Patent Publication Number: US-2023136325-A1

Title: Estimating vehicle velocity

Description:
BACKGROUND 
     A vehicle may include various sensors, which may be utilized for many different purposes. For example, sensors may be used to detect information about a surrounding environment (e.g., other vehicles, roadway conditions, pedestrians, street signs, etc.), as well as to monitor vehicle operations (e.g., braking, accelerating, steering, system(s) status, vehicle position, etc.). In some instances, data derived from sensor data may be consumed by downstream operations. For example, vehicle velocity may be used for localization processes. As such, accuracy and reliability of the determinates derived from sensor data is important to allow the vehicle to safely and reliably navigate through an environment. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The detailed description is described with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. The use of the same reference numbers in different figures indicates similar or identical components or features. 
         FIG.  1 A  illustrates a perspective view of an example vehicle with two wheels turned at an angle. 
         FIG.  1 B  illustrates a plan view of the vehicle of  FIG.  1 A  showing an estimated wheel angle and a measured command angle for each of the two wheels, as described herein. 
         FIG.  2    illustrates a schematic of a vehicle traversing a turn with two wheels rotated at respective angles, the schematic including variables that may be used to describe the turn or a component of the vehicle, as described herein. 
         FIG.  3    illustrates a schematic of a vehicle traversing a turn with four wheels rotated at respective angles, the schematic including variables that may be used to describe the turn or a component of the vehicle, as described herein. 
         FIG.  4    includes a flow diagram illustrating an example process for determining estimated steering data, as described herein. 
         FIG.  5    is a block diagram illustrating an example system for performing techniques as described herein. 
     
    
    
