Abstract:
A vehicle stability control system diagnostic strategy, wherein the diagnostic strategy may be adaptively applied based upon the identified maneuver states of the vehicle. The diagnostic architecture contains three vehicle state observers (i.e., models) each based on inputs from only two of the three sensors (yaw rate, lateral acceleration and hand wheel angle). More particularly, the first observer does not consider lateral acceleration input. The second observer does not consider yaw rate sensor input and the third does not consider hand wheel angle (HWA) sensor input in determining the vehicle state. However, estimated vehicle speed input is used by all the observers. For example, the first observer detects a maneuver state based on yaw rate and HWA and vehicle speed inputs. Then it diagnoses the lateral acceleration sensor failure based on the observer output. The diagnostics are based on vehicle dynamics correlations that hold in steady state linear range conditions. Similarly, the other two observers detect maneuver state and diagnose the respective signals. Advantageous variants include the use of a proactive sensor diagnostics strategy that provides increased coverage during steady state linear range maneuvers while simultaneously detecting faults within the required fault response time.

Description:
BACKGROUND  
       [0001]     The disclosure is directed to vehicular stability control, and more particularly, to a method for enhancing vehicle stability control.  
         [0002]     A vehicle stability control (VSC) system works by detecting when a driver has lost some degree of control. These systems are also known as ESP (electronic stability program) systems or VSE (vehicle stability enhancement) systems in the art. These systems automatically stabilize the vehicle to help the driver regain control. A central processor takes information from a number of sensors, and then determines whether the car is in a stable or unstable state. By combining the data from wheel speed sensors, steering angle sensors, yaw rate sensors (measuring the amount a vehicle rotates around its vertical center axis), and lateral acceleration sensors (measuring the amount of sideways acceleration generated by the vehicle), the central processing unit can actually detect when a vehicle is behaving in a way inconsistent with how the driver intends. If the processor does detect instability such as a slide produced by a sudden swerve, it automatically applies brake pressure to a select wheel (or wheels) to maintain or restore control.  
         [0003]     ESP system safety analysis has identified that sensor faults, specifically faults of the yaw rate, lateral acceleration and hand wheel angle signals, require detection within a short period of time. One component integrated in the ESP system is an on-line sensor monitoring system that is mainly used for detecting faults in sensors as early as possible so the fail control system does not activate unnecessarily. Those faults, which cause the sensor output to exceed the operational range of the measured variable (for example, lateral acceleration significantly exceeding 10 m/s 2 ) are relatively easy to detect and can typically be detected by the sensor circuit. Those faults resulting in erroneous sensor outputs, but still within the normal range of the measured signals, are more difficult to detect, and are the subject of this disclosure.  
         [0004]     Current systems have a dynamic model based diagnostic strategy whose intent is to detect a failure of a sensor in the normal range for the measured signal. One available strategy performs sensor diagnostics only when the ESP system is active and does not activate failure detection when the vehicle is in the linear range of handling (that is during normal operation). If model based signal correlation discrepancy exists for more than several seconds after ESP goes active, a fault is declared. The first drawback with this strategy is that it is a reactive approach to a fault rather than a proactive one. If it is a sensor failure that caused an unwanted activation, this strategy can wait several seconds before declaring it a fault. The second drawback is that it can declare a false fault if the vehicle is in a true ESP maneuver for a prolonged period, even when there is no true fault (for example, in case of testing, demo, etc.). The third drawback is that it does not monitor sensor condition during normal driving.  
         [0005]     Accordingly, there is a need for an ESP system capable to only use two of the three signals (steering angle sensors, yaw rate sensors and lateral acceleration sensors) in detecting a maneuver state, configured to detect even small deviations of the third missing signal successfully in steady state linear handling range of the vehicle. Additionally, there is a need for an ESP system able to selectively apply diagnostic thresholds based on the maneuver state and also if the vehicle is going straight or is in a turning maneuver. Furthermore, there is a need for an ESP system having the ability to isolate a fault successfully within a short period of time and not falsely call it a fault if the vehicle is truly in a quick transient or in a highly non-linear maneuver.  
