Patent Publication Number: US-11029706-B2

Title: Flight control system for determining a fault based on error between a measured and an estimated angle of attack

Description:
INTRODUCTION 
     The present disclosure relates to flight control systems. More specifically, the present disclosure relates to flight control systems that determine the presence of a fault when the error between a measured angle of attack and an estimated angle of attack exceeds a threshold value. 
     BACKGROUND 
     A Common Mode Monitor (CMM) or fault detector is typically used to detect pitot tube faults, such as detecting when pitot tubes may be blocked with ice. Pitot tubes provide information that is used to calculate the speed and altitude of an aircraft. In operation, each pitot tube, or channel, sends data to the CMM. Because pitot tubes are pressure based sensors, when a pitot tube is blocked, its output may be inaccurate. Thus, it is desirable to generate a signal that can be used in lieu of the pitot tube signal when a pitot tube fault is suspected. 
     SUMMARY 
     According to several aspects, a flight control system for an aircraft is disclosed. The flight control system includes one or more processors and a memory coupled to the one or more processors. The memory stores data comprising a database and program code that, when executed by the one or more processors, causes the flight control system to receive as input a measured angle of attack that is based on a raw angle of attack. The flight control system also receives as input an estimated angle of attack that is based on a total pressure. The flight control system also compares the measured angle of attack with the estimated angle of attack to determine an error. In response to determining that the error between the measured angle of attack and the estimated angle of attack exceeds a threshold value, the flight control system determines the presence of a fault with an angle of attack value. 
     In an additional aspect of the present disclosure, a flight control system for an aircraft is disclosed. The flight control system includes one or more processors and a plurality of angle of attack sensors in communication with the one or more processors, where the plurality of angle of attack sensors are configured to measure a raw angle of attack. The flight control system also includes a plurality of pitot tubes in communication with the one or more processors, where the plurality of pitot tubes measure a total pressure. The flight control system also includes a memory coupled to the one or more processors, the memory storing data comprising a database and program code that, when executed by the one or more processors, causes the flight control system to receive as input a measured angle of attack that is based on the raw angle of attack. The flight control system also receives as input an estimated angle of attack that is based on the total pressure. The flight control system compares the measured angle of attack with estimated angle of attack to determine an error. In response to determining that the error between the measured angle of attack and the estimated angle of attack exceeds a threshold value, the flight control system determines the presence of a fault with a majority of the plurality of angle of attack sensors. 
     In yet another aspect of the disclosure, a method of determining a fault with an angle of attack value for an aircraft is disclosed. The method includes receiving as input, by a computer, a measured angle of attack that is based on a raw angle of attack. The method also includes receiving as input, by the computer, an estimated angle of attack that is determined based on a total pressure. The method further includes comparing, by the computer, the measured angle of attack with the estimated angle of attack to determine an error. In response to determining the error between the measured angle of attack and the estimated angle of attack exceeds a threshold value, the method includes determining the presence of the fault with the angle of attack value. 
     The features, functions, and advantages that have been discussed may be achieved independently in various embodiments or may be combined in other embodiments further details of which can be seen with reference to the following description and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way. 
         FIG. 1  is a schematic diagram of an exemplary flight control system of an aircraft according to an exemplary embodiment; 
         FIG. 2  is an elevated perspective view of the aircraft illustrating various control surfaces and sensors according to an exemplary embodiment; 
         FIG. 3  is a flowchart illustrating the flight control system during a normal mode of operation according to an exemplary embodiment; 
         FIG. 4  is a flowchart of the flight control system shown in  FIG. 3  responding to a common mode pneumatic event according to an exemplary embodiment; 
         FIG. 5  is a block diagram of an extended Kalman filter for determining an estimated dynamic pressure according to an exemplary embodiment; 
         FIG. 6  illustrates a control module for determining the estimated dynamic pressure according to an exemplary embodiment; 
         FIG. 7  is an elevated perspective view of the aircraft illustrating a center of gravity according to an exemplary embodiment; 
         FIG. 8  is a process flow diagram illustrating an exemplary method for detecting a fault by a common mode monitoring system based on the estimated dynamic pressure according to an exemplary embodiment; 
         FIG. 9  is a flowchart illustrating the flight control system during a normal mode of operation, where a measured angle of attack is used according to an exemplary embodiment; 
         FIG. 10  is a flowchart of the flight control system shown in  FIG. 9  utilizing an estimated angle of attack instead of the measured angle of attack in response to detecting a fault according to an exemplary embodiment; 
         FIG. 11  is a block diagram of an extended Kalman filter for determining an estimated angle of attack according to an exemplary embodiment; 
         FIG. 12  illustrates a control module for determining the estimated angle of attack according to an exemplary embodiment; 
         FIG. 13  is a process flow diagram illustrating an exemplary method of determining the estimated angle of attack according to an exemplary embodiment; 
         FIG. 14  is an illustration of a system for detecting the common mode pneumatic event based on the measured dynamic pressure and the angle of attack, where the system includes a first detector and a second detector according to an exemplary embodiment; 
         FIG. 15  is an illustration of the first detector of the system shown in  FIG. 14  for detecting a synchronous fault of a plurality of pitot tubes according to an exemplary embodiment; 
         FIG. 16  is an illustration of the second detector of the system shown in  FIG. 14  for detecting an asynchronous fault of the plurality of pitot tubes according to an exemplary embodiment; 
         FIG. 17  is a process flow diagram illustrating an exemplary method for determining the synchronous fault based on the system shown in  FIG. 15  according to an exemplary embodiment; 
         FIG. 18  is a process flow diagram illustrating an exemplary method for determining the asynchronous fault based on the system shown in  FIG. 16  according to an exemplary embodiment; and 
         FIG. 19  is an illustration of a computer system used by the flight control system of  FIG. 1  according to an exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure is directed towards a flight control system for an aircraft that detects a fault based on an angle of attack value. The flight control system switches from a measured angle of attack to an estimated angle of attack value in response to detecting the fault. The measured angle of attack is determined based on data collected from a plurality of angle of attack sensors. In contrast, the estimated angle of attack is not based on the values measured by the angle of attack sensors. Instead, the estimated angle of attack is determined based on a total pressure measured by a plurality of pitot tubes that are part of the aircraft. 
     In one embodiment, in response to determining the presence of a common mode pneumatic event is detected, the flight control system determines the measured angle of attack without using the for true air speed of the aircraft and the measured Mach number. A common mode pneumatic event represents a condition where a majority of the plurality of pitot tubes are blocked or do not produce accurate readings. 
     The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses. 
     Referring to  FIG. 1 , an exemplary schematic diagram of an aircraft  10  including a flight control system  18  is shown. The flight control system  18  includes a flight control module  16  configured to determine trusted air speed signals that are sent to one or more aircraft systems  20 . The trusted air speed signals include an estimated Mach number M MDL , a calibrated air speed Vcas MDL , and a true air speed of the aircraft Vt MDL . The flight control module  16  determines a measured dynamic pressure Q bar(m)  and a synthetic or estimated dynamic pressure Q bar(e) . The measured dynamic pressure Q bar(m)  is determined by an air data control module  28  based on data collected from a plurality of air data sensors  22 . Specifically, the air data sensors  22  include a plurality of pitot tubes  40  ( FIG. 2 ). However, the estimated dynamic pressure Q bar(e)  is an estimated value determined by an estimator control module  30 . The estimated dynamic pressure Q bar(e)  is based on data collected from a plurality of control surfaces, inertial, and angle of attack sensors  24 . It is to be appreciated that the estimated dynamic pressure Q bar(e)  is not determined based on data collected from air data sensors  22  (i.e., the plurality of pitot tubes  40 ). 
     The flight control system  18  includes a common mode pneumatic event (CMPE) fault detection and signal selector, which is referred to as a CMPE control module  36 . In the present disclosure, the common mode pneumatic event occurs when a majority of the plurality of pitot tubes  40  ( FIG. 2 ) are blocked or otherwise not operating correctly simultaneously or within a relatively short amount of time (e.g., about 0.001 to about 10 seconds in one embodiment). For example, the plurality of pitot tubes  40  may be blocked because of icing or by foreign particles such as volcanic ash. The plurality of pitot tubes  40  are each configured to measure pressure, and the readings from each pitot tube  40  are combined into a single measurement. The measurements from each pitot tube  40  may be combined by averaging or a mid-value select, which in turn produces a total pressure P TOT . However, when blocked the plurality of pitot tubes  40  produce a total pressure P TOT  that is not accurate. Specifically, the reading for total pressure P TOT  is very low, which results in an unrealistic calculated air speed. The calculated airspeed is provided to the aircraft systems  20 . 
     Referring to  FIG. 1 , the measured dynamic pressure Q bar(m)  is used to determine the estimated Mach number M MDL , the calibrated air speed Vcas MDL , and the true air speed of the aircraft Vt MDL  (i.e., the trusted air speed values) during normal operating conditions. For purposes of the present disclosure, normal operating conditions or the normal mode of operation is when a majority of the plurality of pitot tubes  40  ( FIG. 2 ) are functioning. However, it is to be appreciated that the normal mode of operation is also based on other operating parameters of the aircraft  10  such as, for example, inertial data sensors. 
     In response to receiving a notification that a majority of pitot tubes  40  are blocked (i.e., the air speed value is now unrealistically low), the CMPE control module  36  switches from measured dynamic pressure Q bar(m)  to the estimated dynamic pressure Q bar(e)  to determine the estimated Mach number M MDL , the calibrated air speed Vcas MDL , and the true air speed of the aircraft Vt MDL . In other words, when a majority of the plurality of pitot tubes  40  are not blocked, the flight control system  18  determines the trusted air speeds based on measurements from the plurality of pitot tubes  40 . However, once the flight control system  18  determines a majority of the pitot tubes are blocked, then the flight control system  18  determines the trusted air speeds based on the estimated dynamic pressure Q bar(e) . 
     The aircraft systems  20  include both hardware and software for providing aircraft maneuver control. In one embodiment, the aircraft systems  20  include, but are not limited to, integrated flight control electronic computers, avionic computers, engine electronic control computers, and the displays and crew alerting computers. The integrated flight control electronic computers may include software partitions to provide functionality such as, but not limited to, primary flight control, autopilot, integrated signal management, air data reference function. The avionic computers provide autothrottle control, flight plans, and waypoint guidance. The engine electronic control computers may provide propulsion controls for engine thrusts. The displays and crew alerting computers may provide real-time aircraft state information such as, but not limited to, altitude, air speed, pitch and bank angles, air temperature, and any system warning messages. 