     DETAILED DESCRIPTION 
     This application relates to techniques for using a set of variables to estimate a vehicle velocity of a vehicle. As discussed above, accuracy and reliability of determinates derived from sensor data are important to allow a vehicle to safely and reliably navigate through an environment. As used in this disclosure, the vehicle velocity is the velocity of the body of the vehicle along the longitudinal orientation or axis of the vehicle. In some examples, the estimated vehicle velocity may be estimated using an optimization, such as a least square fit or regression of one or more variables. 
     In examples of this disclosure, a yaw rate (e.g., from an inertial measurement unit, gyroscope, etc.), linear speeds at or near the wheels (e.g., from an encoder, tracked features from image sensors, etc.), wheel steering angles (e.g., a direction in which the wheel is pointed relative the longitudinal orientation or axis of the vehicle) and/or vehicle dimensions (e.g., distance between the wheels and a turn-center reference line), can be used to estimate the vehicle velocity. 
     In some examples, a least square regression may be performed to fit the sensor measurements (e.g., wheel speeds, steering angles and yaw rate) to a vehicle model. In some examples, the least square regression may include estimating a location of the center of rotation of the vehicle. A vehicle&#39;s velocity may be transformed to a wheel to generate respective estimated wheel velocities for one or more, including all, wheels. Errors may be computed between the magnitude of the estimated wheel velocities and the measured wheel speeds at the wheels and between the orientation of the estimated wheel velocities and the measured steering angles of the wheels along with associated Jacobians. Loss functions may also be applied. An iterative reweighted Gauss-Newton function, or other optimization technique, may then be solved for the vehicle velocity. 
     Among other things, estimated vehicle velocities may provide redundancy (e.g., when determined in parallel with sensor based vehicle velocities) and validation and may be less susceptible to inaccuracies from loss of tire traction (e.g., in the case of wheel spins, etc.), model inaccuracies, and the like. In addition, estimated vehicle velocities may be used in various manners, such as for estimating vehicle pose or position. 
     As mentioned above, vehicle velocity estimation may compensate for inaccuracies or errors in sensor data. For example, a vehicle may include wheel speed encoders that may report wheel speed based on rotations of the wheel. The rotation rate reported may be multiplied by the tire radius to determine the linear speed at the wheel. Such sensors may be inaccurate at low speeds due to a lack of rotations of the wheel. In some examples, the wheel speed encoder data may be supplemented by another sensor such as sensor that reports a rotation speed of a gear box. However, such gear box data may be low pass filtered and/or delayed. In addition to sensor inaccuracies, the wheel may lose traction against pavement, which can cause an inconsistency between the wheel speed reported by the wheel speed sensors and the speed the wheel is moving relative to the ground. 
     Additionally, a vehicle may include a steering motor that generates a rotational output, which is transferred to a wheel and/or to linear travel of a steering rack. A steering sensor may measure the rotation of the steering motor, and the rotation may be used to determine (e.g., from a correlation between rotation and linear rack travel) steering rack travel. In other examples, steering rack travel may be directly measured or may be derived from other sensor data associated with the steering system or the suspension assembly. This steering data (e.g., motor rotation data, rack travel distance, etc.) may in turn be used to estimate an angle of a wheel. In some instances, steering components (e.g., belts, racks, pinions, gear teeth, etc.) may experience slippage (e.g., mechanical slip) that can affect the accuracy of the steering angle. 
     In examples of this disclosure, by estimating a vehicle velocity, the determination may avoid or mitigate inaccuracies that can arise from relying solely on data from the sensor systems. The estimated vehicle velocity may be used in various respects to control vehicle operations. 
     For example, the estimated vehicle velocity may be compared to a sensor data to detect and/or flag conditions, such as wheel slip. In additional examples, the estimated vehicle velocity may be combined with a sensed velocity (e.g., averaged) for use by downstream components (e.g., localization). In addition, the estimated vehicle velocity may be directly used (e.g., independent of the sensed velocity) by downstream processes to determine vehicle position or other vehicle states, which may be used for localization or other map-related operations. 
     The techniques described herein can be implemented in a number of ways to estimate vehicle velocity. Examples are provided below with reference to  FIGS.  1 - 5   . Examples are discussed in the context of autonomous vehicles; however, the methods, apparatuses, and components described herein can be applied to a variety of components (e.g., a sensor component or a robotic platform), and are not limited to autonomous vehicles. In one example, the techniques described herein may be utilized in driver-controlled vehicles. Furthermore, the techniques described herein can be used with real data (e.g., captured using sensor(s)), simulated data (e.g., generated by a simulator), or any combination of the two. 
       FIG.  1 A  and  FIG.  1 B  illustrate different views of an example vehicle  102  with components for estimating a velocity of the vehicle  102 .  FIG.  1 A  depicts a perspective view of the vehicle  102 , which is ghosted in broken lines to help illustrate internally positioned components; and  FIG.  1 B  presents a plan view of the vehicle  102 . Among other things, the vehicle  102  includes a front end  104 , a rear end  106 , a left side  108 , and a right side  110 . In addition, for reference in this disclosure, the vehicle  102  includes a longitudinal axis  112  extending along a front-to-back orientation (e.g., longitudinal orientation) and a lateral axis  114  extending along a side-to-side orientation (e.g., lateral orientation) and substantially perpendicular to the longitudinal axis  112 . Furthermore, a vertical axis  116  may extend top-to-bottom and perpendicular to the longitudinal axis  112  and to the lateral axis  114 .  FIG.  1 A  also depicts a yaw action  118 , which indicates the vehicle  102  may rotate relative to the vertical axis  116 , such as when the vehicle  102  executes a turn. For example, the vehicle  102  includes four wheels  120   a - 120   d,  each oriented in a direction indicated by a respective directional arrow  122   a - 122   d.  In  FIGS.  1 A and  1 B , the front wheels  120   a  and  120   b  are depicted rotated at a steering angle towards the left in a direction indicated by a respective directional arrow  122   a  and  122   b.  The placement of the yaw action  118  in  FIG.  1 A  illustrates an example, and a yaw action, yaw event, or yaw rotation may occur at various locations or positions of the vehicle  102 . 
     In one example, the vehicle  102  is a bidirectional vehicle having a first drive module positioned in the front end  104  and a second drive module positioned in the rear end  106 . As used herein, a bidirectional vehicle is one that is configured to switch between traveling in a first direction of the vehicle and a second, opposite, direction of the vehicle. In other words, there is no fixed “front” or “rear” of the vehicle  102 . Rather, whichever longitudinal end of the vehicle  102  is leading at the time becomes the “front” and the trailing longitudinal end becomes the “rear.” In other examples, the techniques described herein may be applied to vehicles other than bidirectional vehicles. Also, whether or not the vehicle is bidirectional, the first drive and second drive modules may be different from one another. For example, one drive module may have a subset of the features of the other drive module. In one such example, the first drive module may include a first, comprehensive set of vehicle systems (e.g., drive motor, battery, steering system, braking system, suspension system, HVAC, sensors, lights, body panels, facia, etc.) while the second drive module includes a limited subset of vehicle systems (e.g., suspension system, braking system, sensors, lights, and facia). In various instances, the wheels positioned in the front end  104  are steerable, and the wheels positioned in the rear end  106  are also steerable, such that the vehicle  102  includes four-wheel steering (e.g., including each set of wheels having the respective steering components). In other examples, the drive modules may have one or more distinct or mutually exclusive vehicle systems (e.g., one drive module has an HVAC system and the other drive module has a drive motor). As another non-limiting example of such, one module may have a first HVAC system while the other drive module has a second HVAC system that is different from the first HVAC system. 
     In addition, the vehicle  102  may include various sensors for detecting one or more different conditions. For example, the vehicle  102  may include sensors  124   a - 124   d,  any number of which may include a perception sensor for capturing data of an environment around the vehicle  102  (e.g., lidar, camera, time-of-flight, sonar, radar, etc.). These sensors  124   a - 124   d  may be used for various operations, such as object detection, route planning, localization, etc. In at least one example, the vehicle  102  may also include a yaw rate sensor  125 , such as an inertial measurement unit (IMU), gyroscope, or other sensor for measuring a yaw rate of the vehicle  102 . The position of the yaw rate sensor  125  is an example, and the yaw rate sensor  125  may include various other positions and/or orientations about the vehicle  102  and, in some examples, there may be multiple such sensors at those varying positions and/or orientations. In a further example, the vehicle  102  may include one or more sensors  126   a - 126   d  (e.g., encoders) for measuring a wheel speed of a respective wheel (e.g., determining a linear speed of the vehicle  102  at a wheel). In  FIG.  1 A , the sensors  126   a  and  126   c  are depicted in broken lines to convey that, in some examples, the sensors  126   a  and  126   c  may be obscured behind a respective wheel (at least from the perspective provided in  FIG.  1 A ). Additionally, or alternatively, an imaging sensor displaced proximate a wheel may be used to estimate linear velocity proximate the wheel based on, for example, tracking features detected on a road surface. These are just some examples of sensors, and the vehicle may include other sensors, such as those described with respect to the system  500 . In addition, the placement of the sensors relative to the vehicle  102  in  FIG.  1 A  is an example, and in other examples, the sensors (e.g.,  124   a - 124   d  and  125 ) may be arranged at other positions on the vehicle  102 . 
     In additional examples, the vehicle  102  may include various steering components, such as a steering motor  128  and a steering rack  130  that operate to affect a steering angle of wheels  120   a - 120   d.  For example, the steering motor  128  may generate a rotational output based on steering input (e.g., direction and amount) from a manually operated steering wheel (not shown), from a computing device (e.g., planning  536  in  FIG.  5   ), or from a combination thereof. The rotational output may be transferred to the steering rack  130  to create linear steering rack travel in one direction or another. The steering rack  130  may interface with a wheel at a knuckle of the suspension assembly or some other coupling that transfers the linear rack travel to the wheel to cause the wheel to pivot or rotate about an axis. In examples, the vehicle  102  may include one or more steering sensors  132  for determining steering data associated with the steering angle of the wheels  120   a - 120   d.  For example, referring to  FIG.  1 B , the orientations of the front wheels  120   a  and  120   b  are illustrated with the directional arrows  122   a  and  122   b  with the wheel angles  136   a  and  136   b  (e.g.,  136   a/ Θ and  136   b/ Θ′ of wheels  120   a  and  120   b,  respectively. 