       SUMMARY OF THE INVENTION  
       [0006]     In one aspect, a vehicle stability control system diagnostic strategy, may include a diagnostic strategy that is adaptively applied based upon the identified maneuver states of the vehicle. The diagnostic architecture may contain three vehicle state observers (i.e., models), each based on inputs from only two of the three sensors (yaw rate, lateral acceleration and hand wheel angle). More particularly, the first observer may not consider lateral acceleration input. The second observer may not consider yaw rate sensor input and the third may not consider hand wheel angle (HWA) sensor input in determining the vehicle state. However, estimated vehicle speed input may be used by all the observers. For example, the first observer may detect a maneuver state based on yaw rate and HWA and vehicle speed inputs. Then, it may diagnose the lateral acceleration sensor failure based on the observer output. The diagnostics may be based on vehicle dynamics correlations that hold in steady state linear range conditions. Similarly, the other two observers may detect maneuver state and diagnose the respective signals. Advantageous variants may include the use of a proactive sensor diagnostics strategy that provides increased coverage during steady state linear range maneuvers while simultaneously detecting faults within the required fault response time. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]      FIG. 1  is a schematic diagram of an active brake control system incorporating the disclosed vehicular stability control system;  
         [0008]      FIG. 2  is a flowchart showing one aspect of the disclosed vehicle stability control diagnostic strategy;  
         [0009]      FIG. 3  is a flowchart showing one aspect of the disclosed vehicle stability control algorithm to diagnose a lateral acceleration signal;  
         [0010]      FIG. 4  is a flowchart showing another aspect of the disclosed vehicle stability control algorithm to diagnose a yaw rate signal;  
         [0011]      FIG. 5  is a flowchart showing yet another aspect of the disclosed vehicle stability control algorithm to diagnose a hand wheel angle signal;  
         [0012]      FIG. 6  is a graph of measured HWA test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0013]      FIG. 7  is a graph of measured lateral acceleration test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0014]      FIG. 8  is a graph of ESC control output test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0015]      FIG. 9  is a graph of yaw Rate fault status output in accordance with one aspect of the disclosed vehicular stability control system;  
         [0016]      FIG. 10  is a graph of measured brake pressure test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0017]      FIG. 11  is a graph of measured vehicle speed test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0018]      FIG. 12  is a graph of measured yaw rate test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0019]      FIG. 13  is a graph of lateral acceleration fault status output test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0020]      FIG. 14  is a graph of HWA fault status output test data in accordance with one aspect of the disclosed vehicular stability control system;  
         [0021]      FIG. 15  is a graph of measured HWA test data in accordance with  FIG. 3 ;  
         [0022]      FIG. 16  is a graph of measured lateral acceleration test data in accordance with  FIG. 3 ;  
         [0023]      FIG. 17  is a graph of ESC control output test data in accordance with  FIG. 3 ;  
         [0024]      FIG. 18  is a graph of lateral acceleration fault status output, yaw rate fault status output and steering wheel angle fault status output test data in accordance with  FIG. 3 ;  
         [0025]      FIG. 19  is a graph of measured vehicle speed test data in accordance with  FIG. 3 ;  
         [0026]      FIG. 20  is a graph of measured yaw rate test data in accordance with  FIG. 3 ;  
         [0027]      FIG. 21  is a graph of measured slip angle test data in accordance with  FIG. 3 ;  
         [0028]      FIG. 22  is a graph of measured brake pressure test data in accordance with  FIG. 3 ;  
         [0029]      FIG. 23  is a graph of measured HWA test data in accordance with  FIG. 4 ;  
         [0030]      FIG. 24  is a graph of measured lateral acceleration test data in accordance with  FIG. 4 ;  
         [0031]      FIG. 25  is a graph of ESC control output test data in accordance with  FIG. 4 ;  
         [0032]      FIG. 26  is a graph of lateral acceleration fault status output, yaw rate fault status output and steering wheel angle fault status output test data in accordance with  FIG. 4 ;  
         [0033]      FIG. 27  is a graph of measured vehicle speed test data in accordance with  FIG. 4 ;  