       FIG. 2  is an elevated perspective view of an exterior  42  of the aircraft  10 . The plurality of pitot tubes  40  are placed on a nose  46  of the aircraft, adjacent to a radome  44 . Specifically, in one non-limiting example, two of the plurality of pitot tubes  40  are placed on a left hand side  50  of the aircraft and another pitot tube  40  is located on a right side  52  of the aircraft  10  (not visible in  FIG. 2 ). The pitot tubes  40  on the left and right hand sides  50 ,  52  of the aircraft  10  correspond to a pilot, a co-pilot, and a backup. Although three pitot tubes  40  are described, it is to be appreciated that more pitot tubes or fewer pitot tubes may be used as well. In the present example, at least two of the three pitot tubes  40  would be blocked or inoperable to trigger the common mode pneumatic event. 
     In addition to the plurality of pitot tubes  40 , in the exemplary embodiment as shown in  FIG. 2  the aircraft  10  also includes a plurality of angle of attack sensors  60  (only one is visible in  FIG. 2 ) and two total air temperature (TAT) probes  62  (only one is visible in  FIG. 2 ). The plurality of angle of attack sensors  60  and the probes  62  are located on the left hand side  50  and the right hand side  52  of the nose  46  of the aircraft  10 . The aircraft  10  also includes static ports  64  located on both the left hand side  50  and the right hand side  52  of the aircraft  10  (only the left side is visible in  FIG. 2 ). The static ports  64  are located on a fuselage  66  in a location aft of the plurality of pitot tubes  40 , and adjacent to the wings  70 . 
     A nacelle  74  is attached to each wing  70  by a pylon  76 . Each nacelle  74  houses a corresponding aircraft engine  78 . An engine total air temperature (TAT) probe (not visible in  FIG. 2 ) is positioned in an inlet cowl  82  of each nacelle. An engine speed sensor (not visible in  FIG. 2 ) measures the rotational speed of a corresponding one of the aircraft engines  78 . In an embodiment, the engine speed sensor is located within an engine core in front of the high pressure stator vane rings (not visible in  FIG. 2 ). 
     The control surfaces  68  ( FIG. 3 ) of the aircraft  10  are now described. The wings  70  both include a leading edge  84  and a trailing edge  86 . Both wings  70  include corresponding leading edge slats  88  located at the leading edge  84  of each wing  70  and corresponding trailing edge flaps  90  located at the trailing edge  86  of each wing  70 . The wings  70  also include one or more spoilers  92  disposed along an upper surface  94  of each wing  70  and a pair of ailerons  98  located at the trailing edge  86  of each wing  70 . A tail or aft end  100  of the aircraft  10  terminates at an exhaust outlet  102 . The exhaust outlet  102  is for an auxiliary power unit (APU)  104  located at the tail end of the aircraft  10 . The aft end  100  of the aircraft  10  includes a vertical stabilizer  106  and two horizontal stabilizers  108 . A rudder  110  is located at a trailing edge  112  of the vertical stabilizer  106 , and an elevator  114  is located at a trailing edge  116  of each horizontal stabilizer  108 . The rudder  110  is moveable to control the yaw of the aircraft  10  and the elevators  114  are moveable to control the pitch of the aircraft  10 . 
       FIG. 3  is a block diagram illustrating a normal mode of operation of the aircraft  10 . During the normal mode of operation, a majority of the plurality of pitot tubes  40  ( FIG. 2 ) are not blocked. In the embodiment as shown in  FIG. 3 , no common mode pneumatic event has occurred. Thus, an output  96  generated by the CMPE control module  36  is set to a FALSE value (i.e., CMPE FAULT=FALSE). Referring to both  FIGS. 2 and 3 , the total pressure P TOT  from the plurality of pitot tubes  40  and the static pressure Ps from the static ports  64  are sent to an air data reference function block  120 . The air data reference function block  120  determines the measured dynamic pressure Q bar(m)  based on the total air pressure P TOT  from the plurality of pitot tubes  40  and the static pressure Ps. Specifically, the measured dynamic pressure Q bar(m)  is the difference between the total air pressure P TOT  and the static pressure Ps. In the embodiment as shown in  FIG. 3 , the measured dynamic pressure Q bar(m)  is accurate because the plurality of pitot tubes  40  are not blocked. Accordingly, the measured dynamic pressure Q bar(m)  determined by the air data reference function block  120  is received as input by a primary flight control module  140 , an autopilot control module  142 , an autothrottle control module  144 , and one or more displays  146 . 
     Referring to  FIGS. 1 and 3 , the flight control system  18  determines the trusted air speeds (the estimated Mach number M MDL , the calibrated air speed Vcas MDL , and the true air speed of the aircraft Vt MDL ) as long as the aircraft  10  is in the normal mode of operation. A flight envelope protection mode, an autopilot feature, and an autothrottle feature are available during the normal mode of operation. 
     The plurality of displays  146  may include a Crew Alerting System (CAS) display. The messages shown on the CAS display are triggered by measurements and events outside normal thresholds or tolerances of the aircraft  10  and are visible to a pilot  130  and other crew members. When the aircraft  10  is in the normal mode of operation, the measured dynamic pressure Q bar(m)  determined by the air data reference function block  120  is received as input by the primary flight control module  140 , the autopilot control module  142 , the autothrottle control module  144 , and the plurality of displays  146 . However, when a majority of the plurality of pitot tubes  40  ( FIG. 2 ) are blocked the aircraft  10  switches from the normal mode of operation and into an extended mode of operation, which is explained in greater detail below and is shown in  FIG. 4 . 
     Referring to  FIG. 3 , when the aircraft  10  is in the normal mode of operation and the autopilot feature is engaged, then the autopilot control module  142  sends autopilot commands to the primary flight control module  140 . The primary flight control module  140  determines surface control commands that are sent to the control surfaces  68 , and the autothrottle control module  144  determines engine thrusts  145  of the aircraft engines  78  ( FIG. 2 ). When the aircraft  10  is in the normal operating mode but the autopilot feature is not engaged, then wheel and column commands generated by the pilot  130  are processed by the primary flight control module  140  in accordance with aircraft control laws such as, for example, pitch control laws and lateral control laws. Additionally, the flight envelope control protect feature is engaged. 
     An extended Kalman Filter (EKF) control module  122  determines the estimated dynamic pressure Q bar(e) . The EKF control module  122  is described in greater detail below and is illustrated in  FIGS. 5 and 6 . A common mode monitor (CMM)  126  receives as input the measured dynamic pressure Q bar(m)  from the air data reference function block  120 , the estimated dynamic pressure Q bar(e)  from the EKF control module  122 , and the output  96  from the CMPE control module  36 . The CMM  126  determines a common mode failure, which is also referred to as a fault, of the measured dynamic pressure Q bar(m) . The common mode failure of the measured dynamic pressure Q bar(m)  represents a failure of a majority of the plurality of pitot tubes  40  ( FIG. 2 ). 
     The common mode failure of the measured dynamic pressure Q bar(m)  is determined based on a difference between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e) . Specifically, the CMM  126  determines a common mode failure of the measured dynamic pressure Q bar(m)  has occurred when a difference between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  exceeds a threshold value for a threshold amount of time. In one exemplary embodiment, the threshold value is more than fifty percent and the threshold amount of time ranges from about five seconds to about fifteen seconds. However, it is to be appreciated that other values may be used as well. In the embodiment as shown in  FIG. 3 , the CMM  126  determines no common mode fault has occurred (e.g., the threshold value between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  and the output  96  indicates that CMPE FAULT=FALSE). Accordingly, the CMM  126  sends an output  99  to the primary flight control module  140  indicating the normal mode of operation (i.e., Normal Mode=TRUE). 
     Turning now to  FIG. 4 , the extended normal mode of operation is shown. During the extended normal mode of operation, a majority of the plurality of pitot tubes  40  ( FIG. 2 ) are blocked. Thus, the CMPE control module  36  detects a common mode pneumatic event. However, during the extended mode of operation, the CMPE control module  36  suppresses the common mode pneumatic event during a time delay, which is accomplished by continuing to generate an output  96  that indicates no common mode pneumatic event is detected (i.e., CMPE FAULT=FALSE). In other words, even though a common mode pneumatic event is detected, the CMPE control module  36  sends a message to the CMM  126  indicating that no common mode pneumatic event has occurred. However, the CMM  126  determines that a common mode fault has occurred (i.e., the difference between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  exceeds the threshold value for the threshold amount of time). In response to receiving the FALSE value from the CMPE control module  36  (which indicates no common mode pneumatic event) while simultaneously determining the presence of a common mode fault, the CMM  126  continues to send generate an output  99  indicating normal mode operation (i.e., Normal Mode=TRUE). The CMPE control module  36  continues to suppress the common mode pneumatic event during the time delay. In one embodiment, the time delay is about 120 seconds. This amount may vary based on the length of time that an intermittent common mode pneumatic event may occur, however, is to be appreciated that there is a limit on the length of the time delay. The time delay is required to be at least 60 seconds. As seen in  FIG. 4 , when the aircraft  10  is in the extended normal mode of operation the estimated dynamic pressure Q bar(e)  determined by the EKF control module  122  is sent to the primary flight control module  140 , the autopilot control module  142 , the autothrottle control module  144 , and the plurality of displays  146 . 
     In some types of aircraft, the flight envelope protection system, pitch control, lateral control, and autopilot features are not available when the flight control system is in a secondary mode of operation. Instead, only simple pitch and roll controls are available. In other types of aircraft, a secondary autopilot feature may be available which provides basic autopilot maneuver controls that are independent of pitot air data signals. In the embodiment as shown in  FIG. 4 , the extended mode of operation allows for the primary flight control module  140 , the autopilot control module  142 , and the autothrottle control module  144  to operate as if no fault had been detected during the time delay. However, once the time delay is complete, then the common mode pneumatic event is no longer suppressed. Thus, if the CMPE control module  36  continues to detect a common mode pneumatic event, then the output  96  is now set to TRUE (i.e., CMPE FAULT=TRUE), and the aircraft  10  now switches into the secondary mode of operation. 
       FIG. 5  is a block diagram of an extended Kalman filter of the EKF control module  122 . The block diagram represents a system  148  for determining estimated dynamic pressure Q bar(e)  based on data collected from the plurality of control surface, inertial, and angle of attack sensors  24  ( FIG. 1 ). In other words, the estimated dynamic pressure Q bar(e)  is not determined based on the measurements from the plurality of pitot tubes  40  ( FIG. 2 ). The EKF control module  122  includes a measurement model  150 , a dynamic control module  152 , a Kalman gain block  154 , an integrator block  156 , an error block  158 , a multiplier  160 , and an adder  162 . The measurement model  150  predicts expected values of measured accelerations (longitudinal acceleration Ax, normal acceleration Az) in Equation 1 as: 
                     h   ⁡     (     x   ^     )       =       [             A   ^     X                 A   ^     Z           ]     =       1   m     ⁢       R   ⁡     (   α   )       ⁡     [               C   D     ⁡     (     α   ,     x   ^     ,     P   S       )       ⁢   S                   C   L     ⁡     (     α   ,     x   ^     ,     P   S       )       ⁢   S           ]                   Equation   ⁢           ⁢   1               
where m represents the mass of the aircraft  10 , C D  represents a coefficient of drag of the aircraft  10 , C L  represent a coefficient of lift of the aircraft  10 , P S  is static pressure, S is the reference area of a wing planform, α is the angle of attack, x is the estimated quantity (the estimated dynamic pressure Q bar(e) ), and R(a) is a rotational matrix of the forward stability-axis X S  relative to the body-axis X B  and the body-axis Z B  of the aircraft  10  ( FIG. 7 ). It is to be appreciated that the angle of attack α is assumed to be a measured value (i.e., measured by the plurality of angle of attack sensors  60 ).
 