     In some examples, the steering sensor  132  may determine an amount of steering-motor rotation, an amount of steering rack travel, or other data, which may be related to the steering angle of each wheel. In some examples, a steering angle may be estimated based on non-steering variables (e.g., due to a difference between intended or commanded steering angles and the actual steering angles of the wheels). In at least one example, the steering angle may be estimated as described in U.S. patent application Ser. No. 17/364,161 (titled “Estimating Angle Of A Vehicle Wheel Based On Non-Steering Variables” and filed Jun. 30, 2021), which is incorporated herein by reference in its entirety and for all purposes. In  FIGS.  1 A and  1 B , a steering assembly is depicted in the front end  104  and rear end  106  of the vehicle. In other aspects, only one end of the vehicle may include a steering assembly while the other end may be fixed. Alternative aspects of the disclosure may include a different steering arrangement. For example, each suspension assembly may include a respective steering motor that, without a shared or common steering rack, affects the steering angle of a wheel (e.g., by rotating about a steering axis). As such, the steering motor rotation may affect the wheel steering angle without relying on the shared or common steering rack. 
       FIG.  2    schematically depicts vehicle  102  executing a curved trajectory  200  (or turn maneuver), which is illustrated by the dashed line circles in  FIG.  2   . In  FIG.  2   , the curved trajectory  200  includes a turn center  204  (or rotation center), and a turn-center reference line  140  (see also the turn-center reference line  140  in  FIG.  1 B ), which extends through the turn center  204  and normal to the longitudinal axis  112  of the vehicle  102 . In addition, based on the dimensions of the vehicle  102 , an offset distance  142  for the wheel  120   b  and an offset distance  251  for the wheel  120   a  ( FIGS.  1 B and  2   ) extends perpendicularly from the turn-center reference line  140  to the center of the wheel  120   b.  In general, the offset distances  142  and  251  extend from the wheel (e.g., a rotation axis of the wheel) to a position aligned with the turn center  204  and/or the turn-center reference line  140  (e.g., aligned along a plane or line extending through the turn center  204  and normal to the longitudinal orientation of the vehicle). 
     The turn center  204  and the turn-center reference line  140  may be established using various techniques. For example, if a vehicle is executing a turn using only front-wheel steering (while the rear wheel do not rotate about a steering axis), such as the vehicle  102  in  FIG.  2    in which the front left wheel  120   b  and the front right wheel  120   a  rotate about a steering axis, then the turn-center reference line  140  is co-axial with a rear axle of the vehicle, and the offset distance may be pre-determined based on vehicle dimensions. In other examples, the turn center  204  may be at an intersection of a radius (R′)  246  (e.g., of the curve or arc traversed by the front left wheel  120   b ) and a radius (R)  247  (e.g., of the curve or arc traversed by the front right wheel  120   a ). These radii (and the resulting turn center) may be estimated from various data, such as the steering angles of the wheels (e.g., wheel angles  136   a  and  136   b.    
     Furthermore, in some examples of this disclosure, a yaw rate (ω)  218  may be received from a yaw rate sensor (e.g., IMU, gyroscope, etc.) and a linear velocity at each wheel (e.g., linear velocity (V)  243  and linear velocity (V′)  244 ) may be derived from a variety of different sources. For example, in some instances, linear velocity at each wheel may be derived from data received from an encoder (or other sensor, such as radar). 
       FIG.  2    depicts additional variables with respect to each of the front wheels  120   a  and  120   b.  For example,  FIG.  2    depicts a wheel angle  136   a  (Θ) associated with the wheel  120   a,  as well as a central angle  249  (Θ CA ) between the turn-center reference line  140 , the turn center  204 , and a radius (R)  247  intersecting the center of the wheel  120   a.  In addition,  FIG.  2    depicts a wheel angle  136   b  (Θ′) associated with the wheel  120   b,  as well as a central angle  248  (Θ CA ′) between the turn-center reference line  140 , the turn center  204 , and a radius (R′)  246  intersecting the center of the wheel  120   a.  In examples, the wheel angle associated with a wheel is equal to the central angle associated with the wheel. 
     Referring to  FIG.  3   , another example is depicted including a schematic of a vehicle  302  executing a curved trajectory  300 , which is illustrated by the dashed line circles. In  FIG.  3   , the vehicle  302  includes four-wheel steering, such that the front wheels  320   a  and  320   b  and the back wheels  320   c  and  320   d  pivot or rotate about a respective steering axis to an angle when executing the curved trajectory. In examples of this disclosure, as between the vehicle  102  executing two-wheel steering and the vehicle  302  executing four-wheel steering, the respective turn-center reference lines may be different. For example, in  FIG.  3   , the curved trajectory  300  includes a turn center  304 , and a turn-center reference line  340 , which extends through the turn center  304  and normal to the longitudinal axis  312  of the vehicle  302 . As explained above, the turn center  304  and the turn center-reference line  340  may be determined in various manners, such as based on the steering angles of the wheels (e.g., at an intersection of a radius of two or more of the wheels). For example, a radius  346  of the curve or arc traversed by each wheel extends from the turn center  304  to the respective wheel. In some examples, the turn center  304  may be determined as the intersection of the radius of wheels  320   b  and  320   c  (e.g., radius  346   b  and radius  346   c ). In addition, where the left-side wheels (e.g., front-left wheel and back-left wheel) include similar angles (except in different directions) and the right-side wheels (e.g., front-right wheel and back-right wheel) includes similar angles (except in different directions), then the turn-center reference line  340  may bisect a gap spacing apart the front axle and the rear axle. Furthermore, based on the dimensions of the vehicle  302 , an offset distance  342  extends perpendicularly from the turn-center reference line  340  to the center of each wheel. Furthermore, a yaw rate (ω)  318  may be received from a yaw rate sensor (e.g., IMU, gyroscope, etc.) and a linear wheel velocity (V)  344  may be derived from data (e.g., rotation rate) received from an encoder (or other sensor).  FIG.  3    illustrates the variables as they relate to the wheel  320   c,  and similar (but respective) variables may be determined for each of the other wheels  320   a,    320   b,  and  320   d.    
     Based on the variables depicted in  FIGS.  2  and  3   , various functions may be expressed to describe relationships among the variables (e.g., a function to determine the turn center as discussed above). Further, as discussed below with respect to  FIG.  4   , using variables shown in  FIGS.  1 - 3   , an estimated vehicle velocity  260  or  360  may be estimated using a least squares method or algorithm (e.g., an iterative reweighted Gauss-Newton algorithm). Among other things, a vehicle velocity may be used to estimate relative positions (e.g., poses) of the vehicle as the vehicle executes one or more maneuvers, and in this respect, the relative position may be at least partially based on the wheel angle, yaw and wheel speed sensor data. In some examples, a relative position of the vehicle may be based at least partially on the estimated vehicle velocity as determined based on the least squares method. 
       FIG.  4    is a flowchart showing an example process involving techniques as described herein. The process illustrated in  FIG.  4    may be described with reference to components and elements described above with reference to  FIGS.  1 A,  1 B,  2   , and/or  3  for convenience and ease of understanding. However, the process illustrated in  FIG.  4    is not limited to being performed using these components, and the components are not limited to performing the process illustrated in  FIG.  4   . The process illustrated in  FIG.  4    is illustrated as a logical flow graph, each operation of which represents a sequence of operations that can be implemented in hardware, software, or a combination thereof. In the context of software, the operations represent computer-executable instructions stored on one or more computer-readable storage media that, when executed by one or more processors, perform the recited operations. Generally, computer-executable instructions include routines, programs, objects, components, data structures, and the like that perform particular functions or implement particular abstract data types. The order in which the operations are described is not intended to be construed as a limitation, and any number of the described operations can be omitted or combined in any order and/or in parallel to implement the process. 
       FIG.  4    includes a flow diagram with operations or blocks for a process  400  for determining an estimated vehicle velocity (e.g., estimated velocity), the estimated vehicle velocity being usable to control an operation of the vehicle. For example, the process  400  may be used to determine an estimated vehicle velocity  260  or  360 . 
     The process  400  may include, at block  402 , receiving sensor data and/or determinates thereof such as wheel speed sensor data, yaw sensor data, wheel steering angle data, etc. For example, sensor data may be received from the yaw rate sensor  124  (e.g., IMU, gyroscope, etc.), wheel speed encoders  126  and steering sensors  132 . At block  404 , the process  400  may include determining a turn center of the vehicle (e.g., turn center  204  or  304 ). At block  406 , the process  400  may include determining an initial vehicle velocity (V). The initial vehicle velocity (V) may include an orientation perpendicular to a radius to the turn center and a magnitude that may be computed as the average of the linear wheel speeds (e.g., calculated based on a wheel sensor reported rotation speed multiplied by tire circumference). 
     Generally, blocks  408 - 412  may be performed for each wheel (e.g., as determined by block  414 ), followed by block  416 . Blocks  408 - 416  may in turn be performed iteratively for one or more iterations (e.g., as determined by block  418 ), followed by block  420 . For example, block  418  may iterate the operations of blocks  408 - 416  for a set number of iterations or until a condition is met (e.g., minimization of a sum of squares or until a sum of squares is below a threshold). 
     Turning to block  408 , the process  400  may include transforming the current estimated velocity (V) to an estimated velocity at a current wheel (V w ). More particularly, the transformation from the current estimated velocity to the estimated velocity at the current wheel may be determined as: 
     