         [0034]      FIG. 28  is a graph of measured yaw rate test data in accordance with  FIG. 4 ;  
         [0035]      FIG. 29  is a graph of measured slip angle test data in accordance with  FIG. 4 ;  
         [0036]      FIG. 30  is a graph of measured brake pressure test data in accordance with  FIG. 4 ;  
         [0037]      FIG. 31  is a graph of measured HWA test data in accordance with  FIG. 5 ;  
         [0038]      FIG. 32  is a graph of measured lateral acceleration test data in accordance with  FIG. 5 ;  
         [0039]      FIG. 33  is a graph of ESC control output test data in accordance with  FIG. 5 ;  
         [0040]      FIG. 34  is a graph of lateral acceleration fault status output, yaw rate fault status output and steering wheel angle fault status output test data in accordance with  FIG. 5 ;  
         [0041]      FIG. 35  is a graph of measured vehicle speed test data in accordance with  FIG. 5 ;  
         [0042]      FIG. 36  is a graph of measured yaw rate test data in accordance with  FIG. 5 ;  
         [0043]      FIG. 37  is a graph of measured slip angle test data in accordance with  FIG. 5 ;  
         [0044]      FIG. 38  is a graph of measured brake pressure test data in accordance with  FIG. 5 ; 
     
    
     DETAILED DESCRIPTION  
       [0045]     For the purposes of this disclosure, the acronyms VSC (vehicle stability control) and ESP (electronic stability program) may be used interchangeably with a vehicular stability control system. A control process for controlling the driving stability of a motor vehicle is known in the prior art. For example, a method of improving vehicle handling and stability utilizing a desired yaw rate and lateral velocity of a vehicle in a steady-state condition is disclosed in U.S. Pat. No. 6,658,342 to Hac, which is incorporated herein by reference. Another vehicle stability control method utilizing yaw rate and side angle slip (i.e., angle between a vehicle&#39;s actual direction of travel and the direction towards which it is pointing) is disclosed in U.S. Pat. No. 6,035,251 to Hac et al., which is incorporated herein by reference. Furthermore, a method for estimating the yaw rate of a vehicle is disclosed in U.S. Pat. No. 6,623,089 to Amberkar, which is incorporated herein by reference.  
         [0046]     Referring to  FIG. 1 , a vehicle stability control system, generally designated  10 , may include an active brake control system with a conventional microprocessor-based controller  11  for controlling brakes  20 ,  22 ,  24  and  26 , for respective vehicle wheels  12 ,  14 ,  16  and  18 . The controller  11  may include such conventional elements (not shown) as a central processing unit (CPU) having control circuitry and arithmetic logic circuitry, memory devices including read only memory devices (ROM) for permanent read only data storage and random access memory devices (RAM) for both volatile and nonvolatile read/write data storage.  
         [0047]     The controller  11 , when activated in response to manual application of ignition power thereto, may execute a series of control and diagnostic operations for reading various input signals applied thereto and for issuing control and diagnostic signals to various vehicle actuators and indicators. The input signals applied to the controller  11  may include an output signal on line  15  from a conventional yaw rate sensor  13 , an output signal on line  19  from conventional accelerometer  17  indicating lateral vehicle acceleration, an output signal on line  25  from a conventional digital steering wheel angle sensor  23  indicating the degree of rotational displacement of steering wheel  21  away from a predetermined initial angle, output signals on lines  36 ,  38 ,  40  and  42  from respective conventional wheel speed sensors  28 ,  30 ,  32 , and  34 , output signal on line  54  from conventional brake pedal displacement sensor  52  indicating a degree of depression of the brake pedal  50  away from a rest position, output signal on line  58  from conventional brake pedal switch  56  indicating whether the brake pedal  50  is depressed away from a rest position. Alternatively, a master cylinder brake pressure sensor  72  can be used instead of, or in addition to, the brake pedal displacement sensor  52  to indicate the magnitude of brake input by the driver.  
         [0048]     Wheel speed sensor output  36 ,  38 ,  40  and  42  can be used to determine if a vehicle (not shown) is turning a corner. For example, during cornering the outside tires of a vehicle have to travel further than the inside tires, so they rotate faster than the inside tires. Furthermore, during an intervention of the VSC system, the system automatically applies braking to individual wheels, resulting in differences in wheel speeds. These differences in wheel speeds can be calculated to help modify stability control operation in corners.  