     Continuing to refer to  FIG. 5 , the dynamic control module  152  determines a rate of change for the estimated dynamic pressure, which is referred to as an estimated rate of change of the dynamic pressure {dot over (Q)} bar(e) . The estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  is determined based on an estimated longitudinal acceleration component A_D (est)  of the aircraft  10 , which represents longitudinal acceleration along a forward stability-axis X S  (seen in  FIG. 7 ). Specifically, the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  is a function of a barometric altitude, the angle of attack α, a pitch angle θ, the estimated dynamic pressure Q bar(e) , and an estimated longitudinal acceleration component A_D (est)  of the aircraft  10 . In one embodiment, the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  is determined based on Equation 2, which is: 
                       Q   .       bar   ⁡     (   e   )         =           2   ⁢     q     bar   ⁡     (   e   )           ρ       ·   ρ   ·     [       g   ·     sin   ⁡     (     α   -   θ     )         -     A     D     (   est   )           ]               Equation   ⁢           ⁢   2               
α is the angle of attack, g is the acceleration of gravity, and ρ is air density.
 
     The Kalman gain block  154  stores a Kalman gain value K. The Kalman gain value K represents the weight given to the current state of the aircraft  10  (i.e., the operating conditions). The Kalman gain value K is not a scalar value, and instead is represented based on a 2×2 matrix. The Kalman gain value K varies based on the operating parameters of the aircraft  10 . Specifically, the Kalman gain value K is a dynamic value that is determined by a set of look-up tables  226  (seen in  FIG. 6 ) stored on a database  228 . The look-up tables  226  are generated based on operating conditions of the aircraft  10 , and the inputs to the look-up tables are the angle of attack α and the estimated Mach number M MDL  of the aircraft  10 . 
     The error block  158  receives as input the estimated longitudinal acceleration Ax (est)  and an estimated vertical acceleration Az (est)  from the measurement model  150  as well as a measured longitudinal acceleration Ax (mea)  and a measured vertical acceleration Az (mea) , which are measured by accelerometers and are explained in greater detail below. The error block  158  determines an acceleration error value E by determining a first difference between the estimated longitudinal acceleration Ax (est)  and the estimated vertical acceleration Az (est)  and a second difference between the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) . The multiplier  160  receives as input the acceleration error value E and the Kalman gain value K, and determines an estimated state update by multiplying the acceleration error value E with and the Kalman gain value K. 
     The adder  162  receives as input the residual Kalman value from the multiplier  160  and the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  from the dynamic control module  152 . The adder  162  combines the residual Kalman value with the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  together. The combined residual Kalman value and the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  are then sent to the integrator block  156 . The integrator block  156  then integrates the sum of the residual Kalman value and the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  to determine the estimated dynamic pressure {dot over (Q)} bar(e) . 
       FIG. 6  is an illustration of the EKF control module  122  including a plurality of submodules  200 ,  202 ,  204 ,  206 ,  208 ,  210 ,  212 . The submodules  200 ,  202 ,  204 ,  206 ,  208 ,  210 ,  212  are shown as distinct components, which may indicate the use of modular programming techniques. However, the software design may decrease the extent to which the submodules  200 ,  202 ,  204 ,  206 ,  208 ,  210 ,  212  are distinct by combining at least some program functions of multiple modules into a single module. Moreover, the functions attributed to the submodules  200 ,  202 ,  204 ,  206 ,  208 ,  210 ,  212  may be distributed in other ways, or on other systems than those depicted. Thus, embodiments of the present disclosure are not limited to the specific arrangement of systems or modules shown in  FIG. 6 . 
     Referring now to both  FIGS. 5 and 6 , the EKF control module  122  and the system  148  correspond to one another. Specifically, a coefficient submodule  200  and a propulsion submodule  202  of the EKF control module  122  both correspond to the measurement model  150  of the system  148 . A measurement submodule  204  of the EKF control module  122  corresponds to the adder  162  of the system  148 . An error submodule  206  of the EKF control module  122  corresponds to the error block  158  of the system  148 . A Kalman gain submodule  208  of the EKF control module  122  corresponds to the Kalman gain block  154  of the system  148 . A dynamic submodule  210  of the EKF control module  122  corresponds to the dynamic control module  152  of the system  148 . Finally, an integration submodule  212  corresponds to the integrator block  156  of the system  148 . 
     The EKF control module  122  receives as input a plurality of operating parameters of the aircraft  10  ( FIGS. 1 and 2 ). The operating parameters include, but are not limited to, the measured acceleration factors Ax (mea)  and Az (mea) , the angle of attack α, the barometric altitude, the pitch angle Θ, a deflection of the control surfaces δ of the aircraft  10 , the total air temperature T TOT , the engine speed N 1  of both aircraft engines  78  ( FIG. 2 ), and the static pressure P S . The deflection of the control surfaces δ include at least some of the control surfaces show in  FIG. 2 . Specifically, in the embodiment as shown in  FIG. 2 , the deflection of the control surfaces δ include the leading edge slats  88 , the trailing edge flaps  90 , the spoilers  92 , the ailerons  98 , the vertical stabilizer  106 , the horizontal stabilizers  108 , the rudder  110 , and the elevator  114 . 
       FIG. 7  illustrates the body axes of the aircraft  10 . The parameters X B , Y B , and Z B  represent the x, y, and z body axes of the aircraft  10  respectively, and CG represents the center of gravity for the aircraft  10 . The angle of attack α is measured between a body-axis X B  of the aircraft  10  and a vector X S , which represents a forward stability-axis of the aircraft  10 . The forward stability-axis X S  is a projection of an air speed direction X W  of the aircraft  10  onto a plane defined by the x and z axes. 
     Referring now to  FIGS. 6 and 7 , the measured longitudinal acceleration Ax (mea)  is the measured acceleration of the aircraft  10  in the direction of the body-axis X B  of the aircraft and the measured vertical acceleration Az (mea)  is the acceleration of the aircraft  10  in the direction of the body-axis Z B . The measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea)  are determined by one or more accelerometers located at the center of gravity CG of the aircraft  10 . However, many types of accelerometers actually measure the load factor. Thus, if the accelerometers do truly measure accelerations, then the corresponding load factor is calculated by subtracting the acceleration due to gravity along each axis. 
     The coefficient submodule  200  receives as input a plurality of first operating parameters that each represent an operating condition of the aircraft  10 . The coefficient submodule  200  determines the drag coefficient C D  and a lift coefficient C L  based on the plurality of first operating parameters. Thus, it is to be appreciated that the EKF control module  122  determines the estimated dynamic pressure Q bar(e)  based on both the drag coefficient C D  and the lift coefficient C L . The first plurality of coefficients include the angle of attack α, the deflection of the control surfaces δ of the aircraft  10 , a previous estimated dynamic pressure Q bar(p)  determined in an iteration immediately before the present iteration, and the estimated Mach number M MDL . It is to be appreciated that at the very beginning of a simulation, the previous estimated dynamic pressure Q bar(p)  is set to the measured dynamic pressure Q bar(m) . 
     The coefficient submodule  200  determines the drag coefficient C D  and the lift coefficient C L  based on one or more coefficient three-dimensional look-up tables  220 . The coefficient three-dimensional look-up tables  220  provide a drag coefficient C D  and a lift coefficient C L  value based on specific values of the plurality of first operating parameters (angle of attack α, the deflection of the control surfaces δ of the aircraft  10 , the previous estimated dynamic pressure Q bar(p) , and the estimated Mach number M MDL ). The coefficient three-dimensional tables  220  are derived from data collected during testing (e.g., wind-tunnel test data) and data collected during flight testing. The coefficient three-dimensional look-up tables  220  are stored on one or more propulsion databases  222 . It is to be appreciated that while the databases  222  are shown as part of the EKF control module  122 , the databases  222  may be located in a location remote from the EKF control module  122  as well, and the embodiment as shown in  FIG. 6  is intended to illustrate only an example of where the three-dimensional look-up tables may be stored. 
     It is to be appreciated that the coefficient three-dimensional look-up tables  220  are based on lift and drag values for the individual control surfaces of the aircraft  10  (e.g., the leading edge slats  88 , the trailing edge flaps  90 , the spoilers  92 , the ailerons  98 , the vertical stabilizer  106 , the horizontal stabilizers  108 , the rudder  110 , and the elevator  114 ). Each control surface includes look-up tables for low speed conditions (i.e., having an estimated Mach number of less than 0.4) and for high speed conditions (i.e., an estimated Mach number of 0.4 or more). Furthermore, each control surface is associated with individual look-up tables for the drag coefficient and the lift coefficient. All of the look-up tables may be influenced by various operating parameters of the aircraft  10  such as, for example, the altitude or the angle of attack. All of the individual look-up tables are combined to determine the drag coefficients and lift coefficients listed in the coefficient three-dimensional look-up tables  220 . 
     The propulsion submodule  202  receives as input a plurality of second operating parameters of the aircraft  10 . Specifically, the plurality of second operating parameters of the aircraft  10  include the barometric altitude, the pitch angle Θ, the total air temperature T TOT , the engine speed N 1  of both aircraft engines  78  ( FIG. 2 ), and the static pressure P S . The propulsion submodule  202  determines an estimated net thrust T of the aircraft  10  based on the plurality of second operating parameters. More specifically, the propulsion submodule  202  determines the estimated net thrust T of the aircraft  10  based on propulsion-based three-dimensional look-up tables  230  that provide the estimated net thrust T based on specific values of the barometric altitude, pitch angle Θ, the total air temperature T TOT , the engine speed N 1  of both aircraft engines  78  ( FIG. 2 ), and the static pressure P S . The three-dimensional look-up tables  230  are generated based on simulations performed for the specific type or model of the aircraft  10 . The three-dimensional look-up tables  230  are stored on one or more propulsion databases  232 . 
     The measurement submodule  204  receives as input the drag coefficient C D , the lift coefficient C L , and the estimated net thrust T. The measurement submodule  204  determines the estimated acceleration Ax (est)  and the estimated acceleration Az (est)  based on the drag coefficient C D , the lift coefficient C L , and the estimated net thrust T. Specifically, the measurement submodule  204  solves for the estimated accelerations Ax (est) , Az (est)  based on an equation of motion that expresses an equivalent force acting upon the aircraft  10 . The equation of motion is expressed in Equation 3 as: 
                     [             A   D     ⁡     (     x   ^     )                   A   L     ⁡     (     x   ^     )             ]     =           S   m     ⁡     [             C   D     ⁡     (     α   ,     x   ^     ,     P   S       )                   C   L     ⁡     (     α   ,     x   ^     ,     P   S       )             ]       ⁢     x   ^       -       1   m     ⁢       R   a   T     ⁡     [             X   T     ⁡     (         h   j     ⁢   t     ,     N     1   ⁢   c       ,     x   ^     ,     P   S       )                   Z   T     ⁡     (         h   j     ⁢   t     ,     N     1   ⁢   c       ,     x   ^     ,     P   S       )             ]                   Equation   ⁢           ⁢   3               
where A D  is the drag acceleration, A L  is the lift acceleration, S is the reference area of a wing planform, m is the mass of the aircraft  10 , α is the angle of attack, P S  is the static pressure, R α   T  is a rotational matrix of the forward stability-axis X S  relative to the body-axis X B  and the body-axis Z B  of the aircraft  10  ( FIG. 7 ), X T  is thrust force in relative to a body-axis X B  of the aircraft  10 , Y T  is thrust force in relative to a body-axis Y B  of the aircraft  10 , h ft  is the barometric altitude, N 1c  is engine speed (corrected for temperature), and x is a state vector. The drag acceleration A D  is determined by subtracting the net thrust force of the body-axis X B  from the drag force and dividing the result by the mass of the aircraft  10 . The lift acceleration A L  is determined by subtracting the net thrust force of the body-axis Z B  from the lift force and dividing the result by the mass of the aircraft  10 .
 