       
      
       V 
       w 
       =V+ω×r  
      
     
     where ω is the yaw rotation rate and r is the lever arm from the position of the center of the vehicle to the position of the wheel and ω×r is the cross product between the vectors ω and r. In other words, in some examples, estimated velocity at each wheel may be determined or solved using the current estimated velocity of the vehicle (e.g., current estimated velocity of the vehicle at the vehicle center), the yaw rate, and a vector between the position (e.g., coordinates) of the center of the vehicle wheel and the position of the wheel. 
     At block  410 , the process may include computing an estimated velocity magnitude error for the current wheel (e.g., an error between ∥V w ∥ and a measured wheel speed) and an associated Jacobian. More particularly, the error (e) and the Jacobian (J) (e.g., the magnitude Jacobian) for the velocity magnitude error of the current wheel may be determined as: 
     
       
         
           
             e 
             = 
             
               
                 
                   ❘ 
                   &#34;\[LeftBracketingBar]&#34; 
                 
                 
                   v 
                   measured 
                 
                 
                   ❘ 
                   &#34;\[RightBracketingBar]&#34; 
                 
               
               - 
               
                  
                 
                   V 
                   w 
                 
                  
               
             
           
         
       
       
         
           
             J 
             = 
             
               
                 V 
                 w 
               
               
                  
                 
                   V 
                   w 
                 
                  
               
             
           
         
       
     
     where v measured  is the sensor based linear speed of the wheel. 
     In some examples, the error and Jacobian may be scaled according to an expected measurement error (σ ws ) for the wheel speed sensors. Additionally, a weighting function, such as the Cauchy weighting function or Cauchy loss function, may be applied. In an example, a Cauchy weight (e.g., magnitude weight) may be determined as: 
     
       
         
           
             
               cauchy 
               ⁢ 
                   
               
                 ( 
                 
                   e 
                   , 
                   k 
                 
                 ) 
               
             
             = 
             
               1 
               
                 1 
                 + 
                 
                   
                     ( 
                     
                       e 
                       k 
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
     
     where k is a constant parameter and may be tuned to reject bad sensor data (e.g., 3 may be a standard value to reject data that is more than three sigma away). 
     At block  412 , the process may include computing an estimated velocity orientation error for the current wheel (e.g., an error between the orientation of V w  and the steering angle) and an associated Jacobian. More particularly, the error (e) for the velocity orientation error of the current wheel may be determined as: 
         e= sin measured −sin predicted  
 
     where sin measured  is the sinus of the measured steering angle (e.g., from the steering sensors for the current wheel) and sin predicted  the sinus of the angle of predicted velocity given by: 
     
       
         
           
             
               sin 
               predicted 
             
             = 
             
               
                 V 
                 wy 
               
               
                 ( 
                 
                   
                      
                     
                       V 
                       w 
                     
                      
                   
                   + 
                   K 
                 
                 ) 
               
             
           
         
       
     
     where K is a regularizer that may have a small value used to take care of the case where ∥V w ∥ is very small, and may be computed as a function of the magnitude of the initial velocity. 
     The corresponding Jacobian for the velocity orientation error (e.g., the orientation Jacobian) may be determined as: 
     
       
         
           
             
               J 
               x 
             
             = 
             
               
                 
                   - 
                   
                     V 
                     wx 
                   
                 
                 ⋆ 
                 
                   V 
                   wy 
                 
               
               
                 
                    
                   
                     V 
                     w 
                   
                    
                 
                 ⋆ 
                 
                   
                     ( 
                     
                       
                          
                         
                           V 
                           w 
                         
                          
                       
                       + 
                       K 
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
       
         
           
             
               J 
               y 
             
             = 
             
               
                 
                   
                     - 
                     
                       V 
                       wx 
                       2 
                     
                   
                   
                      
                     
                       V 
                       w 
                     
                      
                   
                 
                 + 
                 K 
               
               
                 
                   ( 
                   
                     
                        
                       
                         V 
                         w 
                       
                        
                     
                     + 
                     K 
                   
                   ) 
                 
                 2 
               
             
           
         
       
     
     As discussed above, in some examples, the error and Jacobian may be scaled according to an expected measurement error (σ ws ) for the steering angle sensors. Additionally, a weighting function, such as the Cauchy weighting function or Cauchy loss function, may be applied. In an example, a Cauchy weight (e.g., orientation weight) may be determined as: 
     
       
         
           
             
               cauchy 
               ⁢ 
                   
               
                 ( 
                 
                   e 
                   , 
                   k 
                 
                 ) 
               
             
             = 
             
               1 
               
                 1 
                 + 
                 
                   
                     ( 
                     
                       e 
                       k 
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
     