         [0049]     The most common types of slides are referred to as under-steer and over-steer. In an under-steer situation, the front of the vehicle (not shown) plows towards the outside of a turn without following the curve of the turn. When the stability control system detects under-steer, it applies light brake presssure  24  or  26  to the inside rear wheel  16  or  18 , respectively. This helps “tug” the front of the vehicle back onto the intended path around the curve. In an over-steer situation, the rear of the vehicle fishtails toward the outside of a turn, increasing the chance of a spin. To counteract such a situation, the stability system applies braking  20  or  22  to the outside front wheel  12  or  14 , respectively to bring the rear end back in line. The system works when the vehicle starts to slide on a straight road having wet, snowy, or icy conditions the same as it does when turning corners.  
         [0050]     Redundant sensors may be provided for the above sensors to improve fault detection or tolerance. For example, conventional analog steer angle sensors (not shown) may be provided in addition to digital steer angle sensor  23  for transducing a steer angle signal substantially redundant with the digital steer angle  23  output signal on line  25 . In another example, vehicle speed signal on line  62 , such as from a conventional vehicle speed sensor  60  located in the transmission may be redundant to the described output signals on lines  36 ,  38 ,  40  and  42  from respective conventional wheel speed sensors  28 ,  30 ,  32 , and  34 .  
         [0051]     The described conventional sensors  13 ,  17 ,  23 ,  28 ,  30 ,  32 ,  34 ,  54  and  56  are implemented in a manner generally known to those possessing ordinary skill in the art. Vehicle ignition voltage is applied to the sensors and actuators of  FIG. 1  substantially at the time ignition voltage is manually applied to controller  11 , to energize such sensor and actuators in a manner generally understood in the art.  
         [0052]     The control operations of controller  11  provide for vehicle braking control in a plurality of control modes including a base braking mode, an anti-lock braking mode, a traction control braking mode, and a closed-loop yaw rate control mode. Conventional pressure transducer  72  disposed within the master cylinder  70  transduces brake fluid pressure within the master cylinder  70  into an output signal  74  applied to controller  11 , indicating the degree of displacement of the brake pedal  50 . Controller  11  generates and outputs brake pressure modulation commands to dedicated brake pressure control actuators (not shown) for varying the brake pressure at the respective wheels  12 ,  14 ,  16  and  18 .  
         [0053]     A general functional layout of the diagnostic strategy is shown in  FIG. 2 . Referring to  FIG. 2 , the desired yaw rate dynamic (Ω des ) signal  102  may be determined within the reference model  100  of the VSC system and the process of determining it is known to those skilled in the art (see, for example, U.S. Pat. Nos. 6,035,251 and 6,658,342). First, the yaw rate desired steady-state, Ω dss  is calculated as a function of the HWA  202  and vehicle speed  203  from a look up table, subsequently, Ω des  is determined by passing Ω dss  through dynamic filters. Both these signals are not compensated for bank angle and do not use yaw rate  201  or lateral acceleration  208  sensor inputs. The Ω des  signal  102  may be received by at least one or may be received by a plurality of algorithms, such as but not limited to, a lateral acceleration maneuver state algorithm  204 , a yaw rate sensor maneuver state algorithm  209  and a HWA diagnostic algorithm  215 .  
         [0054]     As shown in  FIG. 2 , in order to diagnose a fault of one of the three sensors (HWA  202 , yaw rate  201  and lateral acceleration  208 ), two remaining sensors and vehicle speed input  203  are used to determine whether the vehicle is at steady state and in the linear range of handling, and that it is not on a road with a significant bank angle. If all these conditions are satisfied, then the failure of the investigated sensor is detected when its output sufficiently deviates from the output predicted by the model (observer) using the remaining sensors. The lateral acceleration fault status signal  207 , the yaw rate fault status signal  212  and the HWA fault status signal  216  may be received by the controller  11 , wherein the controller  11  may be configured to take action on a true fault by disabling said vehicle stability control system  10  to prevent unwanted activation, although alternatively, the controller  11  may be configured to take no action on a false fault.  
         [0055]     A method of detecting failure in the lateral acceleration sensor  208  is illustrated in  FIGS. 2 and 3  and mandates steady state and linear handling range computations based on the measured vehicle stability control system  10  inputs of yaw rate  201 , HWA  202 , vehicle speed  203  and the computed yaw rate desired dynamic (Ω des ) input  102 .  
