Patent Publication Number: US-2023150517-A1

Title: Systems and methods for determining an estimated weight of a vehicle

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 17/532,209 filed Nov. 22, 2021 and titled “SYSTEMS AND METHODS FOR DETERMINING AN ESTIMATED WEIGHT OF A VEHICLE”, which claims priority to U.S. Provisional Patent Application No. 63/279,737 filed Nov. 16, 2021 and titled “SYSTEMS AND METHODS FOR DETERMINING AN ESTIMATED WEIGHT OF A VEHICLE”, the contents of which are incorporated herein by reference for all purposes. 
    
    
     FIELD 
     The embodiments described herein generally relate to weight estimation, and in particular, to determining an estimated weight of a vehicle. 
     BACKGROUND 
     The following is not an admission that anything discussed below is part of the prior art or part of the common general knowledge of a person skilled in the art. 
     Knowledge regarding the weight of a vehicle can be useful for a variety of reasons. For example, the weight of a vehicle can affect whether the vehicle is subject to certain regulatory restrictions. Commercial motor vehicles are often subject to regulatory requirements that depend on their load. For instance, commercial motor vehicles may be restricted from carrying loads beyond certain weight limits to prevent overloading. Similarly, commercial motor vehicles may be prohibited from traveling in certain geographical areas based on their weight. Commercial motor vehicles may also be required to meet a particular fuel economy that can be affected by their load. Knowing the weight of a vehicle can be useful to ensure compliance with regulatory requirements. However, it can be difficult to measure the weight of a vehicle. 
     One way of measuring for the weight of a vehicle is using an external weighing device, such as a truck scale or weighbridge. However, these devices are not always available and cannot measure the weight of a vehicle during operation (e.g., when the vehicle is in transport). Another method of measuring the weight of a vehicle is using load sensors installed in the vehicle. However, installing load sensors into commercial motor vehicles can be difficult, expensive, and inaccurate. 
     SUMMARY 
     The following introduction is provided to introduce the reader to the more detailed discussion to follow. The introduction is not intended to limit or define any claimed or as yet unclaimed invention. One or more inventions may reside in any combination or sub-combination of the elements or process steps disclosed in any part of this document including its claims and figures. 
     In accordance with a broad aspect, there is provided a system for determining an estimated weight of a vehicle. The system includes at least one data storage and at least one processor. The at least one data storage is configured to store vehicle data associated with the vehicle. The vehicle data includes a plurality of vehicle parameters collected during operation of the vehicle. The at least one processor is in communication with the at least one data storage. The at least one processor configured to: identify a plurality of vehicle maneuvers based on the vehicle data, each vehicle maneuver being associated with a portion of the vehicle data, each portion of the vehicle data including a measured torque profile; generate a plurality of simulated torque profiles for each vehicle maneuver, each simulated torque profile being generated using a vehicle dynamics model based on at least some of the portion of the vehicle data associated with the corresponding vehicle maneuver and a candidate vehicle weight; generate a plurality of error profiles, an error profile being generated for each vehicle maneuver based on differences between the plurality of simulated torque profiles and the measured torque profile corresponding to that vehicle maneuver; and determine the estimated weight of the vehicle based on the plurality of error profiles. 
     In some embodiments, each portion of the vehicle data associated with one of the plurality of vehicle maneuvers may include a measured speed profile. 
     In some embodiments, each simulated torque profile may be generated using the vehicle dynamics model based on the measured speed profile associated with the corresponding vehicle maneuver and the candidate vehicle weight. 
     In some embodiments, the error profile for each vehicle maneuver may be generated based on differences between an area under a curve of each of the plurality of simulated torque profiles and an area under a curve of the measured torque profile corresponding to that vehicle maneuver. 
     In some embodiments, determining the estimated weight of the vehicle may involve minimizing the plurality of error profiles. 
     In some embodiments, determining the estimated weight of the vehicle may involve identifying a plurality of candidate vehicle weights, a candidate vehicle weight being identified for each error profile, each candidate vehicle weight minimizing the corresponding error profile. 
     In some embodiments, determining the estimated weight of the vehicle may involve determining the estimated weight of the vehicle based on an average of the identified candidate vehicle weights that minimize the corresponding error profiles. 
     In some embodiments, the average of the identified candidate vehicle weights may be a weighted average; and the identified candidate vehicle weights may be weighted based on a sensitivity of the corresponding error profiles. 
     In some embodiments, the sensitivity of each error profile may correspond to a slope of that error profile. 
     In some embodiments, the at least one processor may be further configured to: determine a load state of the vehicle based on the estimated weight of the vehicle. 
     In some embodiments, determining the load state of the vehicle may involve: determining the vehicle is in a loaded state if the estimated weight of the vehicle satisfies a predetermined vehicle weight threshold; and determining the vehicle is in an unloaded state if the estimated weight of the vehicle does not satisfy the predetermined vehicle weight threshold. 
     In some embodiments, the predetermined vehicle weight threshold may be a first predetermined vehicle weight threshold; and determining the load state of the vehicle may involve determining the vehicle is in an overloaded state if the estimated weight of the vehicle satisfies a second predetermined vehicle weight threshold. 
     In some embodiments, the at least one processor may be further configured to: determine a fuel economy of the vehicle based on the estimated weight of the vehicle. 
     In some embodiments, each plurality of simulated torque profiles may correspond to a plurality of candidate vehicle weights; and within each plurality of simulated torque profiles, each simulated torque profile may correspond to a different one of the candidate vehicle weights in the plurality of candidate vehicle weights. 
     In some embodiments, identifying the plurality of vehicle maneuvers may involve: identifying portions of the vehicle data that meet at least one predetermined vehicle condition associated with the vehicle dynamics model. 
