Abstract:
A dynamic load estimation system is provided including: a vehicle load bearing tire; at least one tire sensor mounted to the tire, the sensor operable to measure a tire deformation of the one tire and generate a raw load-indicating signal conveying measured deformation data; road roughness estimation means for determining a road roughness estimation; filtering means for filtering the measured deformation data by the road roughness estimation; and load estimation means for estimating an estimated load on the one tire from filtered measured deformation data. A road profile estimate is fused with the static load estimate in order to obtain an instantaneous tire load estimate.

Description:
FIELD OF THE INVENTION 
     The invention relates generally to tire monitoring systems for collecting measured tire parameter data during vehicle operation and, more particularly, to systems and method generating for estimating tire loading based upon the measured tire parameter data. 
     BACKGROUND OF THE INVENTION 
     Vehicle-mounted tires may be monitored by tire pressure monitoring systems (TPMS) which measure tire parameters such as pressure and temperature during vehicle operation. Data from TPMS tire-equipped systems is used to ascertain the status of a tire based on measured tire parameters and alert the driver of conditions, such as low tire pressure or leakage, which may require remedial maintenance. Sensors within each tire are either installed at a pre-cure stage of tire manufacture or in a post-cure assembly to the tire. 
     Other factors such as tire loading are important considerations for vehicle operation and safety. It is accordingly further desirable to estimate tire loading under real time and driving conditions and communicate load information to a vehicle operator and/or vehicle systems such as braking in conjunction with the aforementioned measured tire parameters of pressure and temperature. 
     SUMMARY OF THE INVENTION 
     According to an aspect of the invention, a dynamic load estimation system is provided including: a vehicle load bearing tire; at least one tire sensor mounted to the tire, the sensor operable to measure a tire deformation of the one tire and generate a raw load-indicating signal conveying measured deformation data; road roughness estimation means for determining a road roughness estimation; unfiltered load estimating means for generating a static load estimation from the raw load-indicating signal, filtering means for filtering the static load estimation by the road roughness estimation; and load estimation means for estimating an estimated load on the one tire on the basis of the filtered load estimation. 
     In a further aspect, the tire sensor functions in the configuration of as an energy harvesting device that generates a signal responsive to tire deformation. 
     According to a further aspect, the filtering means is configured as an adaptive filter such as an adaptive Kalman filter using a recursive-based procedure. The adaptive Kalman filter generates from the unfiltered tire footprint length estimate a footprint length estimation that is adaptively filtered by a road roughness estimation. The filtered footprint length, together with measured tire inflation pressure and tire identification data, are then used to extract an estimated tire load from a tire-specific database. In a first embodiment, the road roughness estimation means operatively applies a surface roughness classification system to the raw load-indicating signal to determine a relative road roughness estimation. The filtering means then operates to filter the measured deformation data by the relative road roughness estimation. Data from the vehicle-mounted sensors is used in an adaptive filter and applied to a static load estimate from the tire to generate a road profile height estimation and a load variation estimate. The estimated road profile height is operatively fused with the filtered load estimation to yield a calculated instantaneous tire load estimation. 
     DEFINITIONS 
     “ANN” or “Artificial Neural Network” is an adaptive tool for non-linear statistical data modeling that changes its structure based on external or internal information that flows through a network during a learning phase. ANN neural networks are non-linear statistical data modeling tools used to model complex relationships between inputs and outputs or to find patterns in data. 
     “Aspect ratio” of the tire means the ratio of its section height (SH) to its section width (SW) multiplied by 100 percent for expression as a percentage. 
     “Asymmetric tread” means a tread that has a tread pattern not symmetrical about the center plane or equatorial plane EP of the tire. 
     “Axial” and “axially” means lines or directions that are parallel to the axis of rotation of the tire. 
     “CAN bus” is an abbreviation for controller area network. 
     “Chafer” is a narrow strip of material placed around the outside of a tire bead to protect the cord plies from wearing and cutting against the rim and distribute the flexing above the rim. 
     “Circumferential” means lines or directions extending along the perimeter of the surface of the annular tread perpendicular to the axial direction. 
     “Equatorial Centerplane (CP)” means the plane perpendicular to the tire&#39;s axis of rotation and passing through the center of the tread. 
     “Footprint” means the contact patch or area of contact created by the tire tread with a flat surface as the tire rotates or rolls. 
     “Groove” means an elongated void area in a tire wall that may extend circumferentially or laterally about the tire wall. The “groove width” is equal to its average width over its length. A grooves is sized to accommodate an air tube as described. 
     “Inboard side” means the side of the tire nearest the vehicle when the tire is mounted on a wheel and the wheel is mounted on the vehicle. 