     The error submodule  206  receives as input the estimated lateral acceleration Ax (est) , the estimated vertical acceleration Az (est) , the measured lateral acceleration factor Ax (mea) , and the measured vertical acceleration factor Az (mea) . The error submodule  206  determines the acceleration error value E by determining a first difference between the estimated longitudinal acceleration Ax (est)  and the estimated vertical acceleration Az (est)  and a second difference between the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) . 
     The Kalman gain submodule  208  receives as input the acceleration error value E from the error submodule  206 . The Kalman gain submodule  208  determines the residual Kalman value by multiplying the acceleration error value E for the first difference and the second difference with the Kalman gain value K. 
     The dynamic submodule  210  receives as input the barometric altitude, the angle of attack α, the pitch angle Θ, the estimated dynamic pressure Q bar(e) , and the estimated longitudinal acceleration Ax (est)  of the aircraft  10 . The dynamic submodule  210  determines the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  based on the input. Specifically, the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  is determined based on Equation 2, which is described above. 
     The integration submodule  212  receives as input the residual Kalman value from the multiplier  160  and the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  from the dynamic control module  152 . The integration submodule  212  combines the residual Kalman value with the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  together, and then integrates the sum of the residual Kalman value and the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e) , which results in the estimated dynamic pressure Q bar(e) . It is to be appreciated that the estimated dynamic pressure Q bar(e)  provides improved accuracy when compared to dynamic pressure values that are calculated using conventional approaches. 
     Referring to both  FIGS. 3 and 6 , the CMM  126  receives as input the measured dynamic pressure Q bar(e)  and the estimated dynamic pressure Q bar(e) . The CMM  126  compares the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  with one another to determine a difference. In response to determining the difference between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  exceeds the threshold value for the threshold amount of time, the CMM  126  determines a fault. It is to be appreciated that the disclosed CMM  126  detects faults with improved accuracy when compared to existing CMM systems. The improved accuracy of the CMM  126  results in fewer false or spurious alarms that are created by the flight control system  18 . 
       FIG. 8  is an exemplary process flow diagram illustrating a method  300  for determining a fault by the CMM  126  based on the estimated dynamic pressure Q bar(e) . Referring to  FIGS. 1, 2, 3, 6, and 8 , the method  300  begins at block  302 . In block  302 , the air data reference function block  120  receives as input the total air pressure P TOT  from the plurality of pitot tubes  40 . The method  300  may then proceed to block  304 . 
     In block  304 , the air data reference function block  120  determines the measured dynamic pressure Q bar(m)  based on the total air pressure P TOT  from the plurality of pitot tubes  40  and the static pressure P S . The method  300  may then proceed to block  306 . 
     In block  306 , the EKF control module  122  determines the estimated dynamic pressure Q bar(e) . Specifically, the method  300  includes subroutine or method  310 , which is performed recursively to determine the estimated dynamic pressure Q bar(e) . 
     The method  310  includes blocks  312 ,  314 ,  316 ,  318 ,  320 ,  322 , and  324 . In block  312 , the EKF control module  122  determines the drag coefficient C D  and the lift coefficient C L  based on the plurality of first operating parameters. The method  310  then proceeds to block  314 , where the EKF control module  122  determines the estimated net thrust T of the aircraft  10  based on the plurality of second operating parameters of the aircraft  10 . The method  310  then proceeds to block  316 , where the EKF control module  122  determines the estimated acceleration Ax (est)  and the estimated acceleration Az (est)  based on the drag coefficient C D , the lift coefficient C L , and the estimated net thrust T. The method then proceeds to block  318 , where the EKF control module  122  determines the acceleration error value E for the first difference between the estimated longitudinal acceleration Ax (est)  and the estimated vertical acceleration Az (est)  and the second difference between the measured longitudinal acceleration Ax(mea) and the measured vertical acceleration Az (mea) . The method  310  then proceeds to block  320 , where the EKF control module  122  determines the residual Kalman value by multiplying the acceleration error value E with the Kalman gain value K. The method  310  then proceeds to block  322 , where the EKF control module  122  determines the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  based on the estimated longitudinal acceleration Ax (est)  of the aircraft  10 . The method  310  may then proceed to block  324 . In block  324 , the residual Kalman value is combined with the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  together, and the sum of the residual Kalman value and the estimated rate of change of the dynamic pressure {dot over (Q)} bar(e)  are integrated to determine the estimated dynamic pressure Q bar(e) . The method  310  may then return to block  312 . 
     Once the estimated dynamic pressure Q bar(e)  is determined, the method  300  may proceed to block  326 . In block  326 , the CMM  126  compares the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  with one another to determine a difference. The method  300  may then proceed to block  328 . 
     In block  328 , if the difference between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  does not exceed the threshold value for the threshold amount of time, then the CMM  126  determines no fault has occurred. The method  300  may then return back to block  302 . However, in response to determining the difference between the measured dynamic pressure Q bar(e)  and the estimated dynamic pressure Q bar(e)  exceeds the threshold value for the threshold amount of time, the method  300  proceeds to block  330 . 
     In block  330 , the CMM  126  determines the presence of a common mode fault of the measured dynamic pressure Q bar(m) . The flight control system  18  then switches from the normal mode of operation as shown in  FIG. 3  and into the extended normal mode of operation shown in  FIG. 4 . The method  300  may then terminate. 
     Referring generally to  FIGS. 1-9 , the disclosed flight control system determines the estimated dynamic pressure based on both the coefficient of lift and the coefficient of drag, which results in improved accuracy. The enhanced accuracy of the estimated dynamic pressure results in fewer spurious alarms generated by the common mode monitor when compared to conventional systems. As a result, there is a reduced occurrence of the aircraft needlessly switching from the normal mode of operation and into the secondary mode of operation. Furthermore, the estimated dynamic pressure also supports full envelope operation of the aircraft. 
     Referring now to  FIGS. 1 and 9 , in another embodiment the flight control module  16  is configured to detect a fault based on a value used for the angle of attack value. In response to detecting a fault, the flight control module  16  determines a synthetic or estimated value for the angle of attack that is not based on the values measured by the plurality of angle of attack sensors  60 . More specifically, the flight control module  16  receives as input a measured angle of attack α m , where the measured angle of attack α m  is based on measurements from the plurality of angle of attack sensors  60  of the aircraft  10 . The flight control module  16  also receives as input an estimated angle of attack α est . Unlike the measured angle of attack α m , the estimated angle of attack α est  is determined without using measurements from the plurality of angle of attack sensors  60 . Instead, the estimated angle of attack α est  is determined based on the total pressure P TOT  measured by the plurality of pitot tubes  40  ( FIG. 2 ). 
     The flight control module  16  compares the measured angle of attack α m  with the estimated angle of attack α est  to determine an error. In response to determining that the error between the measured angle of attack α m  and the estimated angle of attack α est  exceeds a threshold value, the flight control module  16  determines the presence of a fault with an angle of attack value. In some embodiments, the plurality of angle of attack sensors  60  create the fault. Some examples of events that may create a fault with the plurality of angle of attack sensors  60  include, for example, debris that impacts the plurality of angle of attack sensors  60  or, alternatively, icing makes the angle of attack resolver (not shown) stick. 
     The flight control module  16  provides synthetic values representing the angle of attack of the aircraft  10  in response to determining a majority of the angle of attack sensors  60  are not providing accurate data. Specifically, as explained below, new values for the true air speed of the aircraft Vt MDL  and the estimated Mach number M MDL  need to be re-calculated using the estimated dynamic pressure Q bar(e) . This is because the values for the true air speed of the aircraft Vt MDL  and the estimated Mach number M MDL  are erroneously low during a common mode pneumatic event. 
     Referring now to  FIG. 9 , an angle of attack correction module  420  is configured to correct the bias introduced by the plurality of angle of attack sensors  60 . Specifically, the plurality of angle of attack sensors  60  ( FIG. 2 ) are configured to measure a raw angle of attack α raw  using a self-aligning vane. Each angle of attack sensor  60  provides a unique raw angle of attack α raw  value. One of the raw angle of attack α raw  values is selected based on signal selection and failure detection (SSFD) logic. SSFD logic is configured to select a single value from a set of redundant sensors, where the selected value is most likely to be representative of the actual value of the operative parameter measured by sensors. It is to be appreciated that the raw angle of attack α raw , which is measured directly by the plurality of angle of attack sensors  60 , represents a local flow that needs to be adjusted by a correction factor. In one embodiment, the correction factor is about forty-five degrees. The corrected value for the raw angle of attack α raw  is referred to as the measured angle of attack α m . 
     The angle of attack correction module  420  receives as input the raw angle of attack α raw  and the total air pressure P TOT  measured by the plurality of pitot tubes  40  ( FIG. 2 ). The angle of attack correction module  420  determines the measured angle of attack α m  based on a moment arm correction term, (i.e., the correction term based on the self-aligning vane), the raw angle of attack α raw , the true air speed of the aircraft Vt MDL , and the estimated Mach number M MDL . The true air speed of the aircraft Vt MDL , and the estimated Mach number M MDL  are determined based on the total pressure P TOT . 
     It is to be appreciated that during a common mode pneumatic event as explained above, the values for true air speed of the aircraft Vt MDL  and the estimated Mach number M MDL  are re-calculated using the estimated dynamic pressure Q bar(e) . Specifically, in response to the CMM  126  ( FIGS. 3 and 4 ) determining the difference between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  exceeds a threshold value for a threshold amount of time, the CMM  126  determines the presence of a common mode fault of the measured dynamic pressure Q bar(m) . Once the common mode pneumatic event is determined, then the angle of attack correction module  420  determines the measured angle of attack α m  based on the estimated dynamic pressure (Q bar(e) ). Specifically, the angle of attack correction module  420  is determined based on a synthetic Mach number M EKF  (Equation 4) and a synthetic true air speed of the aircraft Vt EKF  (Equation 5): 
     