     where k is a constant parameter and may be tuned to reject bad sensor data (e.g., 3 may be a standard value to reject data that is more than three sigma away). 
     As mentioned above, at block  414 , the process  400  may include determining if blocks  408 - 412  have not been performed for the current estimated velocity (V w ) for another wheel. If so, the process  400  may return to block  408  for the next wheel. Otherwise, the process  400  may continue to  416 . 
     At block  416 , the process  400  may include solving for the next iteration of V. More particularly, the process  400  may include solving the Gauss Newtonian algorithm to update the estimated velocity as: 
         V=V+ ( J   T   J ) −1   J   T *residuals 
     One of ordinary skill in the art would understand how to perform the Gauss-Newton procedure and, as such, the details thereof are not included herein to avoid prolix. 
     At block  418 , the process  400  may include determining if another iteration of blocks  408 - 416  is to be performed. If so, the process  400  may return to  408  for the next iteration based on the updated estimated velocity (V). Otherwise, the process  400  may continue to block  420 . As mentioned above, block  418  may iterate the operations of blocks  408 - 416  for a set number of iterations or until a condition is met (e.g., minimization of a sum of squares, until a sum of squares is below a threshold, until the update portion of the above equation is below a threshold, etc.). 
     At block  420 , the process  400  may include outputting the estimated velocity. As mentioned above, the vehicle may be controlled based on the estimated velocity output at block  420 . For example, the estimated velocity may be used for localization or other downstream operations. In addition, if a difference (e.g., variance) between the estimated velocity and a velocity based on the wheel speed sensors exceeds a threshold, then a slip event (e.g., wheel slip, mechanical slippage, vehicle skid, etc.) may be flagged (e.g., recorded, reported, tracked, etc.) indicating the subject wheel may have lost traction or slipped. This in turn may generate a signal to the vehicle to regain control, such as by adjusting the steering, applying brakes, reducing an acceleration, powering opposite wheels, depressing or releasing a throttle, etc. In further examples, if a total count or frequency of slip events exceeds a threshold, then maintenance may be suggested (e.g., check tire tread or steering components). In additional examples, if slip events are flagged at multiple wheels, then a vehicle-skid event may be flagged indicating the vehicle skidded across a ground surface. 
       FIG.  5    depicts a block diagram of an example system  500  for implementing the techniques described herein. In at least one example, the system  500  can include a vehicle  502 . In the illustrated example system  500 , the vehicle  502  is an autonomous vehicle; however, the vehicle  502  can be any other type of vehicle. The vehicle  502  may be the vehicle  102  depicted in  FIGS.  1 A,  1 B,  2  and  3    and/or perform the process depicted in  FIG.  4   . 
     The vehicle  502  can be a driverless vehicle, such as an autonomous vehicle configured to operate according to a Level  5  classification issued by the U.S. National Highway Traffic Safety Administration, which describes a vehicle capable of performing all safety-critical functions for the entire trip, with the driver (or occupant) not being expected to control the vehicle at any time. In such examples, because the vehicle  502  can be configured to control all functions from start to completion of the trip, including all parking functions, it may not include a driver and/or controls for driving the vehicle  502 , such as a steering wheel, an acceleration pedal, and/or a brake pedal. This is merely an example, and the systems and methods described herein may be incorporated into any ground-borne, airborne, or waterborne vehicle, including those ranging from vehicles that need to be manually controlled by a driver at all times, to those that are partially or fully autonomously controlled. 
     The vehicle  502  can include one or more computing device(s)  504 , one or more sensor system(s)  506 , one or more emitter(s)  508 , one or more communication connection(s)  510  (also referred to as communication devices and/or modems), at least one direct connection  512  (e.g., for physically coupling with the vehicle  502  to exchange data and/or to provide power), and one or more drive system(s)  514 . The one or more sensor system(s)  506  can be configured to capture sensor data associated with an environment. 
     The one or more sensor system(s)  506  can include time-of-flight sensors, location sensors (e.g., GPS, compass, etc.), inertial sensors (e.g., sensor  124  including inertial measurement units (IMUs), accelerometers, magnetometers, gyroscopes, etc.), lidar sensors, radar sensors, sonar sensors, infrared sensors, cameras (e.g., RGB, IR, intensity, depth, etc.), microphone sensors, environmental sensors (e.g., temperature sensors, humidity sensors, light sensors, pressure sensors, etc.), ultrasonic transducers, wheel encoders (e.g.,  126   a - 126   d ), ball joint sensors, chassis position sensors, etc. The one or more sensor system(s)  506  can include multiple instances of each of these or other types of sensors. For instance, the time-of-flight sensors can include individual time-of-flight sensors located at the corners, front, back, sides, and/or top of the vehicle  502 . As another example, the camera sensors can include multiple cameras disposed at various locations about the exterior and/or interior of the vehicle  502 . The one or more sensor system(s)  506  can provide input to the computing device  504 . 
     The vehicle  502  can also include one or more emitter(s)  508  for emitting light and/or sound. The one or more emitter(s)  508  in this example include interior audio and visual emitters to communicate with passengers of the vehicle  502 . By way of example and not limitation, interior emitters can include speakers, lights, signs, display screens, touch screens, haptic emitters (e.g., vibration and/or force feedback), mechanical actuators (e.g., seatbelt tensioners, seat positioners, headrest positioners, etc.), and the like. The one or more emitter(s)  508  in this example also include exterior emitters. By way of example and not limitation, the exterior emitters in this example include lights to signal a direction of travel or other indicator of vehicle action (e.g., indicator lights, signs, light arrays, etc.), and one or more audio emitters (e.g., speakers, speaker arrays, horns, etc.) to audibly communicate with pedestrians or other nearby vehicles, one or more of which may comprise acoustic beam steering technology. 
     The vehicle  502  can also include one or more communication connection(s)  510  that enable communication between the vehicle  502  and one or more other local or remote computing device(s) (e.g., a remote teleoperation computing device) or remote services. For instance, the one or more communication connection(s)  510  can facilitate communication with other local computing device(s) on the vehicle  502  and/or the one or more drive system(s)  514 . Also, the one or more communication connection(s)  510  can allow the vehicle  502  to communicate with other nearby computing device(s) (e.g., other nearby vehicles, traffic signals, etc.). 
     The one or more communications connection(s)  510  can include physical and/or logical interfaces for connecting the computing device  504  to another computing device or one or more external networks  542  (e.g., the Internet). For example, the one or more communications connection(s)  510  can enable Wi-Fi-based communication such as via frequencies defined by the IEEE 802.11 standards, short range wireless frequencies such as Bluetooth, cellular communication (e.g., 2G, 3G, 4G, 4G LTE, 5G, etc.), satellite communication, dedicated short-range communications (DSRC), or any suitable wired or wireless communications protocol that enables the respective computing device to interface with the other computing device(s). 
     In at least one example, the vehicle  502  can include one or more drive system(s)  514 . In some examples, the vehicle  502  can have a single drive system  514 . In at least one example, if the vehicle  502  has multiple drive systems  514 , individual drive systems  514  can be positioned on opposite ends of the vehicle  502  (e.g., the front and the rear, etc.). In at least one example, the drive system(s)  514  can include one or more sensor system(s)  506  to detect conditions of the drive system(s)  514  and/or the surroundings of the vehicle  502 . By way of example and not limitation, the sensor system(s)  506  can include one or more wheel encoders (e.g., rotary encoders) to sense rotation of the wheels of the drive systems, steering sensors to detect wheel angles of the wheels, inertial sensors (e.g., inertial measurement units, accelerometers, gyroscopes, magnetometers, etc.) to measure orientation and acceleration of the drive system, cameras or other image sensors, ultrasonic sensors to acoustically detect objects in the surroundings of the drive system, lidar sensors, radar sensors, etc. Some sensors, such as the wheel encoders can be unique to the drive system(s)  514 . In some cases, the sensor system(s)  506  on the drive system(s)  514  can overlap or supplement corresponding systems of the vehicle  502  (e.g., sensor system(s)  506 ). The drive system(s)  514  may also include one or more steering motors (e.g.,  128 ), steering motor sensors (e.g.,  132 ), and steering racks (e.g.,  130 ). 
     The drive system(s)  514  can include many of the vehicle systems, including a high voltage battery, a motor to propel the vehicle, an inverter to convert direct current from the battery into alternating current for use by other vehicle systems, a steering system including a steering motor and steering rack (which can be electric), a braking system including hydraulic or electric actuators, a suspension system including hydraulic and/or pneumatic components, a stability control system for distributing brake forces to mitigate loss of traction and maintain control, an HVAC system, lighting (e.g., lighting such as head/tail lights to illuminate an exterior surrounding of the vehicle), and one or more other systems (e.g., cooling system, safety systems, onboard charging system, other electrical components such as a DC/DC converter, a high voltage junction, a high voltage cable, charging system, charge port, etc.). Additionally, the drive system(s)  514  can include a drive system controller which can receive and preprocess data from the sensor system(s)  506  and to control operation of the various vehicle systems. In some examples, the drive system controller can include one or more processor(s) and memory communicatively coupled with the one or more processor(s). The memory can store one or more components to perform various functionalities of the drive system(s)  514 . Furthermore, the drive system(s)  514  also include one or more communication connection(s) that enable communication by the respective drive system with one or more other local or remote computing device(s). 
