A linearization-based aircraft sensor measurement error propagation algorithm
By establishing nominal and nonlinear models of aircraft landing, the propagation process of sensor measurement errors was analyzed, the impact of sensor errors on aircraft landing accuracy was resolved, the performance of sensors and flight control systems was optimized, and the accuracy of aircraft landing was improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHENYANG AIRCRAFT DESIGN INST AVIATION IND CORP OF CHINA
- Filing Date
- 2025-05-07
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies cannot quantify the impact of sensor measurement errors on aircraft landing accuracy, which makes it impossible to optimize sensor performance and flight control system performance, thus affecting aircraft landing accuracy.
By establishing a nominal motion model and a nonlinear model for aircraft landing, first-order Taylor expansion linearization is performed using sensor measurement errors, the Jacobian matrix coefficients are calculated, the error propagation equation is obtained and transformed into an error propagation matrix, and the derivative is obtained using a polynomial fitting method to analyze the impact of measurement errors on other flight states.
A transmission model for sensor measurement errors was established, providing theoretical support for optimizing sensor performance and flight control system performance, thereby improving aircraft landing accuracy.
Smart Images
Figure CN120493527B_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of flight control, and specifically relates to a linearized algorithm for the propagation of aircraft sensor measurement errors. Background Technology
[0002] Controlling the safe landing of aircraft has always been a challenging problem in the aerospace field. When studying aircraft flight control systems, it's necessary to consider the errors present in the measurements of flight states such as airspeed, altitude, angle of attack, pitch rate, and pitch angle by the aircraft's onboard sensors. While many current researches on flight control have analyzed the statistical characteristics of errors in sensor measurements of flight states and designed various filtering algorithms to reduce these errors, no research has investigated the impact of sensor errors on the aircraft during landing. Without understanding the propagation process of these errors within the aircraft's mathematical model during landing, it's impossible to quantify their impact on the aircraft's flight state. This hinders the development of theoretical support and performance indicators for optimizing the performance of various sensor measurements and the flight control system, ultimately affecting landing accuracy.
[0003] Therefore, ensuring the landing accuracy of an aircraft is a problem that needs to be solved. Summary of the Invention
[0004] The purpose of this application is to provide a linearized aircraft sensor measurement error propagation algorithm to solve the problem in the prior art that the impact of the error in the sensor measurement of flight state on the aircraft and thus on landing accuracy cannot be determined.
[0005] The technical solution of this application is: a linearized aircraft sensor measurement error propagation algorithm, comprising:
[0006] Based on the aircraft's landing performance requirements, including airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, and pitching angle, a nominal motion model of the ideal landing process is established. The nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitching moment coefficient of the aircraft when it is in a nominal state are calculated using the nominal motion model.
[0007] The aircraft's mass, gravitational acceleration, pitch rate, and altitude are obtained in the aircraft's trajectory coordinate system. The aircraft's motion trajectory is analyzed, and a nonlinear model of the aircraft's landing is established.
[0008] By introducing sensor measurement errors, a first-order Taylor expansion linearizes the nonlinear model of aircraft landing, calculates the Jacobian matrix coefficients, and substitutes the Jacobian matrix coefficients into the nominal motion model to obtain the error propagation equation. Based on the error propagation equation, the state error of the aircraft is selected, and the error propagation equation is transformed into an error propagation matrix based on the state error.
[0009] The error propagation matrix is fitted using a polynomial fitting method. The discrete data in the equation are differentiated to obtain the partial derivatives of the corresponding discrete data, and then substituted into the error propagation equation to obtain the influence of the measurement error on other flight states.
[0010] Preferably, the thrust of the aircraft Lift ,resistance Pitch moment The expression is:
[0011] ;
[0012] ;
[0013] ;
[0014] ;
[0015] in Indicates the throttle position. Indicates air density, Indicates airspeed, Indicates the wing reference area. Indicates the mean aerodynamic chord length; Indicates the thrust coefficient; , These represent the lift coefficient and drag coefficient, respectively. This represents the lifting moment coefficient.
[0016] Preferably, within the nominal motion model, the engine thrust, lift, drag, and pitch moment are decomposed in the aircraft's trajectory system, and the nominal flight state for aircraft landing is solved with the pitch moment set to 0, thereby obtaining the nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitch moment coefficient.
[0017] Preferably, the nonlinear model for aircraft landing is:
[0018] ;
[0019] ;
[0020] ;
[0021] ;
[0022] ;
[0023] ;
[0024] in , , and These represent the aircraft's mass, gravitational acceleration, pitch rate, and altitude, respectively. Let be the moment of inertia in the y-direction. For time, For the angle of attack, The pitch angle, The trajectory tilt angle.