       
         
           
             
               
                 
                   
                     M 
                     EKF 
                   
                   = 
                   
                     
                       
                         Q 
                         
                           bar 
                           ⁡ 
                           
                             ( 
                             e 
                             ) 
                           
                         
                       
                       
                         0.7 
                         × 
                         p 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         s 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
             
               
                 
                   
                     Vt 
                     EKF 
                   
                   = 
                   
                     
                       
                         2 
                         × 
                         
                           Q 
                           
                             bar 
                             ⁡ 
                             
                               ( 
                               e 
                               ) 
                             
                           
                         
                       
                       ρ 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     Continuing to refer to  FIG. 9 , an extended Kalman filter (EKF) control module  422  is configured to determine the estimated angle of attack α est , which is described in greater detail below and is shown in  FIGS. 11 and 12 . However, it is to be appreciated that unlike the measured angle of attack α m , the estimated angle of attack α est  is not based on measurements obtained by the plurality of angle of attack sensors  60 . An angle of attack common mode monitor CMM  426 , which is referred to as the CMM  426 , receives as input the measured angle of attack α m , the estimated angle of attack α est , and the output  96  from the CMPE control module  36 . The CMM  426  determines a common mode failure, which is also referred to as a fault. Specifically, the CMM  426  determines a fault has occurred when the error between the measured angle of attack α m  and the estimated angle of attack α est  exceeds the threshold value for a threshold amount of time. 
     The threshold value is determined based on the accuracy of the plurality of angle of attack sensors  60  (i.e., a relatively high rate of accuracy results in a relatively low threshold value). For example, a relatively slow error rate may be about fifteen seconds while a relatively fast error rate includes a much longer persistence of about fifteen seconds. However, it is to be appreciated that other values may be used as well. 
       FIG. 9  illustrates a non-fault condition where no fault has been detected by the CMM  426 . Accordingly, the measured angle of attack α m  is received as input by the primary flight control module  140 , the autopilot control module  142 , the autothrottle control module  144 , and the plurality of displays  146 . It should also be appreciated that the aircraft  10  is operating in the normal mode of operation.  FIG. 10  illustrates a fault condition detected by the CMM  426 . In response to the CMM  426  detecting a fault with respect to the angle of attack value, the estimated angle of attack α est  is provided to the primary flight control module  140 , the autopilot control module  142 , the autothrottle control module  144 , and the plurality of displays  146 . In the embodiments as shown in  FIGS. 9 and 10 , no common mode failure of the estimated dynamic pressure Q bar(e)  exists (i.e., a majority of the plurality of pitot tubes  40  are not blocked). Thus, the output  96  generated by the CMPE control module  36  is set to a FALSE value (i.e., CMPE FAULT=FALSE). However, in response to detecting a common mode failure, the values for true air speed of the aircraft Vt MDL  and the estimated Mach number M MDL  may no longer be accurate. Instead, the angle of attack correction module  420  uses the synthetic Mach number M EKF  (Equation 4) and the synthetic true air speed of the aircraft Vt EKF  (Equation 5) to preserve the estimated angle of attack α est  signal that is used by the flight control module  140 . 
       FIG. 11  is a block diagram of an extended Kalman filter of the EKF control module  422 . The block diagram represents a system  448  for determining the estimated angle of attack α est  based on data collected from the air data sensors  22  ( FIG. 1 ). The EKF control module  422  includes a measurement model  450 , a dynamic control module  452 , a Kalman gain block  454 , an integrator block  456 , an error block  458 , a multiplier  460 , and an adder  462 . Similar to the measurement model  150  shown in  FIG. 5 , the measurement model  450  predicts expected values of measured accelerations (e.g., the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) ) based on Equation 1 (shown above). 
     The dynamic control module  452  determines a rate of change for the estimated angle of attack, which is referred to as an estimated rate of change of the angle of attack {dot over (α)} (e) . The estimated rate of change of the angle of attack {dot over (α)} (e)  is determined based on an estimated normal acceleration component A_N (est)  of the aircraft  10 , where the estimated normal acceleration component A_N (est)  is the vertical acceleration in a stability frame of the aircraft  10 . Specifically, the estimated rate of change of the angle of attack {dot over (α)} (e)  is a function of a pitch q (dps) , the true air speed of the aircraft Vt MDL , the pitch angle Θ, the estimated normal acceleration component A_N (est , and the estimated angle of attack α est . In one embodiment, the estimated rate of change of the estimated angle of attack α est  is determined based on Equation 6, which is: 
                       a   .     est     =       q     (   dps   )       +       [         (     cos   ⁡     (     θ   -   a     )       )     ×   g     -     A     N     (   est   )           ]     ·     1     Vt   MDL                   Equation   ⁢           ⁢   6               
where g represents the gravitational constant.
 