     The computing device  504  can include one or more processor(s)  516  and memory  518  communicatively coupled with the one or more processor(s)  516 . In the illustrated example, the memory  518  of the computing device  504  stores a perception component  520 , a localization component  524 , a velocity monitor  530 , a prediction component  534 , a planning component  536 , a maps component  538 , and one or more system controller(s)  540 . Though depicted as residing in the memory  518  for illustrative purposes, it is contemplated that the perception component  520 , the localization component  524 , the velocity monitor  530 , the prediction component  534 , the planning component  536 , the maps component  538 , and the one or more system controller(s)  540  can additionally, or alternatively, be accessible to the computing device  504  (e.g., stored in a different component of vehicle  502 ) and/or be accessible to the vehicle  502  (e.g., stored remotely). 
     The perception component  520  can include functionality to perform object detection, segmentation, and/or classification. In some examples, the perception component  520  can provide processed sensor data that indicates a presence of an entity that is proximate to the vehicle  502  and/or a classification of the entity as an entity type (e.g., car, pedestrian, cyclist, building, tree, road surface, curb, sidewalk, unknown, etc.). In additional and/or alternative examples, the perception component  520  can provide processed sensor data that indicates one or more characteristics associated with a detected entity and/or the environment in which the entity is positioned. In some examples, characteristics associated with an entity can include, but are not limited to, an x-position (global position), a y-position (global position), a z-position (global position), an orientation, an entity type (e.g., a classification), a velocity of the entity, an extent of the entity (size), etc. Characteristics associated with the environment can include, but are not limited to, a presence of another entity in the environment, a state of another entity in the environment, a time of day, a day of a week, a season, a weather condition, an indication of darkness/light, etc. In one example, the perception component  520  may detect a ground surface and determine a ride height based on sensor data. 
     Further, the perception component  520  can include functionality to store perception data generated by the perception component  520 . In some instances, the perception component  520  can determine a track corresponding to an object that has been classified as an object type. For purposes of illustration only, the perception component  520 , using sensor system(s)  506  can capture one or more images of an environment, which may be used to determine information about an environment. 
     The stored perception data can, in some examples, include fused perception data captured by the vehicle. Fused perception data can include a fusion or other combination of sensor data from sensor system(s)  506 , such as image sensors, lidar sensors, radar sensors, time-of-flight sensors, sonar sensors, global positioning system sensors, internal sensors, and/or any combination of these. The stored perception data can additionally or alternatively include classification data including semantic classifications of objects (e.g., pedestrians, vehicles, buildings, road surfaces, etc.) represented in the sensor data. The stored perception data can additionally or alternatively include track data (positions, orientations, sensor features, etc.) corresponding to motion of objects classified as dynamic objects through the environment. The track data can include multiple tracks of multiple different objects over time. This track data can be mined to identify images of certain types of objects (e.g., pedestrians, animals, etc.) at times when the object is stationary (e.g., standing still) or moving (e.g., walking, running, etc.). In this example, the computing device determines a track corresponding to a pedestrian. 
     In general, the perception component  520  can detect (among other things) semantic objects represented by sensor data. In some examples, the perception component  520  can identify such semantic objects and can determine a two-dimensional or a three-dimensional bounding box associated with the object. The perception component  520  can determine additional information such as a location, orientation, pose, and/or size (e.g., length, width, height, etc.) associated with the object. The perception component  520  can send data to other components of the system  500  for localization and/or determining calibration information, as discussed herein. 
     The localization component  524  can include functionality to receive data from the sensor system(s)  506  and/or other components to determine a position of the vehicle  502 . For example, the localization component  524  can include and/or request/receive a three-dimensional map of an environment and can continuously determine a location of the autonomous vehicle within the map. In some instances, the localization component  524  can use SLAM (simultaneous localization and mapping) or CLAMS (calibration, localization and mapping, simultaneously) to receive time-of-flight data, image data, lidar data, radar data, sonar data, IMU data, GPS data, wheel encoder data, or any combination thereof, and the like to accurately determine a location of the autonomous vehicle. In some instances, the localization component  524  can provide data to various components of the vehicle  502  to determine an initial position of an autonomous vehicle for generating a trajectory or for initial calibration. In examples of this disclosure, the localization component  524  may determine a position of the vehicle  502  based on the estimated vehicle velocity. That is, the estimated vehicle velocity may be directly used to determine position and/or may be used to validate other information (e.g., measured velocities and/or speeds) for determining position. 
     The velocity monitor  530  may determine an estimated vehicle velocity of the vehicle  502  (e.g., as discussed above with respect to  FIGS.  1 A- 4   ). For example, the velocity monitor  530  may communicate with (or receive data provided by) the sensor system(s) (e.g., yaw rate sensor, wheel encoder, steering sensor, etc.), and, based on data from the sensor system(s) determine an estimated vehicle velocity as discussed above with respect to  FIG.  4   . The velocity monitor  530  may communicate the estimated vehicle velocity to other systems (e.g., localization  524 ) or may use the estimated vehicle velocity to validate measured velocities and speeds. Furthermore, the velocity monitor  530  may also execute other operations described in this disclosure, including those described with respect to  FIGS.  1 A- 4   . 
     The prediction component  534  can generate one or more probability maps representing prediction probabilities of possible locations of one or more objects in an environment. For example, the prediction component  534  can generate one or more probability maps for vehicles, pedestrians, animals, and the like within a threshold distance from the vehicle  502 . In some instances, the prediction component  534  can measure a track of an object and generate a discretized prediction probability map, a heat map, a probability distribution, a discretized probability distribution, and/or a trajectory for the object based on observed and predicted behavior. In some instances, the one or more probability maps can represent an intent of the one or more objects in the environment. 
     The planning component  536  can determine a path for the vehicle  502  to follow to traverse through an environment. For example, the planning component  536  can determine various routes and paths and various levels of detail. In some instances, the planning component  536  can determine a route to travel from a first location (e.g., a current location) to a second location (e.g., a target location). For the purpose of this discussion, a route can be a sequence of waypoints for traveling between two locations. As non-limiting examples, waypoints include streets, intersections, global positioning system (GPS) coordinates, etc. Further, the planning component  536  can generate an instruction for guiding the autonomous vehicle along at least a portion of the route from the first location to the second location. In at least one example, the planning component  536  can determine how to guide the autonomous vehicle from a first waypoint in the sequence of waypoints to a second waypoint in the sequence of waypoints. In some examples, the instruction can be a path, or a portion of a path. In some examples, multiple paths can be substantially simultaneously generated (i.e., within technical tolerances) in accordance with a receding horizon technique. A single path of the multiple paths in a receding data horizon having the highest confidence level may be selected to operate the vehicle. 
     In other examples, the planning component  536  can alternatively, or additionally, use data from the perception component  520  and/or the prediction component  534  to determine a path for the vehicle  502  to follow to traverse through an environment. For example, the planning component  536  can receive data from the perception component  520  and/or the prediction component  534  regarding objects associated with an environment. Using this data, the planning component  536  can determine a route to travel from a first location (e.g., a current location) to a second location (e.g., a target location) to avoid objects in an environment. In at least some examples, such a planning component  536  may determine there is no such collision free path and, in turn, provide a path which brings vehicle  502  to a safe stop avoiding all collisions and/or otherwise mitigating damage. 