         [0056]     As shown in  FIG. 3 , a method for diagnosing a lateral acceleration sensor  208  fault in a vehicle stability control system  10  includes receiving at least one signal indicative of a vehicular measured yaw rate  201 ; receiving at least one signal indicative of a vehicular measured velocity  203 ; receiving at least one signal indicative of a vehicular measured hand wheel angle  202 ; receiving at least one signal indicative of a vehicular computed yaw rate desired  102 ; selecting a lateral acceleration estimator  301 ,  304  in accordance with a steady-state  301  and a linear range of handling conditions  304 ; estimating a lateral acceleration in accordance with the selected linear acceleration estimator  301 ,  304 ; applying a plurality of estimated lateral acceleration thresholds  303 ,  306  to determine a vehicle maneuver state, wherein the plurality of estimated lateral acceleration thresholds  303 ,  306  may be vehicle specific; selectively apply diagnostic thresholds  206 ,  307  to the estimated lateral acceleration  310  based on the maneuver state, wherein the selectively applied diagnostic thresholds  206 ,  307  may be vehicle specific; measuring a lateral acceleration  208  with a lateral acceleration sensor  208 ; comparing the measured lateral acceleration  208  with the estimated lateral acceleration  310 ; detecting a true fault  313  with the lateral acceleration sensor  208  when the comparison is not within a selected comparison threshold value  311 , wherein the selected comparison threshold value  311  may be vehicle specific; detecting a false fault  312  with the lateral acceleration sensor  208  when the comparison is within the selected comparison threshold value  311 ; supplying a microprocessor controller  11  to the vehicle stability control system  10 , wherein the controller  11  may be configured to take action on the true fault  313  by disabling  315  the vehicle stability control system  10  to prevent unnecessary activation; although alternatively, the controller  11  may be configured to take no action on the false fault  312 . Referring to  FIG. 3 , failed performance criteria signals include  302 ,  305 ,  308  and  313 , while affirmed performance criteria signals include  303 ,  306 ,  309  and  312 .  
         [0057]     As shown in  FIG. 3 , the vehicle can be assumed to be in steady-state when: (i) the time derivative of measured yaw rate, dΩ/dt is small in magnitude (less than YRder_thresh, for example, less than about 0.2 rad/s 2 ) AND (ii) the time derivative of the desired yaw rate dΩ des /dt is small in magnitude (less than YRder_thresh, for example, less than about 0.2 rad/s 2 ) AND (iii) the time derivative of the product of the steering angle and speed [d(v x * HWA)/dt] is small in magnitude (less than HWAspeedder_thresh 1 , for example, less than 9 m*rad/s 2 ). It should be noted that the last condition may be redundant for some vehicles, although at high speeds, yaw rates are fairly small and a transient condition may not be detected when considering only the yaw rates.  
         [0058]     Specific numerical values for the thresholds are provided in the above and below descriptions, as illustrated in  FIGS. 3-5 , with the understanding that they may be slightly different for other vehicles (not shown) as they depend upon vehicle parameters, in particular the under-steer gradient.  
         [0059]     Under-steer gradient is defined as the ratio of change in the (front) steering angle to the change in lateral acceleration during a constant radius turn with very slowly varying speed. For most vehicles, as the speed of the vehicle in a constant radius turn increases, the steering angle has to increase as well. The ratio K u  is the under-steer gradient and may be expressed as K u =Δδ/(Δa y ). Here Δδ is the change in the steering angle and Δa y  is the change in the lateral acceleration. The commonly used units are [rad/(m/s 2 )]. In the linear handling range the under-steer gradient can be expressed as a function of vehicle and tire parameters as follows: K u =m f /C f −m r /C r =[(C r *b−C f *a)*M]/(C f *C r *L). Here m f =m*b/L is vehicle mass per front axle, m r =m*a/L is the vehicle mass per rear axle, m is the total mass of vehicle, a and b are the distances of vehicle center of mass to the front and rear axle, respectively, L=a+b is the vehicle wheel-base, C f  and C r  are the cornering stiffness values of both front and both rear tires, respectively.  