     The Kalman gain block  454  stores the Kalman gain value K. Similar to the embodiment as shown in  FIG. 5 , the Kalman gain value K represents the weight given to the current state of the aircraft  10  (i.e., the operating conditions), and is a dynamic value that is determined by a set of look-up tables  526  (seen in  FIG. 12 ) stored on a database  528 . The error block  458  receives as input the estimated longitudinal acceleration Ax (est)  and an estimated vertical acceleration Az (est)  from the measurement model  450  as well as the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) , and determines the acceleration error value E by determining a first difference between the estimated longitudinal acceleration Ax (est)  and the estimated vertical acceleration Az (est)  and a second difference between the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) . The multiplier  460  receives as input the acceleration error value E and the Kalman gain value K, and determines an estimated state update by multiplying the acceleration error value E with and the Kalman gain value K. 
     The adder  462  receives as input the residual Kalman value from the multiplier  460  and the estimated rate of change of the angle of attack {dot over (α)} (e)  from the dynamic control module  452 . The adder  462  combines the residual Kalman value with the estimated rate of change of the angle of attack {dot over (α)} (e)  together. The combined residual Kalman value and the estimated rate of change of the angle of attack {dot over (α)} (e)  are then sent to the integrator block  456 . The integrator block  456  then integrates the sum of the residual Kalman value and the estimated rate of change of the angle of attack {dot over (α)} (e)  to determine the estimated angle of attack α est . 
       FIG. 12  is an illustration of the EKF control module  422  including a plurality of submodules  480 ,  482 ,  484 ,  486 ,  488 ,  490 ,  492 . The submodules  480 ,  482 ,  484 ,  486 ,  488 ,  490 ,  492  are shown as distinct components, which may indicate the use of modular programming techniques. Referring now to both  FIGS. 11 and 12 , the EKF control module  422  and the system  448  correspond to one another. Specifically, a coefficient submodule  480  and a propulsion submodule  482  of the EKF control module  422  both correspond to the measurement model  450  of the system  448 . A measurement submodule  484  of the EKF control module  422  corresponds to the adder  462  of the system  448 . An error submodule  486  of the EKF control module  422  corresponds to the error block  458  of the system  448 . A Kalman gain submodule  488  of the EKF control module  422  corresponds to the Kalman gain block  454  of the system  448 . A dynamic submodule  490  of the EKF control module  422  corresponds to the dynamic control module  452  of the system  448 . Finally, an integration submodule  492  corresponds to the integrator block  456  of the system  448 . 
     The EKF control module  422  receives as input a plurality of operating parameters of the aircraft  10  ( FIGS. 1 and 2 ). The operating parameters include, but are not limited to, the measured acceleration factors Ax (mea)  and Az (mea) , the pitch q (dps) , true air speed of the aircraft Vt MDL , the pitch angle Θ, the estimated normal acceleration component A_N (est) , the estimated angle of attack α est , the previous estimated dynamic pressure Q bar(p) , the estimated Mach number M MDL , the barometric altitude, the deflection of the control surfaces δ of the aircraft  10 , the engine speed N 1  of both aircraft engines  78  ( FIG. 2 ), and the static pressure Ps. Similar to the coefficient submodule  200  shown in  FIG. 6 , the coefficient submodule  480  receives as input the plurality of first operating parameters that each represent an operating condition of the aircraft  10 , which include the estimated angle of attack α est , the deflection of the control surfaces δ of the aircraft  10 , the measured dynamic pressure Q bar(m) , and a measured Mach number M. The coefficient submodule  480  determines the drag coefficient C D  and the lift coefficient C L  based on the plurality of first operating parameters and one or more coefficient three-dimensional look-up tables  520  stored in database  522 . The coefficient three-dimensional look-up tables  520  provide a drag coefficient C D  and a lift coefficient C L  value based on specific values of the plurality of first operating parameters. 
     Similar to the propulsion submodule  202  shown in  FIG. 6 , the propulsion submodule  482  receives as input the plurality of second operating parameters of the aircraft  10 , which include the barometric altitude, the pitch angle Θ, true air speed of the aircraft Vt MDL , the engine speed N 1  of both aircraft engines  78  ( FIG. 2 ), the total air temperature T TOT , and the static pressure Ps. The propulsion submodule  482  determines the estimated net thrust T of the aircraft  10  based on the plurality of second operating parameters and propulsion-based three-dimensional look-up tables  530  stored in database  532  that provide the estimated net thrust T based on specific values of the plurality of second operating parameters. 
     The measurement submodule  484  receives as input the drag coefficient C D , the lift coefficient C L , and the estimated net thrust T. The measurement submodule  484  determines the estimated acceleration Ax (est)  and the estimated acceleration Az (est)  based on the drag coefficient C D , the lift coefficient C L , and the estimated net thrust T based on the equation of motion is expressed in Equation 3 above. 
     The error submodule  486  receives as input the estimated lateral acceleration Ax (est) , the estimated vertical acceleration A (est) , the measured lateral acceleration factor Ax (mea) , and the measured vertical acceleration factor Az (mea) . The error submodule  486  determines the acceleration error value E by determining a first difference between the estimated longitudinal acceleration Ax (est)  and the estimated vertical acceleration Az (est)  and a second difference between the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) . 
     The Kalman gain submodule  488  receives as input the acceleration error value E from the error submodule  486 . The Kalman gain submodule  488  determines the residual Kalman value by multiplying the acceleration error value E for the first difference and the second difference with the Kalman gain value K. 
     The dynamic submodule  490  receives as input the pitch q (dps) , the true air speed of the aircraft Vt MDL , the pitch angle θ, the estimated normal acceleration component A_N (est) , and the estimated angle of attack α est , and determines the estimated rate of change of the angle of attack {dot over (α)} (e)  based on Equation 6, which is described above. The integration submodule  492  receives as input the residual Kalman value from the multiplier  460  and the estimated rate of change of the angle of attack {dot over (α)} (e)  from the dynamic submodule  490 . The integration submodule  492  combines the residual Kalman value with the estimated rate of change of the angle of attack {dot over (α)} (e)  together, and then integrates the sum of the residual Kalman value and estimated rate of change of the angle of attack {dot over (α)} (e) , which results in the estimated angle of attack α est . 
     Referring to  FIG. 9 , the CMM  426  receives as input the measured angle of attack α m  and the estimated angle of attack α est . The CMM  426  compares the measured angle of attack α m  and the estimated angle of attack α est  with one another to determine a difference. In response to determining the difference between the measured angle of attack α m  and the estimated angle of attack α est  exceeds the threshold value for the threshold amount of time, the CMM  426  determines there is a fault that affects the angle of attack value. 
       FIG. 13  is an exemplary process flow diagram illustrating a method  570  for determining a fault of the angle of attack value by the CMM  426 . Referring to  FIGS. 1, 9, 10, 11, 12 and 13 , the method  570  begins at block  572 . In block  572 , the angle of attack correction module  420  receives as input the raw angle of attack α raw  and the total air pressure P TOT  measured by the plurality of pitot tubes  40  ( FIG. 2 ). The method  570  may then proceed to block  574 . 
     In block  574 , the angle of attack correction module  420  determines the measured angle of attack α m  based on a moment arm correction term, the raw angle of attack α raw , the synthetic true air speed of the aircraft Vt EKF , and the estimated Mach number M MDL . As mentioned above, during a common mode pneumatic event, the values for synthetic true air speed of the aircraft Vt EKF  and the synthetic Mach number M EKF  are calculated using the estimated dynamic pressure Q bar(e)  (see Equations 4 and 5). The method  570  may then proceed to block  576 . 
     In block  576 , the EKF control module  422  determines the estimated angle of attack α est . Specifically, the method  570  includes subroutine or method  580 . The method  580  is performed recursively to determine the estimated angle of attack α est . 
     The method  580  includes blocks  582 ,  584 ,  586 ,  588 ,  590 ,  592 , and  594 . In block  582 , the EKF control module  422  determines the drag coefficient C D  and the lift coefficient C L  based on the plurality of first operating parameters. The method  580  then proceeds to block  584 , where the EKF control module  422  determines the estimated net thrust T of the aircraft  10  based on the plurality of second operating parameters of the aircraft  10 . The method  580  then proceeds to block  586 , where the EKF control module  422  determines the estimated acceleration Ax (est)  and the estimated acceleration Az (est)  based on the drag coefficient C D , the lift coefficient C L , and the estimated net thrust T. The method  580  then proceeds to block  588 , where the EKF control module  422  determines the acceleration error value E for the first difference between the estimated longitudinal acceleration Ax (est)  and the estimated vertical acceleration Az (est)  and the second difference between the measured longitudinal acceleration Ax (mea)  and the measured vertical acceleration Az (mea) . The method  580  then proceeds to block  590 , where the EKF control module  422  determines the residual Kalman value by multiplying the acceleration error value E with the Kalman gain value K. The method  580  then proceeds to block  592 , where the EKF control module  422  determines the estimated rate of change of the angle of attack {dot over (α)} e  based on the estimated normal acceleration component A_N (est)  of the aircraft  10 . The method  580  may then proceed to block  594 . In block  594 , the residual Kalman value is combined with the estimated rate of change of the angle of attack {dot over (α)} e  together, and the sum of the residual Kalman value and the estimated rate of change of the angle of attack {dot over (α)} e  are integrated to determine the estimated angle of attack α est . The method  580  may then return to block  582 . 
     Once the estimated angle of attack α est  is determined, the method  570  may proceed to block  596 . In block  596 , the CMM  426  compares the measured angle of attack α m  and the estimated angle of attack α est  with one another to determine the error. The method  580  may then proceed to block  598 . 
     In block  598 , if the error does not exceed the threshold value for the threshold amount of time, then the CMM  426  determines no fault has occurred. The method  570  may then return back to block  572 . However, in response to determining the error exceeds the threshold value for the threshold amount of time, the method  570  proceeds to block  599 . 
     In block  599 , the CMM  426  determines the presence of a common mode fault of the angle of attack value. The flight control system  18  then switches from utilizing the measured angle of attack α m  (shown in  FIG. 9 ) and instead uses the estimated angle of attack α est  (shown in  FIG. 10 ). The method  570  may then terminate. 
     Referring generally to  FIGS. 9-13 , the disclosed system provides an approach for determining an estimated angle of attack that is independent from the measurements collected by the angle of attack sensors. Therefore, the system substitutes the estimated angle of attack in response to determining that the measured angle of attack is no longer useable. Furthermore, in the event a common mode pneumatic event is detected (i.e., a majority of the pitot tubes of the aircraft are blocked), the disclosed system also provides an approach for determining the measured angle of attack without using the for true air speed of the aircraft and the measured Mach number. It is to be appreciated that during a common mode pneumatic event the values for the true air speed of the aircraft and the estimated Mach number are erroneously low, and therefore any value determined based on these values may not be accurate. Accordingly, the system determines synthetic values for the true air speed of the aircraft and the estimated Mach number based on the estimated dynamic pressure. 
     Detection of the common mode pneumatic event by the CMPE control module  36  shall now be described. Referring now to  FIG. 14 , the CMPE control module  36  receives as input the measured dynamic pressure Q bar(m)  and the estimated angle of attack α est  and determines a common mode pneumatic event based on the input. More specifically, the CMPE control module  36  determines the presence of a common mode pneumatic event (e.g., CMPE FAULT=TRUE) in response to detecting either a synchronous fault or an asynchronous fault with the plurality of pitot tubes  40 . It is to be appreciated that in the embodiments as described in  FIGS. 14-18 , the estimated angle of attack α est  is the value as described with reference to  FIGS. 9-13  (i.e., the measured angle of attack is not used). 
     The CMPE control module  36  includes a first CMPE detector  600  and a second CMPE detector  602 . The first CMPE detector  600  receives as input the measured dynamic pressure Q bar(m)  and the estimated angle of attack α est  and determines a first common mode pneumatic event based on both inputs. More specifically, the first CMPE detector  600  is configured to detect the first common mode pneumatic event. The first common mode pneumatic event is a synchronous common mode pneumatic event based on a majority of the plurality of pitot tubes  40  experiencing a simultaneous failure. In contrast, the second CMPE detector  602  is configured to detect a second common mode pneumatic event, which is an asynchronous fault, based on only the measured dynamic pressure Q bar(m) . An asynchronous fault is based on the plurality pitot tubes  40  failing at time intervals that are offset from one another during a specific interval of time. For example, an asynchronous fault occurs when one of the plurality of pitot tubes  40  fails first, then about two seconds later a second pitot tube  40  fails, and then a third pitot tube  40  fails about two seconds after the second pitot tube  40 . 