     “Kalman Filter” is a set of mathematical equations that implement a predictor-corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance—when some presumed conditions are met. 
     “Lateral” means an axial direction. 
     “Lateral edges” means a line tangent to the axially outermost tread contact patch or footprint as measured under normal load and tire inflation, the lines being parallel to the equatorial centerplane. 
     “Luenberger Observer” is a state observer or estimation model. A “state observer” is a system that provide an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications. 
     “MSE” is an abbreviation for Mean square error, the error between and a measured signal and an estimated signal which the Kalman Filter minimizes. 
     “Net contact area” means the total area of ground contacting tread elements between the lateral edges around the entire circumference of the tread divided by the gross area of the entire tread between the lateral edges. 
     “Non-directional tread” means a tread that has no preferred direction of forward travel and is not required to be positioned on a vehicle in a specific wheel position or positions to ensure that the tread pattern is aligned with the preferred direction of travel. Conversely, a directional tread pattern has a preferred direction of travel requiring specific wheel positioning. 
     “Outboard side” means the side of the tire farthest away from the vehicle when the tire is mounted on a wheel and the wheel is mounted on the vehicle. 
     “Peristaltic” means operating by means of wave-like contractions that propel contained matter, such as air, along tubular pathways. 
     “Piezoelectric Film Sensor” a device in the form of a film body that uses the piezoelectric effect actuated by a bending of the film body to measure pressure, acceleration, strain or force by converting them to an electrical charge. 
     “PSD” is Power Spectral Density (a technical name synonymous with FFT (Fast Fourier Transform). 
     “Radial” and “radially” means directions radially toward or away from the axis of rotation of the tire. 
     “Rib” means a circumferentially extending strip of rubber on the tread which is defined by at least one circumferential groove and either a second such groove or a lateral edge, the strip being laterally undivided by full-depth grooves. 
     “Sipe” means small slots molded into the tread elements of the tire that subdivide the tread surface and improve traction, sipes are generally narrow in width and close in the tires footprint as opposed to grooves that remain open in the tire&#39;s footprint. 
     “Tread element” or “traction element” means a rib or a block element defined by having a shape adjacent grooves. 
     “Tread Arc Width” means the arc length of the tread as measured between the lateral edges of the tread. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described by way of example and with reference to the accompanying drawings in which: 
         FIG. 1  is a diagrammatic view of a vehicle showing tire-mounted sensors. 
         FIG. 2  is an exploded perspective view of a portion a tire to which a sensor package mounts. 
         FIG. 3  is a graph showing a characteristic waveform for one tire revolution. 
         FIG. 4  is a graph showing raw signal amplitude vs. surface roughness. 
         FIG. 5  is a diagram showing methods of signal comparison for use in a signal comparison algorithm. 
         FIG. 6A  is a graph showing reference signal data for one tire rotation under smooth asphalt conditions at 60 kph. 
         FIG. 6B  is a graph showing test data for one tire rotation under smooth asphalt conditions at 60 kph. 
         FIG. 6C  is a graph showing the cross-correlation coefficient (R) for a smooth vs. smooth classification case, R max  approximately equal 0.85. 
         FIG. 7A  is a graph showing reference signal data for one tire rotation under smooth asphalt conditions at 60 kph. 
         FIG. 7B  is a graph showing test data for one tire rotation under rough asphalt conditions at 60 kph. 
         FIG. 7C  is a graph the cross-correlation coefficient (R) for a showing smooth vs. rough classification case, R max  approximately equal 0.6. 
         FIG. 8A  is a graph showing reference data for one tire rotation under smooth asphalt conditions at 60 kph. 
         FIG. 8B  is a graph showing test data for one tire rotation under very rough asphalt conditions at 60 kph. 
         FIG. 8C  is a graph showing the cross-correlation coefficient (R) for a smooth vs. very rough case, R max  approx. equal 0.3. 
         FIG. 9A  is a graph showing reference signal data for one tire rotation under smooth asphalt conditions at 90 kph. 
         FIG. 9B  is a graph showing test data for one tire rotation under smooth asphalt conditions at 90 kph. 
         FIG. 9C  is a graph showing the cross-correlation coefficient (R) for a smooth vs. smooth classification case, R max  approximately equal 0.85. 
         FIG. 10A  is a graph showing reference signal data for one tire rotation under smooth asphalt conditions at 90 kph. 
         FIG. 10B  is a graph showing test signal data for one tire rotation under smooth asphalt conditions at 9 kph. 
         FIG. 10C  is a graph showing the cross-correlation coefficient (R) for a smooth vs. rough classification case, R max  approximately equal 0.6. 
         FIG. 11A  is a graph showing reference signal data for one tire rotation under smooth asphalt conditions at 90 kph. 
         FIG. 11B  is a graph showing test signal data for one tire rotation under very rough asphalt conditions at 90 kph. 
         FIG. 11C  is a graph showing the cross-correlation coefficient (R) for a smooth vs. very rough classification case, R max  approximately equal 0.3. 