         [0060]     As shown in  FIG. 3 , the vehicle is in the linear handling range when: (i) the product of the desired yaw rate and speed |Ω des *v x | is small in magnitude (less than YRspeed_thresh, for example, less than 4 m/s 2 ). AND (ii) the yaw rate error, defined as a difference between the desired and measured yaw rate, that is |Ω des −Ω| is small in magnitude for a specified period of time (less than YRerr_thresh 1 , for example less than 0.07 rad/s for a Δt of about 0.5 second).  
         [0061]     If vehicle is in a steady-state and in the linear range of handling, then the lateral acceleration signal may be diagnosed as shown in  FIG. 3 . The difference between the measured lateral acceleration filtered (a ymfilt ) and the product of measured yaw rate and speed |a ymfilt −v x *Ω| should not exceed a threshold value (LAerr_thresh 1 , for example, less than 2 m/s 2 ), otherwise a failure of lateral acceleration sensor occurred. If vehicle is not at steady-state or not in the linear handling range, the value of the threshold LAerr_thresh 1  increases. It should be further noted that the condition |a ymfilt −v x *Ω|&lt;LAerr_thresh 1  could be triggered by a very large spike in measurement noise, and thereby necessitates that the measured lateral acceleration signal must be filtered.  
         [0062]     The lateral acceleration signal is filtered by passing the signal through a noise filter. For example, a noise filter with the transfer function a yfilt (s)/a y (s)=ω f /(s+ω f ) may be utilized. Here s is the Laplace operand and ω f  is the filter contrast (representing a suitable cut-off frequency). The transfer function can be implemented on a digital processor using the following time-domain equation: a yfilt (t)=(1ω f *Δt)*a yfilt (t−Δt)+(ω f *Δt)*a y (t). Here Δt is the sampling time. Typical sources of measurement noise in accelerometers are mechanical vibrations of the sensor attachment and electrical noise in the circuit of the sensor due to external disturbances (of magnetic or electric field) which may cause variations of current and voltage in this circuit.  
         [0063]     A method of detecting failure in the yaw rate sensor  201  is illustrated in  FIGS. 2 and 4  and mandates steady state and linear handling range computations based on the measured vehicle stability control system  10  inputs of lateral acceleration  208 , HWA  202 , vehicle speed  203  and computed yaw rate desired dynamic (Ω des ) input  102 .  
         [0064]     As shown in  FIG. 4 , a method for diagnosing a yaw rate sensor  201  fault in a vehicle stability control system  10 , includes receiving at least one signal indicative of a vehicular measured lateral acceleration  208 ; receiving at least one signal indicative of a vehicular measured velocity  203 ; receiving at least one signal indicative of a vehicular measured hand wheel angle  202 ; receiving at least one signal indicative of a vehicular computed yaw rate desired  102 ; selecting a yaw rate estimator  401 ,  404  in accordance with a steady-state  401  and a linear range of handling conditions  404 ; estimating a yaw rate in accordance with the selected yaw rate estimator  401 ,  404 ; applying a plurality of estimated yaw rate thresholds  403 ,  406  to determine a vehicle maneuver state, wherein the plurality of estimated yaw rate thresholds  403 ,  406  may be vehicle specific; selectively apply diagnostic thresholds  211 ,  407  to the estimated yaw rate  410  based on the maneuver state, wherein the selectively applied diagnostic thresholds  211 ,  407  may be vehicle specific; measuring a yaw rate  201  with a yaw rate sensor  201 ; comparing the measured yaw rate  201  with the estimated yaw rate  410 ; detecting a true fault  413  with the yaw rate sensor  201  when the comparison is not within a selected comparison threshold value  411 , wherein the selected comparison threshold  411  value can be vehicle specific; detecting a false fault  412  with the yaw rate sensor  201 when the comparison is within the selected comparison threshold value  411 ; supplying a microprocessor controller  11  to the vehicle stability control system  10 , wherein the controller  11  may be configured to take action on the true fault  413  by disabling  415  the vehicle stability control system  10  to prevent unnecessary activation; although alternatively, the controller  11  may be configured to take no action on the false fault  412 . Referring to  FIG. 4 , failed performance criteria signals include  402 ,  405 ,  408  and  413 , while affirmed performance criteria signals include  403 ,  406 ,  409  and  412 .  