     Referring now to  FIG. 15 , the first CMPE detector  600  is now described. The first CMPE detector  600  includes a measured dynamic pressure washout filter  610 , an angle of attack washout filter  612 , a dynamic pressure threshold value  614 , an angle of attack threshold value  616 , a dynamic pressure comparer  618 , an angle of attack comparer  620 , an AND block  622 , and a latch  624 . The first CMPE detector  600  generates an output signal  642  that is set to TRUE when the first common mode pneumatic event is detected and is set to FALSE when no common mode pneumatic event is detected. 
     The plurality of pitot tubes  40  are each configured to measure a pressure value P. For example, in the non-limiting embodiment as shown, three pressure values P are illustrated (i.e., a left pressure value P L , a center pressure value P C , and a right pressure value P R ). The pressure values P L , P C , P R  from each pitot tube  40  are sent to a signal selection and failure detection (SSFD) block  630 . SSFD logic is configured to select a single value from a set of redundant sensors. The selected value is most likely to be representative of the actual value of the operative parameter measured by sensors. Thus, the SSFD block  630  is configured to select one of the pressure values P L , P C , P R . The selected one of the pressure values P L , P C , P R  is the most representative value of the measured dynamic pressure Q bar(m)  when compared to the remaining pressure values P L , P C , P R  measured by the plurality of pitot tubes  40 . The measured dynamic pressure Q bar(m)  is then received as input by the first CMPE detector  600 . 
     The measured dynamic pressure washout filter  610  receives as input the measured dynamic pressure Q bar(m)  and determines a rate of change of the measured dynamic pressure Q bar(m) , which is referred to as {dot over (Q)} bar(m) . Specifically, the measured dynamic pressure washout filter  610  operates as a high-pass filter that rejects steady-state values and passes transient values of the measured dynamic pressure Q bar(m)  to determine the rate of change of the measured dynamic pressure {dot over (Q)} bar(m) . The rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is sent to the dynamic pressure comparer  618 . The dynamic pressure comparer  618  receives as input the dynamic pressure threshold value  614  and the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  and compares the values to one another. In response to determining that the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is less than the dynamic pressure threshold value  614 , the dynamic pressure comparer  618  generates an output signal  636  indicating the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is within limits (e.g., a TRUE signal). However, in response to determining the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is equal to or greater than the dynamic pressure threshold value  614 , the dynamic pressure comparer  618  generates a FALSE signal as the output signal  636 . 
     The dynamic pressure threshold value  614  is representative of a rate of change experienced by the measured dynamic pressure Q bar(m)  when a majority of the plurality of pitot tubes  40  experience a failure (e.g., are blocked). For example, in one embodiment, the rate of change or drop in measured dynamic pressure Q bar(m)  is about negative 100 megabars per second (mBar/sec). The dynamic pressure threshold value  614  is determined based on quantitative assessment data collected from field use. More specifically, the dynamic pressure threshold value  614  is determined by analyzing data collected from previous synchronous common mode pneumatic events that occurred during operation of other aircraft. However, the estimated angle of attack threshold value  616  is determined based on data collected during a simulated synchronous common mode pneumatic event. A simulated synchronous common mode pneumatic event may refer to either a computer simulation as well as test data obtained from test bench data. The estimated angle of attack threshold value  616  is representative of the rate of change of the estimated angle of attack α est  when a majority of the plurality of pitot tubes  40  experience a failure. For example, in one embodiment, the rate of change or the step increase in the estimated angle of attack α est  is about +10 degrees/second. 
     The estimated angle of attack washout filter  612  receives as input the estimated angle of attack α est  and determines a rate of change of the estimated angle of attack {dot over (α)} est . The estimated angle of attack washout filter  612  operates as a high-pass filter that rejects steady-state values and passes transient values of the estimated angle of attack to determine the rate of change of the estimated angle of attack {dot over (α)} est . The estimated angle of attack comparer  620  receives as input the rate of change of the estimated angle of attack {dot over (α)} est  and the estimated angle of attack threshold value  616  and compares the values to one another. In response to determining that the rate of change of the estimated angle of attack {dot over (α)} est  is greater than the estimated angle of attack threshold value  616 , the estimated angle of attack comparer  620  generates an output signal  638  to the AND block  622  indicating the rate of change of the estimated angle of attack {dot over (α)} est  is outside limits (e.g., a TRUE signal). In response to determining that the rate of change of the rate of change of the estimated angle of attack {dot over (α)} est  is greater than the estimated angle of attack threshold value  616 , the estimated angle of attack comparer  620  generates a FALSE signal as the output signal  638 . 
     The AND block  622  receives as input the output signal  636  from the dynamic pressure comparer  618  and the output signal  638  from the estimated angle of attack comparer  620 . In response to both output signals  636 ,  638  being TRUE, the AND block  622  generates an output signal  640  that is sent to the latch  624 . The output signal  640  indicates the first common mode pneumatic event is detected. More specifically, in response to determining the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is less than the dynamic pressure threshold value  614  and the rate of change of the rate of change of the estimated angle of attack {dot over (α)} est  is greater than the estimated angle of attack threshold value  616 , the AND block  622  determines the first common mode pneumatic event has occurred. The first common mode pneumatic event is a synchronous common mode pneumatic event, which is determined based on a majority of the plurality of pitot tubes  40  experiencing a simultaneous failure. 
     In response to the output signal  640  indicating a common mode pneumatic event (e.g., TRUE), the latch  624  is set during the time delay. It is to be appreciated that during the time delay the latch  624  may be reset at any time in response to the measured dynamic pressure Q bar(m)  being accurate. For example, if the measured dynamic pressure Q bar(m)  is determined to be accurate at 26 seconds into the time delay, then the latch  624  is reset and the time delay ends. However, the latch  624  remains set when no reset signal is received. In other words, in response to the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  being below a threshold value, the latch  624  receives a reset signal. However, at the end of the time delay if the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  still exceeds the threshold value, then a persistent common mode pneumatic event is detected. Accordingly, the output signal  642  of the first CMPE detector  600  indicates the presence of the first common mode pneumatic event. 
     Turning now to  FIG. 16 , the second CMPE detector  602  is now described. The second CMPE detector  602  incudes a clamp  650 , a mid-value selector  652 , and a latch  654  that generates an output signal  656 . The second CMPE detector  602  is configured to detect the second common mode pneumatic event based on an asynchronous failure of the plurality of pitot tubes  40 . More specifically, sometimes the plurality of pitot tubes  40  may not become non-operational at the same time. Instead, sometimes only a single pitot tube  40  may become blocked, and then a few seconds later another pitot tube  40  may become blocked. 
     Similar to the first CMPE detector  600 , the pressure values (i.e., the left pressure value P L , the center pressure value P C , and the right pressure value P R ) from each of the plurality of pitot tubes  40  are sent to a SSFD block  648 . The SSFD block  648  receives as input the left pressure value P L , the center pressure value P C , and the right pressure value P R  from each of the plurality of pitot tubes  40 . The SSFD block  648  determines the presence of one or more blocked pitot tubes  40  by comparing the left pressure value P L , the center pressure value P C , and the right pressure value P R  to one another. In response to determining one or more of the pressure values P L , P C , P R  differ from the remaining pressure values P L , P C , P R  by a threshold error value, the SSFD block  648  marks the specific pressure value as a miscompare, which is also referred to as a fault. The threshold error value represents the difference between pitot tube readings when a pitot tube  40  is blocked or otherwise non-operational. In the embodiment as shown, three pressure readings (the left pressure value P L , the center pressure value P C , and the right pressure value P R ) are shown, however it is to be appreciated that more then or less than three pressure readings may be used as well. 
     The clamp  650  receives as input the plurality of pressure values (e.g. the left pressure value P L , the center pressure value P C , and the right pressure value P R ) from the SSFD block  648 , wherein each of the plurality of pressure values correspond to one of the plurality of pitot tubes  40 . The clamp  650  also receives as input a fault indicator for each individual pressure value from the SSFD block  648 . In other words, the left pressure value P L , the center pressure value P C , and the right pressure value P R  are each associated with an indicator. The indicator is set to TRUE when a fault is detected, otherwise the indicator is set to FALSE. In response to determining there are no fault indicators present, the clamp  650  sends the pressure values to the mid-value selector  652 . The mid-value selector  652  then selects one of the pressure values P L , P C , P R . The selected pressure value is set as the total pressure P TOT  based on a mid-value selection algorithm. 
     In response to determining that one or more of the pressure values P L , P C , P R  indicate a fault, then the clamp  650  executes a time delay function that extends a fault during a time interval. In other words, the clamp  650  determines the presence of one or more blocked pitot tubes  40  by comparing the plurality of pressure values to one another, where each blocked pitot tube  40  is a fault condition, and in response to determining a fault condition, the clamp  650  executes the time delay function that extends the fault condition for the time interval. The time interval is set to capture two or more faults that occur in the plurality of pitot tubes  40  during the second (i.e., asynchronous) common mode pneumatic event. In one non-limiting embodiment, the time interval is about two to five seconds. It is to be appreciated that that a fault condition in a particular pitot tube  40  may exist for only a relatively short period of time. In one example, the fault condition may last for only a few tenths of a second. Once a fault condition in one of the plurality of pitot tubes  40  occurs, then a fault condition may occur in a second pitot tube  40  shortly thereafter. However, the fault in the second pitot tube  40  does not occur simultaneously with the other pitot tube fault. In other words, the faults between the plurality of pitot tubes  40  are asynchronous. 
     The mid-value selector  652  detects an asynchronous common mode pneumatic event because the clamp  650  extends the fault for the time interval. In other words, the mid-value selector  652  is unable to detect a majority of the plurality of pitot tubes  40  (e.g., 2 out of 3 pitot tubes  40 ) generating an asynchronous fault unless the fault is extended. The clamp  650  is configured to extend the fault that occurs in one of the pitot tube  40  for the time interval. Therefore, when a fault condition occurs in another pitot tube  40 , the mid-value selector  652  detects the second common mode pneumatic event. For example, the left pressure P L  reading may indicate a fault condition for only 0.5 seconds (e.g., the fault condition is set to TRUE for 0.5 seconds and then goes back to FALSE). However, the clamp  650  extends the fault for the time interval, which is four seconds in this example. Thus, when the center pressure P C  reading indicates a fault condition about one second after the left pressure P L , the mid-value selector  652  still receives two fault conditions from the clamp  650 . 
     The mid-value selector  652  receives as input two or more pressure values and fault indicators. Each pressure value and fault indicator corresponds to one of the plurality of pitot tubes  40 . In response to determining a fault condition, the mid-value selector  652  generates an output signal  660 . The output signal  660  indicates the second common mode pneumatic event has occurred. That is, in other words, the output signal  660  detects an asynchronous fault in the plurality of pitot tubes  40 . The output signal  660  is sent to the latch  654 . In response to receiving the output signal  660  indicating the presence of the second common mode pneumatic event, the latch  654  is set for the time delay. The latch  654  is reset in response to the measured dynamic pressure Q bar(m)  is determined to be accurate (i.e., a majority of the plurality of pitot tubes  40  no longer display a fault). More specifically, in response to the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  being below a threshold value, the latch  654  receives a reset signal. However, at the end of the time delay if the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  still exceeds the threshold value, then a persistent common mode pneumatic event is detected. Accordingly, the output signal  656  of the second CMPE detector  602  indicates the presence of the second common mode pneumatic event. 