         FIGS. 12A ,  12 B,  13 A,  13 B,  14 A and  14 B are summary graphs of the speed dependence study shown Cross-correlation coefficient graphs at speeds of 60 and 90 kph and for the three conditions of smooth vs. smooth, smooth vs. rough, and smooth vs. very rough. The R max  for each is indicated in each graph. 
         FIG. 15  is a diagram illustrating Classification Rules for the Circular Cross-correlation Coefficient. 
         FIG. 16A  shows graphs of the raw sensor signal for smooth and rough surface situations. 
         FIG. 16B  shows an Energy Distribution graph of Wavelet Decompositions Energy. 
         FIG. 17A  shows a selection 1 Visualization of Selected Data graph for the Autocorrelation Coefficient. 
         FIG. 17B  shows a statistical graph for the data of  FIG. 17A . 
         FIG. 18A  shows a selection index 2 Visualization of Selected data. 
         FIG. 18B  shows a statistical distribution graph for the data of  FIG. 18A   
         FIG. 19  is a diagram of a Road Surface Classification algorithm. 
         FIG. 20A  is a graph showing observed straight-line Noisy Sensor Estimate of load vs. Actual Mean Load. 
         FIG. 20B  shows a graph of observed rough surface Noisy Sensor Estimate of load vs. Actual Mean Load. 
         FIG. 21  is a normal distribution curve showing the dependency of standard deviation on surface roughness level. 
         FIG. 22A  is a graph of Load Estimation Algorithm performance vs. Tire Load for Case-1 Smooth Surface Condition. 
         FIG. 22B  is a graph of load Estimation Error over time showing Moving Average Filter performance vs. Kalman Filter Performance results. 
         FIG. 23A  is a graph of Load Estimation Algorithm performance vs. Tire Load for Case-2 Rough Surface Condition. 
         FIG. 23B  is a graph of load Estimation Error as a percent over time showing Moving Average Filter performance vs. Kalman Filter Performance results in Case 2. 
         FIG. 24A  is a graph of estimation error over time for a conventional Kalman filter. 
         FIG. 24B  is a graph of estimation error over time for an adaptive Kalman filter. 
         FIG. 25  is a data flow diagram of the subject load estimation algorithm. 
         FIG. 26  is a data flow diagram of an alternative load estimation algorithm using a quarter-car vehicle model. 
         FIG. 27  is a graph of actual vs. estimated road profile elevation using the algorithm of  FIG. 26 , with a Correlation coefficient (R)=0.966. 
         FIG. 28  is a graph of load over time comparing actual to estimated (using the Kalman filter) for a Correlation coefficient of 67.979. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIGS. 1 and 2 , a vehicle  10  is shown supported by multiple tires  12 , each tire equipped with a sensor package  14 . While the vehicle  10  is in the general form of a passenger automobile, the subject system can be used in any vehicle system. The sensor module  14  is of a type commercially available, suitable for mounting to an inner liner  16  of the vehicle  10 . The sensor module or package  10  includes a pressure sensor and a temperature sensor for respectively measuring the air pressure and temperature of the tire inner cavity during tire operation. In addition, the sensor module  10  pursuant to the invention includes a vibration sensor mounted for measuring tire deformation during tire operation. The vibration sensor is preferably piezo-based and generates a signal indicative of tire deformation. From the signal, the footprint of the tire  12  as it rotates against a ground surface may be roughly estimated (also referred to herein as a “raw” or “unfiltered” estimation) ascertained by means of the methodology taught in co-pending U.S. patent application Ser. No. 13/534,043, filed Jun. 27, 2012 entitled: “Load Estimation System and Method for a Vehicle Tire” and hereby incorporated by reference in its entirety. 
     The piezo-sensor within module  14  generates a signal indicative of tire deformation within a rolling tire footprint. The piezo-sensor transmits a raw signal to a signal processor (not shown). The peak to peak length of the signal is analyzed to ascertain the length of the tire footprint. Appropriate tables are then consulted which provide tire-specific loading information for the tire based on the piezo-sensor measured footprint length, tire air pressure, and tire cavity temperature data. 
     The estimation of tire loading pursuant to the above-identified application may utilize a filtering model such as a Kalman filter. Determining tire loading from measurement of tire deflection, however, is problematic because of the presence of a “noise” contribution to tire deformation. As used herein, “noise” refers to external influences on a tire, other than tire loading, which affect tire deformation and thereby render load estimates based on measurement of such tire deformation inaccurate. For example, road roughness affects tire deformation, the greater the roughness of the road surface on which the tire is riding, the greater the potential for noise distortion in any static tire load estimate based on tire deformation. The subject invention proposes to minimize the effect of noise contribution in the form of road roughness on tire load estimation through the implementation of an adaptive filter which takes into account road surface roughness in the load estimation procedure. 
     The use of an algorithm is proposed that utilizes a tire mounted sensor, preferably a piezo-sensor, to estimate both tire load and road roughness. The algorithm adapts to the effect of road roughness variation for the purpose of load estimation, an important aspect in real-world driving conditions. The system and method disclosed herein uses a piezo-energy harvester signal for both tire load and road roughness estimation. The aforementioned objective of minimizing “noise” effect on load estimation is achieved by using an adaptive Kalman filter as will be explained. The information of the global load and of the load distribution can subsequently be profitably used by advanced brake control systems like the electronic brake distribution (EBD) system to optimize the system performance and reduce vehicle stopping distance. In the case of a commercial vehicle application, the weight estimated on each wheel can be averaged to produce an estimate of the vehicle weight. The vehicle weight may then be broadcast to a central location, hence eliminating the need for weigh stations. 