         [0065]     As shown in  FIG. 4 , the vehicle can be assumed to be in steady-state when: (i) the time derivative of the desired yaw rate dΩ des /dt is small in magnitude (less than YRder_thresh, for example, less than about 0.2 rad/s 2 ) AND (ii) the time derivative of measured lateral acceleration, sometimes termed “lateral jerk”, d(a ymfilt )/dt, is small in magnitude (less than LAder_thresh, for example, less than 3 m/s 3 ) AND (iii) the time derivative of a product of the steering angle and speed d(v x *HWA)/dt] is small in magnitude (less than HWAspeedder_thresh 2 , for example, less than 10 m*rad/s 2 ).  
         [0066]     As shown in  FIG. 4 , the vehicle is in the linear handling range when: (i) the product of the desired yaw rate and speed |Ω des *v x | is small in magnitude (less than YRspeed_thresh, for example, less than 4 m/s 2 , and depends on the under-steer gradient of the vehicle), AND (ii) the difference between the measured and filtered lateral acceleration and the product of desired yaw rate and speed |a ymfilt −v x *Ω des | is small in magnitude for a specific period of time (less than LAerr_thresh 2 , for example, less than 1.0 m/s 2  for At of about 1 second), AND (iii) the measured lateral acceleration filtered, a ymfilt , is small in magnitude (less than Lat_thresh, for example, less than 4 m/s 2 ).  
         [0067]     If vehicle is in a steady-state and in the linear range of handling, then the yaw rate signal may be diagnosed as shown in  FIG. 4 . The difference between the desired and measured yaw rates |Ω des −Ω| should not exceed a threshold value YRerr_thresh 2  (for example, less than 0.175 rad/s), otherwise a failure of yaw rate sensor occurred. If vehicle is not at steady-state or not in the linear handling range, the value of the threshold YRerr_thresh 2  is increased. It should be noted that the last threshold may be tighter during straight driving as |Ω des *v x |, and |a ymfilt | may both be very small in magnitude (for example, about 1 m/s 2  for Δt of about 1 second).  
         [0068]     A method of detecting failure in the HWA sensor  202  is illustrated in  FIGS. 2 and 5  and mandates steady state and linear handling range computations based on the measured vehicle stability control system  10  inputs of lateral acceleration  208 , yaw rate  201  and vehicle speed  203 .  
         [0069]     As shown in  FIG. 5 , a method for diagnosing a hand wheel angle (HWA) sensor  202  fault in a vehicle stability control system  10 , includes receiving at least one signal indicative of a vehicular measured lateral acceleration  208 ; receiving at least one signal indicative of a vehicular measured velocity  203 ; receiving at least one signal indicative of a vehicular measured yaw rate  201 ; selecting a HWA estimator  501 ,  504  in accordance with a steady-state  501  and a linear range of handling conditions  504 ; estimating a HWA in accordance with the selected HWA estimator  501 ,  504 ; applying a plurality of estimated HWA thresholds  503 ,  506  to determine a vehicle maneuver state, wherein the plurality of estimated HWA thresholds  503 ,  506  can be vehicle specific; selectively apply diagnostic thresholds  215 ,  507  to the estimated HWA  510  based on the maneuver state, wherein the selectively applied diagnostic thresholds  215 ,  507  may be vehicle specific; measuring a HWA  202  with a HWA sensor  202 ; comparing the measured HWA  202  with the estimated HWA  510 ; detecting a true fault  513  with the HWA sensor  202  when the comparison is not within a selected comparison threshold  511  value, wherein the selected comparison threshold  511  value may be vehicle specific; detecting a false fault  513  with the HWA sensor  202  when the comparison is within the selected comparison threshold value  511 ; supplying a microprocessor controller  11  to the vehicle stability control system  10 , wherein the controller  11  may be configured to take action on the true fault  513  by disabling  515  the vehicle stability control system  10  to prevent unnecessary activation; although alternatively, the controller  11  may be configured to take no action on the false fault  512 . Referring to  FIG. 5 , failed performance criteria signals include  502 ,  505 ,  508  and  513 , while affirmed performance criteria signals include  503 ,  506 ,  509  and  512 .  