     In some embodiments, the at least one predetermined vehicle condition may include propulsion of the vehicle. 
     In some embodiments, the at least one predetermined vehicle condition may include non-turning of the vehicle. 
     In some embodiments, the at least one predetermined vehicle condition may include non-braking of the vehicle. 
     In some embodiments, the at least one predetermined vehicle condition may include changes in vehicle elevation being less than a predetermined elevation change threshold. 
     In some embodiments, the at least one processor may be remotely located from the vehicle. 
     In accordance with a broad aspect, there is provided a method for determining an estimated weight of a vehicle. The method involves operating at least one processor to: receive vehicle data associated with the vehicle, the vehicle data including a plurality of vehicle parameters collected during operation of the vehicle; identify a plurality of vehicle maneuvers based on the vehicle data, each vehicle maneuver being associated with a portion of the vehicle data, each portion of the vehicle data including a measured torque profile; generate a plurality of simulated torque profiles for each vehicle maneuver, each simulated torque profile being generated using a vehicle dynamics model based on at least some of the portion of the vehicle data associated with the corresponding vehicle maneuver and a candidate vehicle weight; generate a plurality of error profiles, an error profile being generated for each vehicle maneuver based on differences between the plurality of simulated torque profiles and the measured torque profile corresponding to that vehicle maneuver; and determine the estimated weight of the vehicle based on the plurality of error profiles. 
     In some embodiments, each portion of the vehicle data associated with one of the plurality of vehicle maneuvers may include a measured speed profile. 
     In some embodiments, each simulated torque profile may be generated using the vehicle dynamics model based on the measured speed profile associated with the corresponding vehicle maneuver and the candidate vehicle weight. 
     In some embodiments, the error profile for each vehicle maneuver may be generated based on differences between an area under a curve of each of the plurality of simulated torque profiles and an area under a curve of the measured torque profile corresponding to that vehicle maneuver. 
     In some embodiments, determining the estimated weight of the vehicle may involve minimizing the plurality of error profiles. 
     In some embodiments, determining the estimated weight of the vehicle may involve identifying a plurality of candidate vehicle weights, a candidate vehicle weight being identified for each error profile, each candidate vehicle weight minimizing the corresponding error profile. 
     In some embodiments, determining the estimated weight of the vehicle may involve determining the estimated weight of the vehicle based on an average of the identified candidate vehicle weights that minimize the corresponding error profiles. 
     In some embodiments, the average of the identified candidate vehicle weights may be a weighted average; and the identified candidate vehicle weights may be weighted based on a sensitivity of the corresponding error profiles. 
     In some embodiments, the sensitivity of each error profile may correspond to a slope of that error profile. 
     In some embodiments, the method may further involve operating the at least one processor to: determine a load state of the vehicle based on the estimated weight of the vehicle. 
     In some embodiments, determining the load state of the vehicle may involve: determining the vehicle is in a loaded state if the estimated weight of the vehicle satisfies a predetermined vehicle weight threshold; and determining the vehicle is in an unloaded state if the estimated weight of the vehicle does not satisfy the predetermined vehicle weight threshold. 
     In some embodiments, the predetermined vehicle weight threshold may be a first predetermined vehicle weight threshold; and determining the load state of the vehicle may involve determining the vehicle is in an overloaded state if the estimated weight of the vehicle satisfies a second predetermined vehicle weight threshold. 
     In some embodiments, the method may further involve operating the at least one processor to: determine a fuel economy of the vehicle based on the estimated weight of the vehicle. 
     In some embodiments, each plurality of simulated torque profiles may correspond to a plurality of candidate vehicle weights; and within each plurality of simulated torque profiles, each simulated torque profile may correspond to a different one of the candidate vehicle weights in the plurality of candidate vehicle weights. 
     In some embodiments, identifying the plurality of vehicle maneuvers may involve: identifying portions of the vehicle data that meet at least one predetermined vehicle condition associated with the vehicle dynamics model. 
     In some embodiments, the at least one predetermined vehicle condition may include propulsion of the vehicle. 
     In some embodiments, the at least one predetermined vehicle condition may include non-turning of the vehicle. 
     In some embodiments, the at least one predetermined vehicle condition may include non-braking of the vehicle. 
     In some embodiments, the at least one predetermined vehicle condition may include changes in vehicle elevation being less than a predetermined elevation change threshold. 
     In some embodiments, the at least one processor may be remotely located from the vehicle. 
     In accordance with a broad aspect, there is provided a method for determining an estimated weight of a vehicle, the method involves operating at least one processor to: receive vehicle data associated with the vehicle, the vehicle data including a plurality of vehicle parameters collected during operation of the vehicle; identify a plurality of vehicle maneuvers based on the vehicle data, each vehicle maneuver being associated with a portion of the vehicle data, each portion of the vehicle data including a measured torque profile; identify a previous comparable vehicle maneuver for each vehicle maneuver; receive a plurality of simulated torque profiles for each previous comparable vehicle maneuver; generate a plurality of error profiles, an error profile being generated for each vehicle maneuver based on differences between the plurality of simulated torque profiles and the measured torque profile corresponding to that vehicle maneuver; and determine the estimated weight of the vehicle by minimizing the plurality of error profiles. 
     In some embodiments, each portion of the vehicle data associated with one of the plurality of vehicle maneuvers can include an identifying profile; and identifying the previous comparable vehicle maneuver for each vehicle maneuver can involve: comparing the identifying profile associated with the vehicle maneuver with a plurality of previous representative identifying profiles associated with a plurality of previous representative vehicle maneuvers. 