     The algorithm used in the subject system uses the piezo-harvester signal for both load and road roughness estimation rather than relying on either an accelerometer or a strain sensor. The algorithm disclosed herein takes into account road roughness during load estimation and, as such, more closely reflects real-world driving conditions. And, since the Kalman filter based approach of the subject algorithm is a recursive procedure, there is no need for historical information to be stored, unlike a moving average method of analysis. 
     A conventional Kalman filter is relatively sensitive to the selection of dynamic model noise level. As such the conventional filter is vulnerable to inaccuracies due to road roughness variation. The subject approach, to the contrary, in using an adaptive Kalman filtering algorithm is more robust and adaptive to sudden changes in road roughness condition. 
     The subject load estimation algorithm is diagrammed in  FIG. 25 . A shown therein, the tire  12  is equipped with a tire attached sensor module  14 , generally including temperature and pressure measuring sensors (TPMS) plus a piezo-sensor for generating a signal indicative of tire deformation within a rolling tire footprint. The module  14  is attached to the inner liner of the tire within the tire crown region by suitable means such as an adhesive. From the module  14 , a raw energy harvester signal is produced that is indicative of tire deformation within a rolling tire footprint. The tire deformation is proportional to the load supported by the tire. The raw signal is used in a footprint length estimation  54  procedure of the type disclosed by co-pending U.S. application Ser. No. 13/534,043 incorporated herein. 
     The raw signal from the piezo-sensor in module  14  is processed at footprint length estimation  54  to yield a raw footprint length. Because the raw footprint length estimation is vulnerable to error from road roughness, the raw footprint length is further filtered by an Adaptive Kalman Filter  56 . The raw signal from piezo-sensor of module  14 , in addition to being used in an initial raw footprint length estimation  54 , is also used in a roughness estimation algorithm  52  shown. The Roughness Estimation Algorithm  52  operates on a Surface Classification System as will be explained. The Adaptive Kalman Filter  56  uses Filter parameters which are tuned as a function of the road surface condition by Roughnesss Estimation Algorithm  52 . Consequently, a Filtered Footprint Length is obtained from the Adaptive Kalman Filter. The Filtered Footprint Length more accurately estimates the tire footprint length after compensating for road roughness. 
     A tire-specific look-up table  58  is empirically created which provides tire loading based on inputs of Footprint Length, Tire Identification, and Tire Inflation Pressure. The tire pressure is obtained from the TPMS module  14  along with Tire Identification. Combined with the Filtered Footprint Length from Adaptive Kalman Filter  56 , the loading for a particular tire at measured inflation pressure and footprint length may be obtained. 
     Referring to  FIG. 3 , a raw signal waveform is shown. The waveform from one tire rotation is indicated. The waveform shown is experimentally derived from a tire at 2.1 bar; and travelling at 60 kph. The graph from  FIG. 3  shows signal amplitude [V] vs. Sample Number. In  FIG. 4 , a raw signal from a tire at 2.9, 60 kph is shown graphically under three road conditions: smooth surface; rough surface; and very rough surface. It will be appreciated that the signal amplitude (from which a tire load will be estimated) fluctuates significantly from surface to surface condition. The present invention acts to characterize the roughness level of a surface in order to compensate for the effect that surface roughness “noise” presents in a raw tire deformation signal. 
     A signal comparison algorithm may be constructed, as seen from  FIG. 5 , using three distinct methods of signal comparison: a maximum circular cross-correlation coefficient (See  FIG. 6 ); a wavelet based feature extraction (See  FIG. 16 ); and an autocorrelation coefficient distribution (See  FIGS. 17 and 18 ). The three methodologies extract different features from the signal comparison based upon the methodology employed. In  FIGS. 6A through 6C , the maximum circular cross-correlation coefficient methodology is demonstrated in graphical form.  FIG. 6A  shows a Case 1 test in which a smooth asphalt reference surface is grafted for one tire rotation at 60 kph.  FIG. 6B  shows a graph for Case 1 for a test surface, also configured as smooth asphalt. In this smooth vs. smooth test, a Cross-correlation Coefficient is examined as a basis for classification. The Cross-correlation Coefficient R is defined as a measure of similarity of two waveforms as a function of a time-lag applied to one of them. For the smooth vs. smooth ( FIGS. 6A and 6B ) Case 1 test, an R max  of approximately 0.95 was empirically determined and is shown graphically in  FIG. 6C . Stated descriptively, a tire undergoing deformation on a smooth surface would be expected to experience a radius deviation from the smooth surface no greater than 0.05. 