         [0070]     As shown in  FIG. 5 , the vehicle can be assumed to be in steady-state when: (i) the time derivative of the measured yaw rate dΩ/dt is small in magnitude (less than YRder_thresh, for example, less than about 0.2 rad/s 2 ) AND (ii) the time derivative of measured lateral acceleration d(a ymfilt )/dt, is small in magnitude (less than LAder_thresh, for example, less than 3 m/s 3 ) AND (iii) the time derivative of the product of yaw rate and speed, [d(Ω*v x )/dt] is small in magnitude (less than YRspeedder_thresh, for example, less than 6 m/s 3 ).  
         [0071]     As shown in  FIG. 5 , the vehicle is in the linear handling range when: (i) the product of the measured yaw rate and speed |Ω*v x | is small in magnitude (less than YRspeed_thresh, for example, less than 4 m/s 2 ), AND (ii) the difference between the measured and filtered lateral acceleration and the product of measured yaw rate and speed |a ymfilt −v x *Ω| is small in magnitude (less than LAerr_thresh 2 , for example, less than 1.0 m/s 2  for Δt of about 1 second), AND (iii) the measured lateral acceleration filtered, a ymfilt , is small in magnitude (less than LA_thresh, for example, less than 4 m/s 2 ).  
         [0072]     If vehicle is in a steady-state and in the linear range of handling, then the HWA may be diagnosed as shown in  FIG. 5 . The difference between the desired and measured yaw rates should not exceed a threshold value that is |Ω des Ω| should be below YRerr_thresh 3  (for example, less than 0.122 rad/s), otherwise a failure of steering sensor occurred. The threshold is tighter during straight driving when |Ω des *v x | and |a ymfilt | may be very small in magnitude (for example, about 1 m/s 2  for some period of time). The threshold becomes larger when vehicle is not in a steady-state condition or not in the linear range.  
         [0073]     The following non-limiting examples enable certain aspects of the disclosure to be more clearly understood.  
       EXAMPLE 1  
       [0074]     The above strategy was tested exhaustively in simulation using a validated vehicle simulation model representing a pick up truck with a hydraulic brake system. The tests included steady state linear and aggressive emergency maneuvers on different surfaces. The results did not show any false diagnosis of a sensor fault. And when a fault was injected, it was isolated and detected correctly within the required fault response time specified by the system safety hazard analysis activity.  
         [0075]     In Example 1, the vehicle was placed in a transient emergency maneuver condition on a slippery, icy surface, and the algorithm results (see  FIGS. 6-14 ) showed all observers (see  FIGS. 9 and 13 - 14 ) successfully identified the maneuver state and the diagnostics (see  FIG. 8 ) did not falsely declare a fault.  
       EXAMPLE 2  
       [0076]     In Example 2, the vehicle was located on a dry surface having a constant radius turning maneuver condition wherein a slow changing lateral acceleration fault was injected (see  FIG. 16 ), and the algorithm results (see  FIGS. 15-22 ) showed all observers (see  FIG. 18 ) successfully identified the maneuver state (i.e., without a measured lateral acceleration input) and the diagnostics (see  FIG. 18 ) successfully detected the lateral acceleration signal fault.  
       EXAMPLE 3  
       [0077]     In Example 3, the vehicle was located on a dry surface having a straight driving maneuver condition wherein a yaw rate fault was injected (see  FIG. 28 ), and the algorithm results (see  FIGS. 23-33 ) showed all observers (see  FIG. 26 ) successfully identified the maneuver state (i.e., without a measured yaw rate input) and the diagnostics (see  FIG. 26 ) successfully detected the yaw rate signal fault.  
       EXAMPLE 4  
       [0078]     In Example 4, the vehicle was located on a dry surface having a straight driving maneuver condition wherein a steering wheel angle fault was injected (see  FIG. 31 ), and the algorithm results (see  FIGS. 31-38 ) showed all observers (see  FIG. 34 ) successfully identified the maneuver state (i.e., without a measured HWA input) and the diagnostics (see  FIG. 34 ) successfully detected the HWA signal fault.  
         [0079]     Having described the disclosure in detail and by reference to specific embodiments thereof, it will be apparent that numerous variations and modifications are possible without departing from the spirit and scope of the disclosure as defined by the following claims.