[0025] Preferably, the sensor measurement error is: In the formula, For flight status error, To control the quantity; For time;
[0026] After linearizing the first-order Taylor expansion, we get: In the formula, This is the deviation amount of flight status error. To control the deviation amount, This is the nominal value of the flight condition error. To control the nominal value;
[0027] Therefore, the error and transmission equations are obtained as follows:
[0028] ;
[0029] ;
[0030] ;
[0031] ;
[0032] ;
[0033] ;
[0034] In the formula, , , , , , , , , These represent the differences in airspeed, thrust, drag, lift, pitch moment, angle of attack, track inclination angle, pitch angle, and altitude of the aircraft, respectively. , , , These represent the nominal state values corresponding to the aircraft's airspeed, thrust, angle of attack, and track inclination angle, respectively.
[0035] Preferably, the method for obtaining the state error is as follows:
[0036] In the absence of airflow disturbance and without considering inputs such as throttle and control surfaces, the error expressions for obtaining the aircraft's longitudinal force and longitudinal moment are as follows:
[0037] ;
[0038] ;
[0039] ;
[0040] ;
[0041] In the formula, , , , , , , , , , , , These are the partial derivatives of the parameters corresponding to each subscript. Indicates the height difference. express The first derivative, express The first derivative;
[0042] Substituting the error expressions for the longitudinal force and longitudinal moment of the aircraft into the error propagation equation, we obtain the state error as follows:
[0043] ;
[0044] ;
[0045] ;
[0046] ;
[0047] ;
[0048] ;
[0049] The state error is represented in vector form:
[0050] ;
[0051] The error propagation equation is transformed into an expression for the error propagation matrix A, which is:
[0052] .
[0053] The linearization-based aircraft sensor measurement error propagation algorithm of this application analyzes the propagation process of sensor measurement errors by studying the longitudinal dynamics and kinematics models of the aircraft landing process and using a linearization method. Finally, a propagation model of airborne sensor measurement errors during aircraft landing is established. This model can provide theoretical support and index requirements for optimizing the measurement performance of various aircraft sensors and the performance of the flight control system, thereby improving the landing accuracy of the aircraft. Attached Figure Description
[0054] To more clearly illustrate the technical solutions provided in this application, the accompanying drawings will be briefly described below. Obviously, the drawings described below are merely some embodiments of this application.
[0055] Figure 1 This is a schematic diagram of the overall process of this application;
[0056] Figure 2 This is a schematic diagram of the aircraft landing process for this application;
[0057] Figure 3 This is a curve fitting the discrete aerodynamic data of this application. Detailed Implementation
[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0059] An algorithm for propagating measurement errors from aircraft sensors based on linearization, such as Figure 1 It includes the following steps:
[0060] Step S100, based on the aircraft's landing performance requirements, including airspeed, thrust, drag, lift, pitch moment, angle of attack, track roll angle, and pitch angle, such as... Figure 2 In the picture , , , , , , , These represent the aircraft's airspeed, thrust, drag, lift, pitch moment, angle of attack, track roll angle, and pitch angle, respectively. A nominal motion model of the ideal landing process of the aircraft is established, and the nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitch moment coefficient of the aircraft under nominal conditions are calculated using the nominal motion model.
[0061] Preferably, the aircraft's thrust Lift ,resistance Pitch moment The expression is:
[0062] ;
[0063] ;
[0064] ;
[0065] ;
[0066] in Indicates the throttle position. Indicates air density, Indicates airspeed, Indicates the wing reference area. This represents the average aerodynamic chord length. Thrust coefficient is a function of airspeed and altitude. , These represent the lift coefficient and drag coefficient, respectively, both of which are functions of angle of attack, airspeed, and flight altitude. The pitching moment coefficient is a function of angle of attack, airspeed, pitch rate, rate of attack, and flight altitude.
[0067] Under nominal conditions, an aircraft needs to maintain its attitude, angle of attack, airspeed, and trajectory roll angle during landing. The nominal angle of attack, pitch angle, airspeed, and trajectory roll angle are typically set as follows: , , , .
[0068] Preferably, within the nominal motion model, the engine thrust, lift, drag, and pitch moment are decomposed in the aircraft's trajectory system, and the nominal flight state for aircraft landing is solved with the pitch moment set to 0, thereby obtaining the nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitch moment coefficient.