       FIGS. 7A and 7B  show graphs for a Case 2 test in which a reference smooth surface is compared against a test surface of rough asphalt. A comparison of the two graphs results in an maximum Circular Cross-Correlation Coefficient R max  for the Case 2 test of approximately 0.6, indicated graphically in  FIG. 7C . Thus, a rough asphalt surface will cause a circular tire deformation greater than that caused by a smooth,  FIGS. 6A ,  6 B, surface. 
     In  FIGS. 8A and 8B , a Case 3 test parameter is used comparing a smooth reference surface graph of  FIG. 8A  with a very rough asphalt test surface shown graphically in  FIG. 8B . The resultant maximum Circular Cross-correlation Coefficient R max  for Case 3 is determined as approximately 0.3, shown graphically in  FIG. 8C . 
       FIGS. 9A ,  9 B,  9 C (Case 1),  FIGS. 10A ,  10 B,  10 C (Case 2), and  FIGS. 11A ,  11 B,  11 C (Case 3) are graphs similar to the test graphs of  FIGS. 6A  through C,  7 A through  7 C, and  8 A through  8 C but conducted at a high speed of 90 kph. The Cross-correlation Coefficient graphs of  FIGS. 9C ,  10 C and  11 C generally correspond with the slow speed graphs of  FIGS. 6C ,  7 C and  8 C, demonstrating that the R max  values under each road surface condition is unchanged over a range of vehicle speeds. A comparative summary of the speed dependence study is graphed in  FIGS. 12A ,  12 B (smooth vs. smooth);  FIGS. 13A ,  13 B (smooth vs. rough); and  FIGS. 14A ,  14 B (smooth vs. very rough). The comparative R max  values at the two speeds validates the use of R max  as a basis for categorizing road surfaces for the purpose of filtering load estimation measurements.  FIG. 15  shows the R max  (Maximum Circular Cross-correlation Coefficient) ranges for each of the three road surface levels, and represents the classification rule(s) that are followed in the algorithm. 
       FIGS. 16A and 16B  show a second approach to constructing a filter that will adapt a load estimation to road surface roughness conditions. A Wavelet Based Feature Extraction Sub-Band Wavelet Entropy methodology is demonstrated graphically for smooth and rough road conditions. 
     The energy distribution of wavelet decompositions energy is shown in  FIG. 16B . Entropy represents the degree of disorder that the filter variable possesses. It will be seen from  FIG. 16B  that a difference in the sub-band energy distribution exists. A Sub-band wavelet entropy may be defined by the mathematical formulation above in terms of the relative energy of the wavelet coefficients. The relative energy of the wavelet coefficients may then be used in an adaptive filtering of the load estimation in order to compensate for the surface conditions. 
       FIGS. 17A ,  17 B,  18 A and  18 B illustrate a third alternative feature for filtering estimated load, the use of Autocorrelation Coefficient differentiation. In  FIG. 17A ,  17 B, the distribution of a first selection index 1 and its corresponding statistical graph, respectively, are shown. In  FIGS. 18A and 18B , a selection index of 2 is graphed, showing the distribution and statistical graph, respectively. The distribution of the autocorrelation function indicates the surface characteristics of the road surface on which the tire is moving. By discerning the distribution function, an assessment of road roughness may be made. As used herein, “autocorrelation correlation” may be defined as the correlation of a time series with its own past and future values. 
     With reference to  FIG. 19 , a summary of the three approaches of feature extraction and their respective alternative use in achieving a surface differentiating classification  18  are shown. The raw signal  20  from the tire piezo-sensor may be analyzed using the Maximum cross-correlation coefficient  24  methodology that employs a Reference Signal in processor memory  22 . The use of the Maximum cross-correlation coefficient as a surface differentiating feature may be used in a Surface Classifier  30  (ANN) to determine relative surface type (smooth, intermediate, or rough). 
     Alternatively, the Sub-band wavelet entropy differentiation based on entropy decomposition  26  may be used as a feature methodology. Decomposition of wavelet entropy may used to determine through the use of the Classifier  30  which of the three surface classifications are being encountered by a tire. As a further alternative, the Autocorrelation correlation 28 may be used as a third alternative feature approach. The distribution of the autocorrelation correlation function is evaluated and from the distribution data, a conclusion may be reached through the Surface Classifier  30  as to which of the three surface types are being encountered by the tire during deformation detection. 
     From  FIGS. 20A and 20B  load variation under constant speed, straight-line test results, the rationale for interest in road roughness level will be appreciated.  FIG. 20A  shows a load variation on a smooth surface, both observed value (Noisy Sensor Estimate) and Actual Mean Load. It will be seen that a 15 to 20 percent variation in load estimates can occur even under smooth surface, straight-line driving conditions. From  FIG. 20B , it will be seen that a rough surface may cause an even greater variance. A 30 to 40 percent variation is reflected in the rough surface test results of  FIG. 20B . 
     From the above, it is useful to consider road roughness in any estimation of tire load. A Kalman Filter is thus employed. A Kalman Filter, given a noisy discrete-time LTI (define) process and a noisy measurement, can determine an optimal estimate of the state that minimizes the MSE (define) quadratic cost function as set forth below. 
             J   =     E   ⁡     [         (         x   ^     k     -     x   k       )     T     ⁢     (         x   ^     k     -     x   k       )       ]             
where ({circumflex over (x)} k −x k ) is the state estimation error vector. Here the state of a discrete time-controlled process is governed by the linear stochastic difference equation:
 