     In some embodiments, comparing the identifying profile with the plurality of previous representative identifying profiles can involve: determining a similarity score between the identifying profile and each previous representative identifying profile. 
     In some embodiments, determining the similarity score between the identifying profile and each previous representative identifying profile can involve using a dynamic time warping algorithm to determine a cumulative distance between the identifying profile and each previous representative identifying profile. 
     In some embodiments, the identifying profile can include an acceleration profile and the plurality of previous representative identifying profiles can include a plurality of previous representative acceleration profiles. 
     In some embodiments, the identifying profile can include an elevation profile and the plurality of previous representative identifying profiles can include a plurality of previous representative elevation profiles. 
     In some embodiments, determining the estimated weight of the vehicle can involve identifying a plurality of candidate vehicle weights, a candidate vehicle weight being identified for each error profile, each candidate vehicle weight minimizing the corresponding error profile. 
     In some embodiments, determining the estimated weight of the vehicle can involve determining the estimated weight of the vehicle based on an average of the identified candidate vehicle weights that minimize the corresponding error profiles. 
     In some embodiments, the average of the identified candidate vehicle weights can be a weighted average; and the identified candidate vehicle weights can be weighted based on a sensitivity of the corresponding error profiles. 
     In some embodiments, identifying the plurality of vehicle maneuvers can involve: identifying portions of the vehicle data that meet at least one predetermined vehicle condition associated with a vehicle dynamics model used to generate the plurality of simulated torque profiles. 
     In accordance with a broad aspect, there is provided a system for determining an estimated weight of a vehicle, the system including: at least one data storage configured to store vehicle data associated with the vehicle, the vehicle data including a plurality of vehicle parameters collected during operation of the vehicle; and at least one processor in communication with the at least one data storage, the at least one processor configured to: identify a plurality of vehicle maneuvers based on the vehicle data, each vehicle maneuver being associated with a portion of the vehicle data, each portion of the vehicle data including a measured torque profile; identify a previous comparable vehicle maneuver for each vehicle maneuver; receive a plurality of simulated torque profiles for each previous comparable vehicle maneuver; generate a plurality of error profiles, an error profile being generated for each vehicle maneuver based on differences between the plurality of simulated torque profiles and the measured torque profile corresponding to that vehicle maneuver; and determine the estimated weight of the vehicle by minimizing the plurality of error profiles. 
     In some embodiments, each portion of the vehicle data associated with one of the plurality of vehicle maneuvers can include an identifying profile; and identifying the previous comparable vehicle maneuver for each vehicle maneuver can involve: comparing the identifying profile associated with the vehicle maneuver with a plurality of previous representative identifying profiles associated with a plurality of previous representative vehicle maneuvers. 
     In some embodiments, comparing the identifying profile with the plurality of previous representative identifying profiles can involve: determining a similarity score between the identifying profile and each previous representative identifying profile. 
     In some embodiments, determining the similarity score between the identifying profile and each previous representative identifying profile can involve using a dynamic time warping algorithm to determine a cumulative distance between the identifying profile and each previous representative identifying profile. 
     In some embodiments, the identifying profile can include an acceleration profile and the plurality of previous representative identifying profiles can include a plurality of previous representative acceleration profiles. 
     In some embodiments, the identifying profile can include an elevation profile and the plurality of previous representative identifying profiles can include a plurality of previous representative elevation profiles. 
     In some embodiments, determining the estimated weight of the vehicle can involve identifying a plurality of candidate vehicle weights, a candidate vehicle weight being identified for each error profile, each candidate vehicle weight minimizing the corresponding error profile. 
     In some embodiments, determining the estimated weight of the vehicle can involve determining the estimated weight of the vehicle based on an average of the identified candidate vehicle weights that minimize the corresponding error profiles. 
     In some embodiments, the average of the identified candidate vehicle weights can be a weighted average; and the identified candidate vehicle weights can be weighted based on a sensitivity of the corresponding error profiles. 
     In some embodiments, identifying the plurality of vehicle maneuvers can involve: identifying portions of the vehicle data that meet at least one predetermined vehicle condition associated with a vehicle dynamics model used to generate the plurality of simulated torque profiles. 
     In accordance with a broad aspect, there is provided a method for preprocessing vehicle weight estimations, the method involving operating at least one processor to: receive vehicle data associated with a plurality of vehicles, the vehicle data including a plurality of vehicle parameters collected during operation of the plurality of vehicles; identify a plurality of vehicle maneuvers based on the vehicle data, each vehicle maneuver being associated with a portion of the vehicle data, each portion of the vehicle data including an identifying profile; identify a plurality of representative vehicle maneuvers from the plurality of vehicle maneuvers based on the identifying profile associated with each vehicle maneuver; generate a plurality of simulated torque profiles for each representative vehicle maneuver, each simulated torque profile being generated using a vehicle dynamics model based on at least some of the portion of the vehicle data associated with the corresponding representative vehicle maneuver and a candidate vehicle weight; and store each plurality of simulated torque profiles in association with the identifying profile for each representative vehicle maneuver. 