     The memory  518  can further include a maps component  538  that can be used by the vehicle  502  to navigate within the environment. For the purpose of this discussion, a map can be any number of data structures modeled in two dimensions, three dimensions, or N-dimensions that are capable of providing information about an environment, such as, but not limited to, topologies (such as intersections), streets, mountain ranges, roads, terrain, and the environment in general. A map can further include an object identifier, an object classification, a three-dimensional location, covariance data (e.g., represented in image data or a multi-resolution voxel space), and the like. In some instances, a map can include, but is not limited to: texture information (e.g., color information (e.g., RGB color information, Lab color information, HSV/HSL color information), and the like), intensity information (e.g., LIDAR information, RADAR information, and the like); spatial information (e.g., image data projected onto a mesh, individual “surfels” (e.g., polygons associated with individual color and/or intensity)), reflectivity information (e.g., specularity information, retroreflectivity information, BRDF information, BSSRDF information, and the like). In one example, a map can include a three-dimensional mesh of the environment. In some instances, the map can be stored in a tiled format, such that individual tiles of the map represent a discrete portion of an environment, and can be loaded into working memory as needed, as discussed herein. In at least one example, the one or more maps  538  can include at least one map (e.g., images and/or a mesh). In some examples, the vehicle  502  can be controlled based at least in part on the map(s) component  538 . That is, the map(s) component  538  can be used in connection with the perception component  520  (and sub-components), the localization component  524  (and sub-components), the prediction component  534 , and/or the planning component  536  to determine a location of the vehicle  502 , identify objects in an environment, generate prediction probabilit(ies) associated with objects and/or the vehicle  502 , and/or generate routes and/or trajectories to navigate within an environment. 
     In at least one example, the computing device  504  can include one or more system controller(s)  540 , which can be configured to control steering, propulsion, braking, safety, emitters, communication, and other systems of the vehicle  502 . These system controller(s)  540  can communicate with and/or control corresponding systems of the drive system(s)  514  and/or other components of the vehicle  502 , which may be configured to operate in accordance with a path provided from the planning component  536 . 
     The vehicle  502  can connect to computing device(s)  544  via network  542  and can include one or more processor(s)  546  and memory  548  communicatively coupled with the one or more processor(s)  546 . In at least one instance, the one or more processor(s)  546  can be similar to the processor(s)  516  and the memory  548  can be similar to the memory  518 . In the illustrated example, the memory  548  of the computing device(s)  544  stores a remote operation component  550  and/or a model component  552 . In at least one instance, the model component  552 , after empirical testing and/or simulations, can include the models for determining a location and/or determining a calibration parameter, as discussed herein. Though depicted as residing in the memory  548  for illustrative purposes, it is contemplated that the remote operation component  550  and the model component  552  can additionally, or alternatively, be accessible to the computing device(s)  544  (e.g., stored in a different component of computing device(s)  544  and/or be accessible to the computing device(s)  544  (e.g., stored remotely). 
     The remote operation component  550  can include functionality to receive an indication of wheel-slip events, vehicle-skid events, steering-component slippage, and/or a request for preventative maintenance (e.g., based on a difference (e.g., variance) between estimated and measured vehicle velocity). In some examples, the remote operation component  550  can schedule a maintenance operation based on a vehicle velocity difference (e.g., variance) or a determination by the vehicle  502  that a difference is indicative of a degraded state (e.g., when sensor data is inconsistent with estimated vehicle velocity). In some examples, a remote operation component  550  can include teleoperators or operators who can control the vehicle  502  or can provide instructions to the vehicle based on a skid event (e.g., where a vehicle skid event suggest a loss of control). 
     The model component  552  can include functionality to generate models for determining a location and/or determine slip or skid events, as discussed herein. For example, the model component  552  can receive sensor data and can determine an estimated vehicle velocity associated with such sensor data. The model component  552  can aggregate data across a plurality of vehicles (e.g., a fleet of vehicles) to determine vehicle velocity variances indicative of normal operations and vehicle velocity variances indicative of degraded operations. Further, the model component  552  can associate a vehicle velocity variance with a time period of operating a sensor and a performance of components associated with such metrics to determine a predictive maintenance schedule associated with various sensors, as discussed herein. 
     The processor(s)  516  of the computing device  504  and the processor(s)  546  of the computing device(s)  544  can be any suitable processor capable of executing instructions to process data and perform operations as described herein. By way of example and not limitation, the processor(s)  516  and  546  can comprise one or more Central Processing Units (CPUs), Graphics Processing Units (GPUs), or any other device or portion of a device that processes electronic data to transform that electronic data into other electronic data that can be stored in registers and/or memory. In some examples, integrated circuits (e.g., ASICs, etc.), gate arrays (e.g., FPGAs, etc.), and other hardware devices can also be considered processors in so far as they are configured to implement encoded instructions. 
     The memory  518  computing device  504  and the memory  548  of the computing device(s)  544  are examples of non-transitory computer-readable media. The memory  518  and  548  can store an operating system and one or more software applications, instructions, programs, and/or data to implement the methods described herein and the functions attributed to the various systems. In various implementations, the memory  518  and  548  can be implemented using any suitable memory technology, such as static random access memory (SRAM), synchronous dynamic RAM (SDRAM), nonvolatile/Flash-type memory, or any other type of memory capable of storing information. The architectures, systems, and individual elements described herein can include many other logical, programmatic, and physical components, of which those shown in the accompanying figures are merely examples that are related to the discussion herein. 
     In some instances, aspects of some or all of the components discussed herein can include any models, algorithms, and/or machine-learning algorithms. For example, in some instances, the components in the memory  518  and  548  can be implemented as a neural network. In some examples, a machine learned model could be trained to determine an estimated vehicle velocity, slip event, skid event, or other condition of the vehicle based on sensor data received from the yaw rate sensor, encoder, steering sensor, etc. 
     As described herein, an exemplary neural network is a biologically inspired algorithm which passes input data through a series of connected layers to produce an output. Each layer in a neural network can also comprise another neural network, or can comprise any number of layers (whether convolutional or not). As can be understood in the context of this disclosure, a neural network can utilize machine learning, which can refer to a broad class of such algorithms in which an output is generated based on learned parameters. 
     Although discussed in the context of neural networks, any type of machine learning can be used consistent with this disclosure. For example, machine learning or machine-learned algorithms can include, but are not limited to, regression algorithms (e.g., ordinary least squares regression (OLSR), linear regression, logistic regression, stepwise regression, multivariate adaptive regression splines (MARS), locally estimated scatterplot smoothing (LOESS)), instance-based algorithms (e.g., ridge regression, least absolute shrinkage and selection operator (LASSO), elastic net, least-angle regression (LARS)), decisions tree algorithms (e.g., classification and regression tree (CART), iterative dichotomiser 3 (ID3), Chi-squared automatic interaction detection (CHAID), decision stump, conditional decision trees), Bayesian algorithms (e.g., naïve Bayes, Gaussian naïve Bayes, multinomial naïve Bayes, average one-dependence estimators (AODE), Bayesian belief network (BNN), Bayesian networks), clustering algorithms (e.g., k-means, k-medians, expectation maximization (EM), hierarchical clustering), association rule learning algorithms (e.g., perceptron, back-propagation, hopfield network, Radial Basis Function Network (RBFN)), deep learning algorithms (e.g., Deep Boltzmann Machine (DBM), Deep Belief Networks (DBN), Convolutional Neural Network (CNN), Stacked Auto-Encoders), Dimensionality Reduction Algorithms (e.g., Principal Component Analysis (PCA), Principal Component Regression (PCR), Partial Least Squares Regression (PLSR), Sammon Mapping, Multidimensional Scaling (MDS), Projection Pursuit, Linear Discriminant Analysis (LDA), Mixture Discriminant Analysis (MDA), Quadratic Discriminant Analysis (QDA), Flexible Discriminant Analysis (FDA)), Ensemble Algorithms (e.g., Boosting, Bootstrapped Aggregation (Bagging), AdaBoost, Stacked Generalization (blending), Gradient Boosting Machines (GBM), Gradient Boosted Regression Trees (GBRT), Random Forest), SVM (support vector machine), supervised learning, unsupervised learning, semi-supervised learning, etc. 
     Additional examples of architectures include neural networks such as ResNet50, ResNet101, VGG, DenseNet, PointNet, and the like. 
     As described above with reference to  FIGS.  1 - 5   , techniques described herein can be useful for estimating a vehicle velocity of a vehicle. As described, a yaw rate, wheel speeds, steering angles and vehicle dimensions can be used to estimate the vehicle velocity. Among other things, the estimated vehicle velocity may provide redundancy (e.g., when determined in parallel with (in addition to) sensor based velocities and/or speeds) and validation and may be less susceptible to inaccuracies from loss of tire traction and other events. 
     EXAMPLE CLAUSES 
     Clause A: A system comprising: one or more processors; and one or more non-transitory computer-readable media storing instructions executable by the one or more processors, wherein the instructions, when executed, cause the system to perform operations comprising: determining, based at least in part on first sensor data associated with a first sensor, a steering angle of a wheel of a plurality of wheels associated with a vehicle; determining, based at least in part on the steering angle, a turn center of the vehicle; determining an estimated velocity of the vehicle comprising performing a least square algorithm based on a yaw rate of the vehicle, the steering angle and a linear wheel speed of the wheel; and controlling an operation of the vehicle based at least in part on the estimated velocity. 