               x   k     =         Ax     k   -   1       +       BU     k   -   1       ⁢           ⁢   and   ⁢           ⁢     y   k         =       Cx   k     +     DU   k               
The matrix Z relates to the state of the previous time step to the state at the current step, in the absence of either a driving function or process noise. The matrix B relates to the operational control input to the state. The matrix C in the measurement equation relates the state to the measurement. The matrix D in the measurement equation relates the control input to the measurement. The real dynamic systems are subjected to a variety of “noise” signals that corrupt the response. The process noise (w k-1 ) corrupts the states and the sensor noise ( K ) corrupts the output. The modified governing equations incorporating the effects of these exogenous inputs can be written as:
 
     
       
         
           
             
               x 
               k 
             
             = 
             
               
                 
                   Ax 
                   
                     k 
                     - 
                     1 
                   
                 
                 + 
                 
                   BU 
                   
                     k 
                     - 
                     1 
                   
                 
                 + 
                 
                   
                     Fw 
                     
                       k 
                       - 
                       1 
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   and 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     y 
                     k 
                   
                 
               
               = 
               
                 
                   Cx 
                   k 
                 
                 + 
                 
                   DU 
                   k 
                 
                 + 
                 
                   κ 
                   . 
                 
               
             
           
         
       
     
     The Kalman Filter operates under certain system assumptions. First, the state dynamics are linear, that is the current state is a linear function of the previous state. Secondly, the noise in the state dynamics is normally distributed. Thirdly, the observation process is linear, that is the observations are a linear function of the state. Finally, the assumption is made that the observation noise is normally distributed. 
     Although a prediction of the process noise ore the measurement noise values is problematic, some knowledge of their statistics is possible. Below are statements setting forth Process Noise and Measurement Noise. Since the mean load does not change under steady state driving conditions sample to sample, the state equation is: 
                   x   k     =       x     k   -   1       +     w     k   -   1           ;           ⁢       i   .   e   .           ⁢   A     =   1       ,     B   =   0     ,     F   =   1           
And the output equation is:
 
     
       
         
           
             
               
                 
                   y 
                   k 
                 
                 = 
                 
                   
                     x 
                     k 
                   
                   + 
                   
                     - 
                     κ 
                   
                 
               
               ; 
               
                   
               
               ⁢ 
               
                 
                   i 
                   . 
                   e 
                   . 
                   
                       
                   
                   ⁢ 
                   C 
                 
                 = 
                 1 
               
             
             , 
             
               D 
               = 
               0 
             
           
         
       
     
