefficient matrix: Among them, Q 1,k represents the covariance of the process noise, is the coefficient matrix to be designed to compensate for system disturbances, Given by the prior information of the disturbance, ζ = 0.5; R k Follow the design of formula (1.4).

2. The method for estimating the airspeed state of an aircraft based on an extended state Kalman filter according to claim 1: in step (1), To satisfy The parameters designed for unbiased measurement, the covariance of the noise in equation (1.3) is set to:

3. The method for estimating the airspeed state of an aircraft based on an extended state Kalman filter according to claim 1: Let R ij,k =R ji,k (i≠j), for the convenience of calculation, the subscript k is omitted in the following formula; 4. According to claim 1, a method for estimating the airspeed state of an aircraft based on an extended state Kalman filter: In step (ii), since the Kalman filter is used in a discrete environment, the airspeed model needs to be discretized: in, t k The airspeed of the aircraft at time t k ) is the pitch angle, φ(t k ) is the roll angle, p(t k ) is the rolling angular rate, q(t k ) is the pitch angular rate, r(t k ) is the yaw rate, is the overload of the aircraft, g is the acceleration of gravity, is the transformation matrix from the ground coordinate system to the body coordinate system, is the derivative of wind speed in the ground coordinate system, t s is the sampling step of the system, t k+1 -t k =t s , 5. According to the method for estimating the airspeed state of an aircraft based on an extended state Kalman filter as claimed in claim 4: the discrete original model (1.7) is set as: in, ω k and η k are process noise and measurement noise respectively.

6. According to the method for estimating the airspeed state of an aircraft based on an extended state Kalman filter according to claim 5: the parameter expression in formula (1.8) is:

7. The method for estimating the airspeed state of an aircraft based on an extended state Kalman filter according to claim 6: an extended state Kalman filter (ESKF) method is designed to estimate the disturbance and airspeed X k ; Construct a discrete system model with an extended state: The above model is equivalent to model (1.8); the above model can be organized as follows:

8. According to the method for estimating the airspeed state of an aircraft based on an extended state Kalman filter according to claim 7: the parameter expression in formula (1.10) is:

9. A method for estimating the airspeed state of an aircraft based on an extended state Kalman filter according to claim 7 or 8: Constructing an ESKF method: in, Represents Z k+1 The estimated value of Q k Parameters to be designed, R k is the equivalent measurement noise η k The covariance of and disturbance The estimated value of is then defined by the angle of attack, sideslip angle and airspeed: Angle of attack, sideslip angle, and airspeed estimates are calculated.

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