     Referring to  FIG. 14 , when either the output signal  642  of the first CMPE detector  600  indicates the presence of the first common mode pneumatic event or the output signal  656  of the second CMPE detector  602  indicates the presence of the second common mode pneumatic event, the output  96  of the CMPE control module  36  is set to TRUE, otherwise the output  96  is set to FALSE. It is to be appreciated that both the first common mode pneumatic event (determined by the first CMPE detector  600 ) and the second mode pneumatic event (determined by the second CMPE detector  602 ) both represent a fast-rate common mode pneumatic event. A fast-rate common mode pneumatic event refers to a majority of the plurality of pitot tubes  40  being blocked by some foreign object (e.g., ice, volcanic ash, etc.), where the pressure of the plurality of pitot tubes  40  drops relatively quickly at a specific rate. For example, in one embodiment, the specific rate is about −100 mBar/second, however it is to be appreciated that the rate may change based on the application. In contrast to the fast-rate common mode pneumatic event, the plurality of pitot tubes  40  may also become blocked based on a slow-rate common mode pneumatic event as well. A slow-rate common mode pneumatic event occurs based on a slower blockage that may occur with the plurality of pitot tubes  40 . Instead, a slow-rate common mode pneumatic event may be detected and addressed based on conventional techniques that already exist. It is to be appreciated that a slow-rate common mode pneumatic event is not detected by the first and second CMPE detectors  600 ,  602 . 
     Referring now to  FIGS. 1, 4, 6, and 14 , when the CMPE control module  36  determines a common mode pneumatic event, the measured dynamic pressure Q bar(m)  is substituted with the estimated dynamic pressure Q bar(e)  when calculating the estimated angle of attack α est . More specifically, when either the first, synchronous common mode pneumatic event is detected by the first CMPE detector  600  or the second, asynchronous pneumatic event is detected by the second CMPE detector  602 , the dynamic pressure Q bar(m)  is substituted with the estimated dynamic pressure Q bar(e)  and the disclosed flight control system  18  is in the extended normal mode of operation. 
       FIG. 17  is an exemplary process flow diagram illustrating a method  700  for determining a synchronous fault of the plurality of pitot tubes  40 . Referring generally to  FIGS. 14 and 17 , the method  700  may begin at block  702 . In block  702 , the CMPE control module  36  receives as input the measured dynamic pressure Q bar(m)  and the estimated angle of attack α est . The method  700  may then proceed to block  704 . 
     In block  704 , the first CMPE detector  600  determines the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  and the rate of change of the estimated angle of attack {dot over (α)} est . Referring specifically to  FIGS. 15 and 17 , the measured dynamic pressure washout filter  610  receives as input the measured dynamic pressure Q bar(m)  and determines the rate of change of the measured dynamic pressure {dot over (Q)} bar(m) . The estimated angle of attack washout filter  612  receives as input the estimated angle of attack α est  the rate of change of the estimated angle of attack {dot over (α)} est . The method  700  may then proceed to block  706 . 
     In block  706 , the dynamic pressure comparer  618  receives as input the dynamic pressure threshold value  614  and the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  and compares the values to one another. Additionally, the estimated angle of attack comparer  620  receives as input the rate of change of the estimated angle of attack {dot over (α)} est  and the estimated angle of attack threshold value  616  and compares the values to one another. The method  700  may then proceed to decision block  708 . 
     In decision block  708 , if the dynamic pressure comparer  618  determines that the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is not less than the dynamic pressure threshold value  614 , and if the estimated angle of attack comparer  620  determines the rate of change of the estimated angle of attack {dot over (α)} est  is not greater than the estimated angle of attack threshold value  616 , then the method  700  proceeds to block  710 . 
     In block  710 , the latch  624  is not set, and the method  700  returns back to block  702 . However, if the dynamic pressure comparer  618  determines that the rate of change of the measured dynamic pressure {dot over (Q)} bar(m)  is less than the dynamic pressure threshold value  614 , and if the estimated angle of attack comparer  620  determines the rate of change of the estimated angle of attack {dot over (α)} est  is greater than the estimated angle of attack threshold value  616 , then the method  700  proceeds to block  712 . 
     In block  712 , the latch  624  is set. The method  700  may proceed to decision block  714 . 
     In decision block  714 , if at any point in time during the time delay the measured dynamic pressure Q bar(m)  is accurate, then method  700  proceeds to block  716 . More specifically, in response to the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  being below a threshold value, the method  700  proceeds to block  716 . In block  716 , the latch  624  receives a reset signal. The method  700  may then return to block  702 . However, if the time delay ends and the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  still exceeds the threshold value, then the method  700  proceeds to block  718 . In block  718 , the latch  624  and the output signal  642  of the first CMPE detector  600  indicates the presence of the first common mode pneumatic event. The method  700  may then terminate. 
       FIG. 18  is an exemplary process flow diagram illustrating a method  800  for determining an asynchronous fault of the plurality of pitot tubes  40 . Referring generally to  FIGS. 16 and 18 , the method  800  may begin at block  802 . In block  802 , the clamp  650  of the second CMPE detector  602  receives as input the pressure values (e.g. the left pressure value P L , the center pressure value P C , and the right pressure value P R ) from the SSFD block  648 . The clamp  650  also receives as input a fault indicator for each individual pressure value from the SSFD block  648 . The method  800  may then proceed to decision block  804 . 
     In decision block  804 , if the indicator is set to FALSE (i.e., no fault is detected), then the method proceeds to block  806 . In block  806  the clamp  650  sends the pressure values to the mid-value selector  652 . The mid-value selector  652  then selects one of the pressure values. The selected pressure value is set as the total pressure P TOT  based on a mid-value selection algorithm. The method  800  may then terminate. 
     If the indicator is set to TRUE (i.e., a fault is detected), then the method  800  may proceed to block  808 . In block  808 , the clamp  650  executes the time delay function that extends the fault for the time interval. As mentioned above, the time interval is set to capture two or more faults that occur in the plurality of pitot tubes  40  during the second (i.e., asynchronous) common mode pneumatic event. The method  800  may then proceed to block  810 . 
     In block  810 , the mid-value selector  652  receives as input two or more pressure values and fault indicators, where each pressure value and indicator correspond to one of the plurality of pitot tubes  40 . The method may then proceed to decision block  812 . 
     In decision block  812 , in response to the mid-value selector  652  determining a fault condition is not present, the method  800  may then terminate. In response to the mid-value selector  652  determining a fault condition is present, the method  800  may proceed to block  814 . In block  814 , the mid-value selector  652  generates the output signal  660 . As mentioned above, the output signal  660  indicates the second common mode pneumatic event is detected. The method  800  may then proceed to block  816 . 
     In block  816 , the output signal  660  is sent to the latch  654 . The method  800  may then proceed to block  818 . 
     In block  818 , in response to receiving the output signal  660 , the latch  654  is set. The method  800  may proceed to decision block  820 . 
     In decision block  820 , if at any point in time during the time delay the measured dynamic pressure Q bar(m)  is accurate, then method  800  proceeds to block  822 . More specifically, in response to the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  being below a threshold value, the method  800  proceeds to block  822 . In block  822 , the latch  654  receives a reset signal. The method  800  may then return to block  802 . However, if the time delay ends and the error between the measured dynamic pressure Q bar(m)  and the estimated dynamic pressure Q bar(e)  still exceeds the threshold value, then the method  800  proceeds to block  824 . In block  824 , the latch  654  and the output signal  656  of the second CMPE detector  602  indicates the presence of the second common mode pneumatic event. The method  800  may then terminate. 
     Referring generally to  FIGS. 14-18 , it is to be appreciated that conventional flight control systems presently available may drop out of the normal mode of operation and immediately switch into the secondary mode of operation in response to determining either a faulty dynamic pressure measurement or a faulty estimated angle of attack measurement. In other words, conventional systems do not attempt to isolate the source of error when a fault is detected with either measurement. In contrast, the disclosed system substitutes the measured dynamic pressure with the estimated dynamic pressure in response to detecting a faulty measured dynamic pressure or estimated angle of attack reading. Therefore, the disclosed flight control system does not switch immediately to the second mode of operation like conventional systems, and instead operates in the extended normal mode of operation. 
     Referring now to  FIG. 19 , the flight control system  18  is implemented on one or more computer devices or systems, such as exemplary computer system  1030 . The computer system  1030  includes a processor  1032 , a memory  1034 , a mass storage memory device  1036 , an input/output (I/O) interface  1038 , and a Human Machine Interface (HMI)  1040 . The computer system  1030  is operatively coupled to one or more external resources  1042  via the network  1026  or I/O interface  1038 . External resources may include, but are not limited to, servers, databases, mass storage devices, peripheral devices, cloud-based network services, or any other suitable computer resource that may be used by the computer system  1030 . 
     The processor  1032  includes one or more devices selected from microprocessors, micro-controllers, digital signal processors, microcomputers, central processing units, field programmable gate arrays, programmable logic devices, state machines, logic circuits, analog circuits, digital circuits, or any other devices that manipulate signals (analog or digital) based on operational instructions that are stored in the memory  1034 . Memory  1034  includes a single memory device or a plurality of memory devices including, but not limited to, read-only memory (ROM), random access memory (RAM), volatile memory, non-volatile memory, static random-access memory (SRAM), dynamic random-access memory (DRAM), flash memory, cache memory, or any other device capable of storing information. The mass storage memory device  136  includes data storage devices such as a hard drive, optical drive, tape drive, volatile or non-volatile solid-state device, or any other device capable of storing information. 
     The processor  1032  operates under the control of an operating system  1046  that resides in memory  1034 . The operating system  1046  manages computer resources so that computer program code embodied as one or more computer software applications, such as an application  1048  residing in memory  1034 , may have instructions executed by the processor  1032 . In an alternative embodiment, the processor  1032  may execute the application  1048  directly, in which case the operating system  1046  may be omitted. One or more data structures  1049  also reside in memory  1034 , and may be used by the processor  1032 , operating system  1046 , or application  1048  to store or manipulate data. 
     The I/O interface  1038  provides a machine interface that operatively couples the processor  1032  to other devices and systems, such as the network  1026  or external resource  1042 . The application  1048  thereby works cooperatively with the network  1026  or external resource  1042  by communicating via the I/O interface  1038  to provide the various features, functions, applications, processes, or modules comprising embodiments of the invention. The application  1048  also includes program code that is executed by one or more external resources  1042 , or otherwise rely on functions or signals provided by other system or network components external to the computer system  1030 . Indeed, given the nearly endless hardware and software configurations possible, persons having ordinary skill in the art will understand that embodiments of the invention may include applications that are located externally to the computer system  1030 , distributed among multiple computers or other external resources  1042 , or provided by computing resources (hardware and software) that are provided as a service over the network  1026 , such as a cloud computing service. 
     The HMI  1040  is operatively coupled to the processor  1032  of computer system  1030  in a known manner to allow a user to interact directly with the computer system  1030 . The HMI  1040  may include video or alphanumeric displays, a touch screen, a speaker, and any other suitable audio and visual indicators capable of providing data to the user. The HMI  1040  also includes input devices and controls such as an alphanumeric keyboard, a pointing device, keypads, pushbuttons, control knobs, microphones, etc., capable of accepting commands or input from the user and transmitting the entered input to the processor  1032 . 
     A database  1044  may reside on the mass storage memory device  1036  and may be used to collect and organize data used by the various systems and modules described herein. The database  1044  may include data and supporting data structures that store and organize the data. In particular, the database  1044  may be arranged with any database organization or structure including, but not limited to, a relational database, a hierarchical database, a network database, or combinations thereof. A database management system in the form of a computer software application executing as instructions on the processor  1032  may be used to access the information or data stored in records of the database  1044  in response to a query, where a query may be dynamically determined and executed by the operating system  1046 , other applications  1048 , or one or more modules. 
     The description of the present disclosure is merely exemplary in nature and variations that do not depart from the gist of the present disclosure are intended to be within the scope of the present disclosure. Such variations are not to be regarded as a departure from the spirit and scope of the present disclosure.