     The term θ k  represents measurement noise accounts for load variations. It is this parameter which can be made adaptive with knowledge about the roughness level. Following are a summary of the five Kalman Filter equations categorized as Prediction and Correction and the equation reduction for the purpose of exemplary explanation. In  FIG. 21 , a normal distribution curve is depicted in which the Mean=0 and a Standard deviation=X percent of average tire load, depending on the surface roughness level. Thus, x is approximately equal to 15 percent for a smooth surface; 25 percent for a rough surface and 35 percent for a very rough surface. Estimation results experimentally obtained are represented in  FIG. 22A  for a Case 1 Smooth Surface road condition. The graph of  FIG. 22A  shows the Load Estimation Algorithm Performance by graphing Tire Load over time comparing: Observed Value (Noisy Sensor Estimate), Moving Average Filter Estimates, Kalman Filter Estimates and Actual Mean Load. In  FIG. 22B , Estimation Error between the Moving Average Filter Performance and the Kalman Filter Performance is shown graphically. The Kalman Filter provided a lower estimation error and an estimation within a 5 percent accuracy band for a static axle load. 
     The Load Estimation Algorithm Performance on a Case 2 Rough Surface is shown graphically in  FIG. 23A  which compares Observed Value (Noisy Sensor Estimate), Moving Average Filter Estimates, Kalman Filter Estimates and Actual Mean Load.  FIG. 23B  shows the Estimation Error between the Moving Average Filter Performance and the Kalman Filter for the Case 2 Rough Surface. The Kalman Filter provided a lower estimation error than the Moving Average Filter and achieved an estimation within a 5 percent accuracy band for a static axle load on a rough surface. 
     In  FIG. 24A  the Estimation Error for a conventional Kalman Filter using constant noise variance is shown, compared against the Moving Average Filter Performance.  FIG. 24B  shows a graph depicting an Adaptive Kalman Filter performance using a noise variance that changes as a function of the road roughness level. As seen in  FIG. 24B , the Adaptive Kalman Filter performance is superior to that of a Moving Average Filter performance. By comparing Adaptive Kalman Filter performance of  FIG. 24B  to Conventional Kalman Filter performance of  FIG. 24A , it will be appreciated that the Adaptive Kalman Filter performance results in a lower percentage error than the Conventional Kalman Filter. Accordingly, the graphs support the conclusion that using an Adaptive Kalman Filter that changes a noise variance to reflect a road roughness level achieves a superior predictive performance to a filter which uses a constant noise level. 
     Referring again to  FIG. 25 , the algorithm for predicting tire load utilizes one of the feature based approaches explained previously in application of the Surface Classification block  52 . The Filter Parameters are thus tuned as a function of the road surface condition. So tuned, the Adaptive Kalman Filter will apply the adaptive filter parameters to the Raw Footprint Length Estimation  54  to create a Filtered Footprint Length. The Filtered Footprint Length can thereafter be used with tire identification and inflation pressure to derive from a Look-up table  58  a load estimation. As explained, the Adaptive Kalman Filter  54  is used because, for a conventional Kalman Filter application, the model statistic noise levels are given before the filtering process and will remain unchanged during the whole recursive process. Commonly, this a priori statistical information is determined by test analysis and certain knowledge about the observation type beforehand. If such a priori information is inadequate to represent the real statistic noise levels, conventional Kalman estimation is not optimal and may cause unreliable results. The subject system and method overcomes such a possibility through the use of adaptive filtering application. 
     From the foregoing, it will be appreciated that the subject algorithm of  FIG. 25  uses a piezo-energy harvester signal for both load and road roughness estimation. Real world driving conditions are addressed through the application of road roughness during load estimation. Moreover, since the Kalman filter based approach is a recursive procedure, historical information does not need to be stored, a decided advantage over other methods such a moving average method. Additionally, a convention Kalman filter is relatively more sensitive to the selection of the dynamic model noise level which remains a constant. In the subject approach an adaptive Kalman filtering algorithm is used, resulting in a more robust load estimate which accounts for sudden changes to road roughness condition. 
       FIGS. 26 ,  27  and  28  show an extension of the above approach to the encompass a road profile height estimation scheme in addition to an estimation of instantaneous tire load.  FIGS. 26 through 28  relate to a road profile height estimation based on a multi-sensor fusion approach via Kalman Filter techniques and its application in an instantaneous tire load estimation algorithm. Road profile is seen as an essential input that affects vehicle dynamics data. An accurate estimate of road profile is thus useful in vehicle dynamics and control system design such as active and semi-active suspension design. The subject adaptation of  FIGS. 26  through  28  provide for a road profile estimation that may be used for the purpose of vehicle control systems as well as in the estimation of a dynamic tire loading. 
     With regard to the road profile, a data flow diagram is set forth in  FIG. 26  and uses a real-time estimation methodology based on use of a Kalman Filter. The method uses measurements from available sensors; accelerometers and suspension deflection sensors. Referring to  FIG. 26 , the algorithm  32  uses a quarter-car vehicle model  34 . In the model  34 : 
     m s =sprung mass 
     m u =unsprung mass 
     K suspension =suspension stiffness 
     C suspension =suspension dampening coefficient 
     K tire =tire stiffness 
     C tire =tire dampening coefficient 
     Z s =sprung mass vertical displacement 
     Z u =unsprung mass vertical displacement 
     Z r =road profile height 
     The standard notational convention for describing a State-space representations is given by: 
     x′=A x+B u}state equations 
     y=C x+D u} output equations 
     where: 
     x(t) State vector 
     x′(t) Derivative of state vector 
     A State matrix 
     B Input matrix 
     u(t) Input vector 
     y(t) output vector 
     C output matrix 
     D Direct transmission matrix 
     The equivalent state space representation of the “quarter car model” used in the Kalman filter has been specified below as: 
     
       
         
           
             A 
             = 
             
               [ 
               
                 
                   
                     
                       
                         0 
                       
                       
                         1 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         0 
                       
                       
                         
                           0 
                           ; 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   - 
                   
                     
                       K 
                       suspension 
                     
                     / 
                     
                       m 
                       s 
                     
                   
                   - 
                   
                     
                       
                         C 
                         suspension 
                       
                       / 
                       
                         m 
                         s 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         K 
                         suspension 
                       
                       / 
                       
                         m 
                         s 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         suspension 
                       
                       / 
                       
                         m 
                         s 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                   
                 
                 ; 
               
             
           
         
       
     
     
       
         
           
             
               
                   
               
               ⁢ 
               
                 
                   
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                   
                   ; 
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                   
                     
                       
                         K 
                         suspension 
                       
                       / 
                       
                         m 
                         u 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         suspension 
                       
                       / 
                       
                         m 
                         u 
                       
                     
                   
                   - 
                   
                     ( 
                     
                       
                         ( 
                         
                           
                             K 
                             suspension 
                           
                           / 
                           
                             m 
                             u 
                           
                         
                         ) 
                       
                       + 
                       
                         ( 
                         
                           
                             K 
                             tire 
                           
                           / 
                           
                             m 
                             u 
                           
                         
                         ) 
                       
                     
                     ) 
                   
                   - 
                   
                     
                       
                         ( 
                         
                           
                             C 
                             suspension 
                           
                           + 
                           
                             C 
                             tire 
                           
                         
                         ) 
                       
                       / 
                       
                         m 
                         u 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         K 
                         tire 
                       
                       / 
                       
                         m 
                         u 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         tire 
                       
                       / 
                       
                         m 
                         u 
                       
                     
                   
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ; 
                 
                 ⁢ 
                 
                   
 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   0 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                 
               
               ] 
             
             ; 
             
               B 
               = 
               
                 [ 
                 
                   0 
                   ; 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ; 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ; 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ; 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                   ; 
                   