     In some embodiments, identifying the plurality of representative vehicle maneuvers from the plurality of vehicle maneuvers can involve: comparing each identifying profile with each other identifying profile. 
     In some embodiments, comparing the identifying profile with the plurality of previous representative identifying profiles can involve: determining a similarity score between each identifying profile; and eliminating at least some of the vehicle maneuvers from being identified as representative vehicle maneuvers based on the similarity score between each identifying profile. 
     In some embodiments, determining the similarity score between each identifying profile can involve using a dynamic time warping algorithm to determine a cumulative distance between each identifying profile. 
     In some embodiments, the identifying profile can include an acceleration profile. 
     In some embodiments, the identifying profile can include an elevation profile. 
     In some embodiments, each portion of the vehicle data associated with one of the plurality of vehicle maneuvers can include a measured speed profile. 
     In some embodiments, each simulated torque profile can be generated using the vehicle dynamics model based on the measured speed profile associated with the corresponding vehicle maneuver and the candidate vehicle weight. 
     In some embodiments, identifying the plurality of vehicle maneuvers can involve: identifying portions of the vehicle data that meet at least one predetermined vehicle condition associated with the vehicle dynamics model. 
     In some embodiments, the at least one predetermined vehicle condition can include acceleration of the vehicle and changes in the elevation of the vehicle satisfying a predetermined threshold. 
     In accordance with a broad aspect, there is provided a system for preprocessing vehicle weight estimations, the system includes: at least one data storage configured to store vehicle data associated with a plurality of vehicles, the vehicle data including a plurality of vehicle parameters collected during operation of the plurality of vehicles; and at least one processor in communication with the at least one data storage, the at least one processor configured to: identify a plurality of vehicle maneuvers based on the vehicle data, each vehicle maneuver being associated with a portion of the vehicle data, each portion of the vehicle data including an identifying profile; identify a plurality of representative vehicle maneuvers from the plurality of vehicle maneuvers based on the identifying profile associated with each vehicle maneuver; generate a plurality of simulated torque profiles for each representative vehicle maneuver, each simulated torque profile being generated using a vehicle dynamics model based on at least some of the portion of the vehicle data associated with the corresponding representative vehicle maneuver and a candidate vehicle weight; and store each plurality of simulated torque profiles in association with the identifying profile for each representative vehicle maneuver. 
     In some embodiments, identifying the plurality of representative vehicle maneuvers from the plurality of vehicle maneuvers can involve: comparing each identifying profile with each other identifying profile. 
     In some embodiments, comparing the identifying profile with the plurality of previous representative identifying profiles can involve: determining a similarity score between each identifying profile; and eliminating at least some of the vehicle maneuvers from being identified as representative vehicle maneuvers based on the similarity score between each identifying profile. 
     In some embodiments, determining the similarity score between each identifying profile can involve using a dynamic time warping algorithm to determine a cumulative distance between each identifying profile. 
     In some embodiments, the identifying profile can include an acceleration profile. 
     In some embodiments, the identifying profile can include an elevation profile. 
     In some embodiments, each portion of the vehicle data associated with one of the plurality of vehicle maneuvers can include a measured speed profile. 
     In some embodiments, each simulated torque profile can be generated using the vehicle dynamics model based on the measured speed profile associated with the corresponding vehicle maneuver and the candidate vehicle weight. 
     In some embodiments, identifying the plurality of vehicle maneuvers can involve identifying portions of the vehicle data that meet at least one predetermined vehicle condition associated with the vehicle dynamics model. 
     In some embodiments, the at least one predetermined vehicle condition can include acceleration of the vehicle and changes in the elevation of the vehicle satisfying a predetermined threshold. 
     In accordance with a broad aspect, there is provided a non-transitory computer readable medium having instructions stored thereon executable by at least one processor to implement any of the methods described herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Several embodiments will be described in detail with reference to the drawings, in which: 
         FIG.  1    is a block diagram of various components interacting with an example fleet management system and a plurality of telematic devices, in accordance with an embodiment; 
         FIG.  2    is a block diagram of the fleet management system shown in  FIG.  1    interacting with one of the telematics devices and vehicles shown in  FIG.  1   , in accordance with an embodiment; 
         FIG.  3    is a free body diagram of one of the vehicles shown in  FIG.  1   , in accordance with an embodiment; 
         FIG.  4    is a flowchart of an example method for determining an estimated weight of a vehicle, in accordance with an embodiment; 
         FIG.  5    is a plurality of graphs of example vehicle data, in accordance with an embodiment; 
         FIG.  6 A  is a graph of example speed data containing a plurality of example measured speed profiles, in accordance with an embodiment; 
         FIG.  6 B  is a graph of example torque data containing a plurality of example measured torque profiles, in accordance with an embodiment; 
         FIG.  7    is a block diagram of an example vehicle dynamics model, in accordance with an embodiment; 
         FIG.  8 A  is a graph of an example measured torque profile, in accordance with an embodiment; 
         FIG.  8 B  is a plurality of graphs of a plurality of example simulated torque profiles corresponding to a plurality of example candidate vehicle weights, in accordance with an embodiment; 
         FIG.  9    is a graph of a plurality of example error profiles, in accordance with an embodiment; 
         FIG.  10    is a flowchart of an example method for preprocessing vehicle weight estimations, in accordance with an embodiment; 
         FIG.  11    is a flowchart of another example method for determining an estimated weight of a vehicle, in accordance with an embodiment; and 
         FIGS.  12 A and  12 B  are graphs illustrating an example implementation of a dynamic time warping algorithm. 
     