[0069] The corresponding state parameters are shown in Table 1:
[0070] Table 1: Nominal Condition Parameters for Aircraft Landing
[0071]
[0072] Step S200: Establish a nonlinear model of the aircraft landing process:
[0073] The aircraft's mass, gravitational acceleration, pitch rate, and altitude are obtained in the aircraft's flight path coordinate system. The aircraft's trajectory is analyzed, and a nonlinear model of the aircraft's landing is established. The nonlinear model of the aircraft's landing is shown below:
[0074] ;
[0075] ;
[0076] ;
[0077] ;
[0078] ;
[0079] ;
[0080] in , , and These represent the aircraft's mass, gravitational acceleration, pitch rate, and altitude, respectively. Let be the moment of inertia in the y-direction. For time, For the angle of attack, The pitch angle, The trajectory tilt angle.
[0081] Step S300: Obtain the error propagation equation for the aircraft state based on the linearization method:
[0082] By introducing sensor measurement errors, a first-order Taylor expansion is performed to linearize the nonlinear model of aircraft landing, and the Jacobian matrix coefficients are calculated. These coefficients are then substituted into the nominal motion model to obtain the error propagation equation. Based on the error propagation equation, the aircraft's state error is selected, and the error propagation equation is transformed into an error propagation matrix based on this state error.
[0083] Preferably, the sensor measurement error is: In the formula, For flight status error, For control parameters, such as rudder deflection and throttle commands; For time;
[0084] After linearizing the first-order Taylor expansion, we get: In the formula, This is the deviation amount of flight status error. To control the deviation amount, This is the nominal value of the flight condition error. To control the nominal value;
[0085] Therefore, the error and transmission equations are obtained as follows:
[0086] ;
[0087] ;
[0088] ;
[0089] ;
[0090] ;
[0091] ;
[0092] In the formula, , , , , , , , , These represent the differences in airspeed, thrust, drag, lift, pitch moment, angle of attack, track inclination angle, pitch angle, and altitude of the aircraft, respectively. , , , These represent the nominal state values corresponding to the aircraft's airspeed, thrust, angle of attack, and track inclination angle, respectively.
[0093] Preferably, the method for obtaining the state error is as follows:
[0094] In the absence of airflow disturbance and without considering inputs such as throttle and control surfaces, the error expressions for obtaining the aircraft's longitudinal force and longitudinal moment are as follows:
[0095] ;
[0096] ;
[0097] ;
[0098] ;
[0099] In the formula, , , , , , , , , , , , These are the partial derivatives of the parameters corresponding to each subscript. Indicates the height difference. express The first derivative, express The first derivative.
[0100] Substituting the error expressions for the longitudinal force and longitudinal moment of the aircraft into the error propagation equation, we obtain the state error as follows:
[0101] ;
[0102] ;
[0103] ;
[0104] ;
[0105] ;
[0106] ;
[0107] The state error is represented in vector form:
[0108] ;
[0109] The error propagation equation is transformed into an expression for the error propagation matrix A, which is:
[0110] .
[0111] Step S400: Calculate the parameters of the error propagation matrix:
[0112] The error propagation matrix is fitted using a polynomial fitting method. The partial derivatives of the discrete data are obtained by taking the derivatives of the discrete data, and then substituting them into the error propagation equation to obtain the influence of the measurement error on other flight states.
[0113] In the error propagation matrix The most complex parameters are the partial derivatives of various aerodynamic forces and moments with respect to different state quantities of the aircraft. Continuous data refers to data with a refresh rate higher than 10Hz; data with a refresh rate lower than 10Hz is discrete data and requires fitting. Since aerodynamic data is generally discrete, it is necessary to fit the discrete points before calculating the derivatives. Specifically, a polynomial fitting method is used to solve for the partial derivative of the lift coefficient with respect to the angle of attack:
[0114]
[0115]
[0116] in This represents the overall lift coefficient of the fuselage and wings. This represents the lift coefficient of the horizontal stabilizer. This indicates the lift coefficient of the canard. It is a fixed parameter.
[0117] Taking the partial derivative of lift with respect to the angle of attack, we can obtain:
[0118]
[0119] With lift coefficient For example, lift coefficient The relationship with the angle of attack is shown in Table 2:
[0120] Table 2: Lift coefficients for different angles of attack value
[0121]
[0122] Then, a third-order polynomial fit is performed on the discrete data to obtain a third-order polynomial function, as shown in the following figure. Figure 3 As shown, the obtained third-order polynomial function is:
[0123]
[0124] In the aircraft's nominal landing state , .
[0125] Other partial derivative terms can be obtained using the same method, thus yielding the error propagation matrix. The parameters are as follows:
[0126] ;
[0127] Finally, a propagation model of the sensor's measurement error is obtained.