     Clause B: The system of clause A, wherein the least square algorithm is further based on an initial estimated velocity of the vehicle, the operations further comprising: determining, based at least in part on second sensor data associated with at least one second sensor, a linear wheel speed of at least two wheels of the plurality of wheels of the vehicle; and determining the initial estimated velocity based at least in part on the turn center and an average linear wheel speed of the at least two wheels of the plurality of wheels of the vehicle. 
     Clause C: The system of clause B, wherein determining the initial estimated velocity comprises: determining an initial estimated velocity orientation based at least in part on the turn center; and determining an initial estimated velocity magnitude based at least in part on the average linear wheel speed of the at least two wheels of the plurality of wheels of the vehicle. 
     Clause D: The system of clause C, wherein operations further comprise: determining, based at least in part on third sensor data from a third sensor, the yaw rate of the vehicle; and wherein the least square algorithm comprises: determining a first estimated wheel velocity by transforming the initial estimated velocity from a position of a center of the vehicle to a position of the wheel based at least in part on the yaw rate, the initial estimated velocity, the position of the center of the vehicle and the position of the wheel. 
     Clause E: The system of clause A, wherein controlling an operation of the vehicle based at least in part on the estimated velocity compensates for a wheel slip of one of the plurality of wheels of the vehicle. 
     Clause F: A method comprising: determining, based at least in part on first sensor data associated with a first sensor, a steering angle of a wheel of a plurality of wheels associated with a vehicle; determining, based at least in part on the steering angle, a turn center of the vehicle; determining an estimated velocity of the vehicle based on a yaw rate of the vehicle, the turn center, the steering angle and a wheel speed of the wheel; and controlling an operation of the vehicle based at least in part on the estimated velocity. 
     Clause G: The method of clause F, wherein determining the estimated velocity of the vehicle is further based on an initial estimated velocity of the vehicle, the method further comprising: determining, based at least in part on second sensor data associated with at least one second sensor, an average linear wheel speed of at least two wheels of the plurality of wheels of the vehicle; and determining the initial estimated velocity based at least in part on the turn center and the average linear wheel speed of the at least two wheels of the plurality of wheels of the vehicle. 
     Clause H: The method of clause G, wherein determining the initial estimated velocity of the vehicle comprises: determining an initial estimated velocity orientation based at least in part on the turn center; and determining an initial estimated velocity magnitude based at least in part on the average linear wheel speed. 
     Clause I: The method of claim G, further comprising: determining, based at least in part on third sensor data from a third sensor, the yaw rate of the vehicle; and wherein determining the estimated velocity comprises performing an iterative least squares algorithm comprising: determining an initial estimated wheel velocity by transforming the initial estimated velocity from a position of a center of the vehicle to a position proximate the wheel based at least in part on the yaw rate. 
     Clause J: The method of clause I, wherein performing the iterative least squares algorithm further comprises: determining a magnitude error between a magnitude of the initial estimated wheel velocity and the wheel speed of the wheel; determining an orientation error between an orientation of the initial estimated wheel velocity and the steering angle; determining a magnitude Jacobian based at least in part on the magnitude of the initial estimated wheel velocity and the wheel speed of the wheel; and determining an orientation Jacobian based at least in part on the orientation of the initial estimated wheel velocity and the steering angle. 
     Clause K: The method of clause J, wherein performing the iterative least squares algorithm further comprises: determining a magnitude weight using a first Cauchy loss function based at least in part on the magnitude error and the magnitude Jacobian; and determining an orientation weight using a second Cauchy loss function based at least in part on the orientation error and the orientation Jacobian. 
     Clause L: The method of clause K, wherein performing the iterative least squares algorithm further comprises: determining the estimated velocity based on the initial estimated velocity, the magnitude error, the magnitude Jacobian, the magnitude weight, the orientation error, the orientation Jacobian and the orientation weight. 
     Clause M: The method of clause F, wherein determining the estimated velocity comprises performing an iterative reweighted Gauss-Newton algorithm. 
     Clause N: One or more non-transitory computer-readable media storing instructions that, when executed, cause one or more processors to perform operations comprising: determining, based at least in part on first sensor data associated with a first sensor, a steering angle of a wheel of a plurality of wheels associated with a vehicle; determining, based at least in part on the steering angle, a turn center of the vehicle; determining an estimated velocity of the vehicle based on a yaw rate of the vehicle, the turn center, the steering angle and a wheel speed of the wheel; and controlling an operation of the vehicle based at least in part on the estimated velocity. 
     Clause O: The one or more non-transitory computer-readable media of clause N, wherein determining the estimated velocity of the vehicle is further based on an initial estimated velocity of the vehicle, the operations further comprising: determining, based at least in part on second sensor data associated with at least one second sensor, an average linear wheel speed of at least two wheels of the plurality of wheels of the vehicle; and determining the initial estimated velocity based at least in part on the turn center and the average linear wheel speed of the at least two wheels of the plurality of wheels of the vehicle. 
     Clause P: The one or more non-transitory computer-readable media of clause O, wherein determining the initial estimated velocity of the vehicle comprises: determining an initial estimated velocity orientation based at least in part on the turn center; and determining an initial estimated velocity magnitude based at least in part on the average linear wheel speed. 
     Clause Q: The one or more non-transitory computer-readable media of clause O, the operations further comprising: determining, based at least in part on third sensor data from a third sensor, the yaw rate of the vehicle; and wherein determining the estimated velocity comprises performing an iterative least squares algorithm comprising: determining an initial estimated wheel velocity by transforming the initial estimated velocity from a position of a center of the vehicle to a position proximate the wheel based at least in part on the yaw rate. 
     Clause R: The one or more non-transitory computer-readable media of clause Q, wherein performing the iterative least squares algorithm further comprises: determining a magnitude error between a magnitude of the initial estimated wheel velocity and the wheel speed of the wheel; determining an orientation error between an orientation of the initial estimated wheel velocity and the steering angle; determining a magnitude Jacobian based at least in part on the magnitude of the initial estimated wheel velocity and the wheel speed of the wheel; and determining an orientation Jacobian based at least in part on the orientation of the initial estimated wheel velocity and the steering angle. 
     Clause S: The one or more non-transitory computer-readable media of clause R, wherein performing the iterative least squares algorithm further comprises: determining a magnitude weight using a first Cauchy loss function based at least in part on the magnitude error and the magnitude Jacobian; determining an orientation weight using a second Cauchy loss function based at least in part on the orientation error and the orientation Jacobian; and determining the estimated velocity based on the initial estimated velocity, the magnitude error, the magnitude Jacobian, the magnitude weight, the orientation error, the orientation Jacobian and the orientation weight. 
     Clause T: The one or more non-transitory computer-readable media of clause N, wherein determining the estimated velocity comprises performing an iterative reweighted Gauss-Newton algorithm. 
     While the example clauses described above are described with respect to one particular implementation, it should be understood that, in the context of this document, the content of the example clauses may also be implemented via a method, device, system, a computer-readable medium, and/or another implementation. Additionally, any of examples A-T may be implemented alone or in combination with any other one or more of the examples A-T. 
     CONCLUSION 
     While one or more examples of the techniques described herein have been described, various alterations, additions, permutations and equivalents thereof are included within the scope of the techniques described herein. 
     In the description of examples, reference is made to the accompanying drawings that form a part hereof, which show by way of illustration specific examples of the claimed subject matter. It is to be understood that other examples can be used and that changes or alterations, such as structural changes, can be made. Such examples, changes or alterations are not necessarily departures from the scope with respect to the intended claimed subject matter. While the steps herein can be presented in a certain order, in some cases the ordering can be changed so that certain inputs are provided at different times or in a different order without changing the function of the systems and methods described. The disclosed procedures could also be executed in different orders. Additionally, various computations that are herein need not be performed in the order disclosed, and other examples using alternative orderings of the computations could be readily implemented. In addition to being reordered, the computations could also be decomposed into sub-computations with the same results.