    
    
     The drawings, described below, are provided for purposes of illustration, and not of limitation, of the aspects and features of various examples of embodiments described herein. For simplicity and clarity of illustration, elements shown in the drawings have not necessarily been drawn to scale. The dimensions of some of the elements may be exaggerated relative to other elements for clarity. It will be appreciated that for simplicity and clarity of illustration, where considered appropriate, reference numerals may be repeated among the drawings to indicate corresponding or analogous elements or steps. 
     DETAILED DESCRIPTION 
     Various systems or methods will be described below to provide an example of an embodiment of the claimed subject matter. No embodiment described below limits any claimed subject matter and any claimed subject matter may cover methods or systems that differ from those described below. The claimed subject matter is not limited to systems or methods having all of the features of any one system or method described below or to features common to multiple or all of the apparatuses or methods described below. It is possible that a system or method described below is not an embodiment that is recited in any claimed subject matter. Any subject matter disclosed in a system or method described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim or dedicate to the public any such subject matter by its disclosure in this document. 
     Referring to  FIG.  1   , there is shown an example fleet management system  110  for managing a plurality of vehicles  120  equipped with a plurality of telematics devices  130 . In operation, the telematics devices  130  can collect various data associated with the vehicles  120  (i.e., vehicle data) and share the vehicle data with the fleet management system  110 . The fleet management system  110  can be remotely located from the telematic devices  130  and the vehicles  120 . 
     The vehicles  120  may include any machines for transporting goods or people. For example, the vehicles  120  can include motor vehicles, such as, but not limited to, motorcycles, cars, trucks, and/or buses. The motor vehicles can be gas, diesel, electric, hybrid, and/or alternative fuel. In some cases, the vehicles  120  may include other kinds of vehicles, such as, but not limited to, railed vehicles (e.g., trains, trams), watercraft (e.g., ships, boats), aircraft (e.g., airplanes, helicopters), and/or spacecraft. Each vehicle  120  can be equipped with a telematics device  130 . 
     The telematics devices  130  can be standalone devices that are removably installed in the vehicles  120 . Alternatively, the telematics devices  130  can be integrated components that are integral with the vehicles  120 . The telematics devices  130  can collect various vehicle data and share the vehicle data with the fleet management system  110 . The vehicle data may include any information, parameters, attributes, characteristics, and/or features associated with the vehicles  120 . For example, the vehicle data can include, but is not limited to, location data, speed data, acceleration data, engine data, fluid level data (e.g., oil, coolant, and/or washer fluid), and/or energy level data (e.g., battery and/or fuel level). 
     The fleet management system  110  can process the vehicle data collected from the telematics devices  130  to provide various analysis and reporting. For example, the fleet management system  110  can process the vehicle data to gain additional information regarding the vehicles  120 , such as, but not limited to, trip distances/times, idling times, harsh braking/driving, usage rate, and/or fuel economy. Various data analytics and machine learning techniques may be used by the fleet management system  110  to process the vehicle data. The vehicle data can then be used to manage various aspects of the vehicles  120 , such as, but not limited to, route planning, vehicle maintenance, driver compliance, asset utilization, and/or fuel management. In this manner, the fleet management system  110  can improve the productivity, efficiency, safety, and/or sustainability of the vehicles  120 . 
     A plurality of computing devices  150  can provide access to the fleet management system  110  to a plurality of users  160 . For example, the users  160  may use the computing devices  150  to retrieve various vehicle data collected and/or processed by the fleet management system  110 . The computing devices  150  can be any computers or computer systems, such as, but not limited to, personal computers, portable computers, wearable computers, workstations, desktops, laptops, smartphones, tablets, smartwatches, PDAs (personal digital assistants), and/or mobile devices. The computing devices  150  can be remotely located from the fleet management system  110 , telematic devices  130  and vehicles  120 . 
     The fleet management system  110 , telematics devices  130 , and computing devices  150  can communicate through a network  140 . The network  140  may include more than one network. The network  140  may be wireless, wired, or a combination thereof. The network  140  may employ any communication protocol and utilize any communication medium. For example, the network  140  may include, but is not limited to, Wi-Fi™ networks, Ethernet networks, Bluetooth™ networks, NFC (near-field communication) networks, radio networks, cellular networks, and/or satellite networks. The network  140  may be private, public, or a combination thereof. For example, the network  140  may include, but is not limited to, LANs (local area networks), WANs (wide area networks), and/or the Internet. The network  140  may also facilitate communication with other devices and systems that are not shown. 
     Reference will now be made to  FIG.  2    to further explain the operation of the fleet management system  110 , telematics devices  130 , and vehicles  120 . In the illustrated example, the fleet management system  110  in communication with a telematics device  130  that is installed in a vehicle  120 . As shown, the fleet management system  110  can include a processor  112 , a data storage  114 , and a communication interface  116 . Each of these components can communicate with each other. Each of these components may be combined into fewer components or divided into additional subcomponents. Two or more of these components and/or subcomponents may be distributed across a wide geographical area. The fleet management system  110  can be implemented using one or more computers or computer systems. For example, the fleet management system  110  may be implemented using one or more servers. The one or more servers can be distributed across a wide geographical area. In some embodiments, the fleet management system  110  may be implemented using a cloud computing platform. 
     The processor  112  can control the operation of the fleet management system  110 . The processor  112  can be implemented using any suitable processing devices or systems, such as, but not limited to, CPUs (central processing units), GPUs (graphics processing units), FPGAs, (field programmable gate arrays), ASICs (application specific integrated circuits), DSPs (digital signal processors), NPUs (neural processing units), QPUs (quantum processing units), microprocessors, and/or controllers. The processor  112  can execute various instructions, programs, and/or software stored on the data storage  114  to implement various methods described herein. For example, the processor  112  can process various vehicle data collected by the fleet management system  110  from the telematics devices  130 . 