[0128] In summary, this application studies the longitudinal dynamics and kinematics models of the aircraft landing process, analyzes the transmission process of sensor measurement errors using a linearization method, and finally establishes a transmission model of airborne sensor measurement errors during aircraft landing. This model can provide theoretical support and performance indicators for optimizing the measurement performance of various aircraft sensors and the performance of the flight control system, thereby improving the landing accuracy of the aircraft.
[0129] Finally, it should be noted that the accompanying drawings of the embodiments disclosed in this invention only involve the structures involved in the embodiments disclosed in this invention. Other structures can refer to the general design. In the absence of conflict, the same embodiment and different embodiments of this invention can be combined with each other.
[0130] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for propagating measurement errors from aircraft sensors based on linearization, characterized in that, include: Based on the aircraft's landing performance requirements, including airspeed, thrust, drag, lift, pitching moment, angle of attack, track inclination angle, and pitching angle, a nominal motion model of the ideal landing process is established. The nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitching moment coefficient of the aircraft when it is in a nominal state are calculated using the nominal motion model. The aircraft's mass, gravitational acceleration, pitch rate, and altitude are obtained in the aircraft's trajectory coordinate system. The aircraft's motion trajectory is analyzed, and a nonlinear model of the aircraft's landing is established. By introducing sensor measurement errors, a first-order Taylor expansion linearizes the nonlinear model of aircraft landing, calculates the Jacobian matrix coefficients, and substitutes the Jacobian matrix coefficients into the nominal motion model to obtain the error propagation equation. The state error of the aircraft is selected based on the error propagation equation, and the error propagation equation is transformed into an error propagation matrix based on the state error. The error propagation matrix is fitted using a polynomial fitting method. The discrete data in the data are differentiated to obtain the partial derivatives of the corresponding discrete data, and then substituted into the error propagation equation to obtain the influence of the measurement error on other flight states. The specific steps for obtaining the error propagation matrix A are as follows: The sensor measurement error is: In the formula, For flight status error, To control the quantity; For time; After linearizing the first-order Taylor expansion, we get: In the formula, This is the deviation amount of flight status error. To control the deviation amount, Nominal value of flight condition error. To control the nominal value; Therefore, the error and transmission equations are obtained as follows: ； ； ； ； ； ； In the formula, where , , and These represent the aircraft's mass, gravitational acceleration, pitch rate, and altitude, respectively. Let be the moment of inertia in the y-direction. For time, For the angle of attack, The pitch angle, The trajectory tilt angle; , , , , , , , , These represent the differences in airspeed, thrust, drag, lift, pitch moment, angle of attack, track inclination angle, pitch angle, and altitude of the aircraft, respectively. , , , These represent the nominal state values corresponding to the aircraft's airspeed, thrust, angle of attack, and track inclination angle, respectively. The method for obtaining the state error is as follows: In the absence of airflow disturbance and without considering the inputs of throttle and control surfaces, the error expressions for obtaining the longitudinal force and longitudinal moment of the aircraft are as follows: ； ； ； ； In the formula, , , , , , , , , , , , These are the partial derivatives of the parameters corresponding to each subscript. Indicates the height difference. express The first derivative, express The first derivative; Substituting the error expressions for the longitudinal force and longitudinal moment of the aircraft into the error propagation equation, we obtain the state error as follows: ； ； ； ； ； ； The state error is represented in vector form: ； The error propagation equation is transformed into an expression for the error propagation matrix A, which is: 。 2. The method for propagating measurement errors of aircraft sensors based on linearization as described in claim 1, characterized in that, The thrust of the aircraft Lift ,resistance Pitch moment The expression is: ； ； ； ； in Indicates the throttle position. Indicates air density, Indicates airspeed, Indicates the wing reference area. Indicates the mean aerodynamic chord length; Indicates the thrust coefficient; , These represent the lift coefficient and drag coefficient, respectively. This represents the lifting moment coefficient.
3. The method for propagating measurement errors of aircraft sensors based on linearization as described in claim 2, characterized in that: Within the nominal motion model, the engine thrust, lift, drag, and pitch moment are decomposed in the aircraft's trajectory system, and the nominal flight state of the aircraft during landing is solved with the pitch moment set to 0, yielding the nominal engine thrust, nominal lift coefficient, nominal drag coefficient, and nominal pitch moment coefficient.
4. The method for propagating measurement errors of aircraft sensors based on linearization as described in claim 2, characterized in that: The nonlinear model for the aircraft landing is as follows: ； ； ； ； ； 。