                     
 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   0 
                 
                 ] 
               
             
             ; 
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 C 
                 = 
                 
                   [ 
                   
                     
                       
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                       ⁢ 
                       
                           
                       
                       - 
                       
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                     ; 
                     
                       
 
                     
                     ⁢ 
                     
                       
                         
                           - 
                           
                             K 
                             suspension 
                           
                         
                         / 
                         
                           m 
                           s 
                         
                       
                       - 
                       
                         
                           
                             C 
                             suspension 
                           
                           / 
                           
                             m 
                             s 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             K 
                             suspension 
                           
                           / 
                           
                             m 
                             s 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             C 
                             suspension 
                           
                           / 
                           
                             m 
                             s 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         0 
                       
                     
                   
                   ] 
                 
               
               ; 
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               
                 D 
                 = 
                 
                   [ 
                   
                     0 
                     ; 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ; 
                     
                       
 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                   
                   ] 
                 
               
               ; 
             
           
         
       
     
     An accelerometer  38  and suspension deflection sensor  40  of commercially available type are affixed to the vehicle and respectively measure the chassis acceleration (Z s ″) and the suspension deflection (Z s −Z u ). Estimated states of the Kalman Linear filter are Z s , Z s ′, Z u , Z u ′, Z r  and Z r ′. The Kalman Filter  42  generates an estimate of the Road Profile Height (Z r ) and that further is used to estimate the tire load variation caused due to road undulations. The load variation is given by the expression F z , load variation=[K tire *(Z u −Z r )+C tire *(Z u ′−Z r ′)]. 
     The Kalman filtering approach allows the achievement of a successful estimation by overcoming the vibrational disturbances that heavily affect the accelerometers. The quarter-vehicle modeling enables the use of a real time estimation methodology. A secondary use of the road profile height estimation is in the calculation of a load (instantaneous) on the tire. An axle load variation estimator  44  receives the road profile height estimation from the Kalman Filter  42  and directs an axle load variation estimation to a tire load estimator  48 . The footprint length of the tire  12  is obtained from implementation of the methodology described previously. A static load estimator  46  receives a piezo-sensor signal from the tire  12  and estimates a static load F z  on the tire. The static load is used by the tire load estimator  48  along with the load variation estimation. From a fusion of the static load estimate and the load variation estimate, the tire load estimator  48  calculates F z , the instantaneous load on the tire. 
     F z , instantaneous=F z  static−F z , load variation 
     
       
         
           
             
               F 
               z 
             
             , 
             
               instantaneous 
               = 
               
                 F 
                 z 
               
             
             , 
             
               static 
               - 
               
                 [ 
                 
                   
                     
                       K 
                       tire 
                     
                     * 
                     
                       ( 
                       
                         
                           Z 
                           u 
                         
                         - 
                         
                           Z 
                           Γ 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       C 
                       tire 
                     
                     * 
                     
                       ( 
                       
                         
                           Z 
                           u 
                           * 
                         
                         - 
                         
                           Z 
                           Γ 
                           * 
                         
                       
                       ) 
                     
                   
                 
                 ] 
               
             
           
         
       
     
       FIG. 27  shows a graph (road profile elevation over time) reflecting experimental results comparing actual road estimation (via a profilometer) to estimated road profile estimation using the system of  FIG. 26 . A close correlation coefficient (R)=0.966 verifies the validity of the subject methodology and system in generating a quantified road profile estimate. In  FIG. 28 , a graph (Load over time) reflecting experimental results between actual load (8 Degrees of Freedom full vehicle suspension dynamic model) and estimated load (Kalman filter) is presented. The graph indicates a correlation coefficient (R)=67.979, whereby validating the subject system and approach of  FIG. 26 . 
     The tire normal load is assumed to be directly related to the contact forces between the tire and the load. The measure of tire load can therefore be useful to implement control strategies oriented to the maximization of the road-holding performance of the vehicle. Moreover, the information of global load and the load distribution between all tires on a vehicle may be used by advanced brake control systems like the electronic brake distribution (EBD) system to optimize system performance and reduce vehicle stopping distance. In the case of a commercial vehicle, the weight estimated on each wheel could be averaged to produce an estimate of the vehicle weight which can then be broadcast to a central location, whereby eliminating the need for weigh stations. The road roughness methodology of  FIGS. 1 through 25  as discussed above and the road profile discussion pertaining to  FIGS. 26 through 28  are related insomuch as road roughness may be considered as micro-road profile changes and road profile change may be considered as a macro-road roughness variation. Use of both or either macro (road profile) and micro (road roughness) variable estimations in an adaptive Kalman Filter analysis will result in a more robust and accurate estimation and thus more closely reflect real-driving conditions. 
     Variations in the present invention are possible in light of the description of it provided herein. While certain representative embodiments and details have been shown for the purpose of illustrating the subject invention, it will be apparent to those skilled in this art that various changes and modifications can be made therein without departing from the scope of the subject invention. It is, therefore, to be understood that changes can be made in the particular embodiments described which will be within the full intended scope of the invention as defined by the following appended claims.