     The data storage  114  can store various data for the fleet management system  110 . The data storage  114  can be implemented using any suitable data storage devices or systems, such as, but not limited to, RAM (random access memory), ROM (read only memory), flash memory, HDD (hard disk drives), SSD (solid-state drives), magnetic tape drives, optical disc drives, and/or memory cards. The data storage  114  may include volatile memory, non-volatile memory, or a combination thereof. The data storage  114  may include non-transitory computer readable media. The data storage  114  can store various instructions, programs, and/or software that can be executed by the processor  112  to implement various methods described herein. The data storage  114  may store various vehicle data collected from the telematics devices  130  and/or processed by the processor  112 . 
     The communication interface  116  can enable communication between the fleet management system  110  and other devices or systems, such as the telematics device  130 . The communication interface  116  can be implemented using any suitable communication devices or systems. For example, the communication interface  116  may include various physical connectors, ports, or terminals, such as, but not limited to, USB (universal serial bus), Ethernet, Thunderbolt, Firewire, SATA (serial advanced technology attachment), PCI (peripheral component interconnect), HDMI (high-definition multimedia interface), and/or DisplayPort. The communication interface  116  can also include various wireless interface components to connect to wireless networks, such as, but not limited to, Wi-Fi™, Bluetooth™, NFC, cellular, and/or satellite. The communication interface  116  can enable various inputs and outputs to be received at and sent from the fleet management system  110 . For example, the communication interface  116  may be used to retrieve vehicle data from the telematics device  130 . 
     The telematics device  130  also can include a processor  132 , a data storage  134 , and a communication interface  136 . Additionally, the telematics device  130  can include a sensor  138 . Each of these components can communicate with each other. Each of these components may be combined into fewer components or divided into additional subcomponents. 
     The processor  132  can control the operation of the telematics device  130 . Like the processor  112  of the fleet management system  110 , the processor  132  of the telematics device  130  can be implemented using any suitable processing devices or systems. The processor  132  can execute various instructions, programs, and/or software stored on the data storage  134  to implement various methods described herein. For example, the processor  132  can process various vehicle data collected from the vehicle components  142  or the sensor  138 . 
     The data storage  134  can store various data for the telematics device  130 . Like the data storage  114  of the fleet management system  110 , the data storage  134  of the telematics device  130  can be implemented using any suitable data storage devices or systems. The data storage  134  can store various instructions, programs, and/or software that can be executed by the processor  132  to implement various methods described herein. The data storage  134  can also store various vehicle data collected from the vehicle components  142  or the sensor  138 . 
     The communication interface  136  can enable communication between the telematics device  130  and other devices or systems, such as the fleet management system  110  and vehicle components  142 . Like the communication interface  116  of the fleet management system  110 , the communication interface  136  of the telematics device  130  can be implemented using any suitable communication devices or systems. The communication interface  116  can enable various inputs and outputs to be received at and sent from the telematics device  130 . For example, the communication interface  116  may be used collect vehicle data from the vehicle components  142  and sensor  138  and/or to send vehicle data to the fleet management system  110 . 
     The sensor  138  can detect and/or measure various environmental events and/or changes. The sensor  138  can include any suitable sensing devices or systems, including, but not limited to, location sensors, velocity sensors, acceleration sensors, orientation sensors, vibration sensors, proximity sensors, temperature sensors, humidity sensors, pressure sensors, optical sensors, and/or audio sensors. When the telematics device  130  is installed in the vehicle  120 , the sensor  138  can be used to collect vehicle data that may not be obtainable from the vehicle components  142 . For example, the sensor  138  may include a satellite navigation device, such as, but not limited to, a GPS (global positioning system) receiver, which can measure the location of the vehicle  120 . Additionally, or alternatively, the sensor  138  may include accelerometers, gyroscopes, magnetometers, and/or IMUs (inertial measurement units), which can measure the acceleration and/or orientation of the vehicle  120 . 
     The telematics device  130  can be installed within the vehicle  120 , removably or integrally. The vehicle  120  can include vehicle components  122  and a vehicle interface  124 . Each of these components may be combined into fewer components or divided into additional subcomponents. 
     The vehicle components  122  can include any subsystems, parts, and/or subcomponents of the vehicle  120 . The vehicle components  122  can be used to operate and control the vehicle  120 . For example, the vehicle components  122  can include, but are not limited to, powertrains, engines, transmissions, steering, braking, seating, batteries, doors, and/or suspensions. The telematics device  130  can collect various vehicle data from the vehicle components  122 . For example, the telematics device  130  may communicate with one or more ECUs (electronic control units) that control the vehicle components  142  and/or one or more internal vehicle sensors. 
     The vehicle interface  124  can facilitate communication between the vehicle components  122  and other devices or systems. The vehicle interface  124  can include any suitable communication devices or systems. For example, the vehicle interface  124  may include, but is not limited to, an ODB-II (on-board diagnostics) port and/or CAN bus (controller area network) port. The vehicle interface  124  can be used by the telematics device  130  to collect vehicle data from the vehicle components  122 . For example, the communication interface  136  of the telematics device  130  can be connected to the vehicle interface  124  to communicate with the vehicle components  122 . 
     Referring to  FIG.  3   , there is shown a free body diagram of a vehicle  120 . As shown, the vehicle  120  can be subject to various forces, including, but not limited to, a drive force (f drive ), a grade resistance (f grade ), a rolling resistance (f roll ), and an air resistance (f air ). The drive force can represent the propulsion of the vehicle  120 , the grade resistance can represent the gravitational effect of the incline of the driving surface, the roll resistance can represent the friction of the driving surface, and the air resistance can represent the drag or friction of the air surrounding the vehicle  120 . One way of determining an estimated weight of the vehicle  120  is an inductive approach by observing the forces applied to the vehicle  120 . The inductive approach can involve measuring, estimating, and/or calculating the net force (f net ) acting on the vehicle  120  and the acceleration (a) of the vehicle  120 . For example, the estimated weight (m) of the vehicle  120  can be determined using the following equation: 
     
       
      
       m=f 
       net 
       /a  
      
     
     The net force (f net ) acting on the vehicle  120  can be determined using the following equation: 
     
       
      
       f 
       net 
       =f 
       drive 
       −f 
       grade 
       −f 
       roll 
       −f 
       air  
      
     
     One disadvantage of this approach is that it can be difficult to measure, estimate, and/or calculate the forces acting on the vehicle  120 . Inaccuracies in determining the forces acting on the vehicle  120  can lead to significant weight estimation errors. For example, it may be difficult to directly measure the grade resistance (f grade ), during operation of the vehicle  120 . However, estimating and/or calculating the rolling resistance (f grade ) may also be difficult because it may depend on various dynamic factors related to the driving surface, such as, but not limited to, material, temperature, moisture, etc. It may not be possible to accurately account for all of these factors at various points during a trip. 
     Referring to  FIG.  4   , there is shown an example method  400  for determining an estimated weight of a vehicle  120 . In contrast with the deductive approach described with reference to  FIG.  3   , method  400  can use an inductive approach based on a vehicle dynamics model. The vehicle dynamics model can be used to simulate various aspects of the vehicle  120 , instead of directly measuring, estimating, and/or calculating them. An advantage of this approach is that method  400  can use vehicle data that is readily available throughout a trip (e.g., from telematics device  130 ) to dynamically generate weight estimates corresponding to various points during the trip. 
     Method  400  can be implemented by the fleet management system  110 , one or more telematics devices  130 , or a combination thereof. That is, method  400  can be implemented by operating at least one processor of the fleet management system  110  and/or one or more telematics devices  130 . For example, method  400  can be implemented by the processor  112  and/or the processor  132  executing instructions stored on the data storage  114  and/or the data storage  134 . An advantage of executing one or more steps of method  400  at the fleet management system  110  (i.e., remote from the telematics device  130  and vehicle  120 ) is that less data processing may be completed at the telematics devices  130 . Hence, the hardware complexity and cost of the telematics devices  130  can be reduced. Furthermore, it may be easier to update and/or modify software running on the fleet management system  110  as compared to a telematics device  130  that has already been installed in a vehicle  120 . An advantage of executing one or more steps of method  400  at the telematics device  130  (i.e., remote from the fleet management system  110 ) is that less data may be transmitted to the fleet management system  110 . Hence, network usage and bandwidth on the network  140  can be reduced. This may reduce usage costs associated with the network  140 . 
     At  402 , vehicle data associated with the vehicle  120  can be received. For example, the telematics device  130  may receive vehicle data from the sensor  138  and/or vehicle components  122 . Alternatively, or additionally, the fleet management system  110  may receive vehicle data from a telematics device  130 . Alternatively, or additionally, the processor  112  and/or processor  132  may receive vehicle data from the data storage  114  and/or data storage  134 . 
     The vehicle data can include a plurality of vehicle parameters collected during operation of the vehicle  120 . As described herein, the vehicle data may include any information, parameters, attributes, characteristics, and/or features associated with the vehicles  120 . The vehicle data may vary depending on the vehicle dynamics model used by the method  400 . 
     Referring now to  FIG.  5   , there is shown example vehicle data  500 . As shown, the vehicle data  500  can include various time series of data points corresponding to various vehicle parameters. Each data point can represent the value of a particular vehicle parameter at a given time. In the illustrated example, the vehicle data  500  includes speed data  502 , torque data  504 , gear ratio data  506 , rotation data  508 , elevation data  510 , and acceleration data  512 . 
     The speed data  502  can represent the velocity, or rate of locational change of the vehicle  120 . The speed data can be obtained from a VSS (vehicle speed sensor), for example, located in the powertrain and/or ABS (anti-lock braking system) of the vehicle  120 . Alternatively, or additionally, the speed data can be calculated based on changes in location data over time, for example, obtained from sensor  138 . 
     The torque data  504  can represent the torque, or twisting/rotational force output by the vehicle  120 . The torque data  504  can be in units of torque and/or a percentage of maximum torque. The torque data  504  can include engine torque data, representing the torque output at the engine of the vehicle  120 , and/or wheel torque data, representing the torque output at the wheel of the vehicle  120 . The engine torque data can be obtained from the engine of the vehicle  120 , for example, from an internal sensor and/or ECU. The wheel torque data can be calculated based on the engine torque data and the gear ratio data  506 . For example, the wheel torque can be determined based on the following equation: 
       wheel torque=effective gear ratio×engine torque
 
     The rotational data  508  can represent the rotational speed, or rpm (revolutions per minute) generated by the vehicle  120 . The rotational data  508  can include engine rotational data, representing the rpm of the engine of the vehicle  120 , and/or wheel rotational data, representing the rpm of the wheels of the vehicle  120 . The engine rotational data can be obtained from a crankshaft position sensor of the vehicle  120 . The wheel rotational data can be obtained based on the speed data  502  and the circumference of the wheels. For example, the wheel rotational data can be determined using the following equation: 
     
       
         
           
             
               wheel 
               ⁢ 
                   
               RPM 
             
             = 
             
               
                 vehicle 
                 ⁢ 
                     
                 speed 
               
               
                 wheel 
                 ⁢ 
                     
                 circumference 
               
             
           
         
       
     
     The gear ratio data  506  can represent the effective gear ratio, or ratio between the rate of rotation output at the engine and at the wheels of the vehicle  120 . The gear ratio data  506  can be calculated based on the rotational data  508  of the vehicle. For example, the effective gear ratio can be determined using the following equation: 
     
       
         
           
             
               effective 
               ⁢ 
                   
               gear 
               ⁢ 
                   
               ratio 
             
             = 
             
               
                 engine 
                 ⁢ 
                     
                 rpm 
               
               
                 wheel 
                 ⁢ 
                     
                 rpm 
               
             
           
         
       
     
     Alternatively, the gear ratio data  506  can be calculated based on the transmission ratio (i e ) and differential ratio (i d ) of the vehicle  120 . For example, the effective gear ratio can be determined using the following equation: 
       effective gear ratio= i   e   i   d    
     The elevation data  510  can indicate the altitude, or distance above sea level of the vehicle  120 . The elevation data  510  can be calculated based on location data, for example, obtained from the sensor  138 . For example, the elevation data  510  can be determined by correlating the location data with topographic data. Alternatively, the elevation data  510  can be obtained from an altimeter of the telematic device  130  (e.g., sensor  138 ) or vehicle  120 . 
     The acceleration data  512  can indicate the acceleration, or the rate of change of the speed of the vehicle  120 . The acceleration data can be obtained from an accelerometer of the telematic device  130  (e.g., sensor  138 ), or vehicle  120 . Alternatively, the acceleration data  512  can be calculated based on the speed data  502 . For example, the acceleration can be determined using the following equation (where v 2  is the velocity of the vehicle at time t 2 , and v 1  is the velocity of the vehicle at time t 1 ): 
     
       
         
           
             acceleration 
             = 
             
               
                 
                   v 
                   2 
                 
                 - 
                 
                   v 
                   1 
                 
               
               
                 
                   t 
                   2 
                 
                 - 
                 
                   t 
                   1 
                 
               
             
           
         
       
     
     In some embodiments, the vehicle data  500  can be preprocessed prior to and/or subsequent to being received. For example, the vehicle data  500  may be received in various formats, standards, and/or protocols. The vehicle data  500  can be reformatted prior to being used for weight estimation. For instance, the vehicle data  500  may include data points that correspond to irregular and/or mismatched points in time. The vehicle data  500  can be interpolated so that the data points in each time series correspond to successive and/or equally spaced points in time. 
     Referring back to  FIG.  4   , at  404 , a plurality of vehicle maneuvers can be identified. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can identify the vehicle maneuvers. Each vehicle maneuver can be associated with a portion of the vehicle data  500 . For example, a vehicle maneuver may be associated with a portion of the speed data  502 , torque data  504 , gear ratio data  506 , rotation data  508 , elevation data  510 , and/or acceleration data  512 . A portion of the vehicle data  500  corresponding to a vehicle maneuver can be referred to as a profile. For example, a portion of the speed data  502  associated with a vehicle maneuver may be referred to as a measured speed profile. Similarly, a portion of the torque data  504  associated with a vehicle maneuver may be referred to as a measured torque profile. In some embodiments, each vehicle maneuver may be associated with a portion of the vehicle data  500  that includes a measured torque profile. In some embodiments, each vehicle maneuver may be associated with a portion of the vehicle data that includes a measured speed profile. 
     The plurality of vehicle maneuvers can be identified based on the vehicle data  500 . The criteria used to identify the vehicle maneuvers and portions of the vehicle data  500  can depend on the vehicle dynamics model used by method  400 . The vehicle maneuvers may be identified by identifying portions of the vehicle data  500  that satisfy one or more predetermined conditions associated with the vehicle dynamics model. The predetermined conditions may be related to underlying assumptions, rules, and/or requirements of the vehicle dynamics model. For example, the predetermined conditions may include the propulsion of the vehicle  120 . That is, the vehicle  120  is in acceleration and is being actively propelled or driven. The predetermined conditions may also include non-turning of the vehicle  120 . That is, the vehicle  120  is traveling in substantially straight trajectory, without turning. The predetermined conditions may also include non-braking of the vehicle  120 . That is, the vehicle  120  is not actively braking or decelerating. The predetermined conditions may also include changes in the elevation of the vehicle  120  being less than a predetermined elevation change threshold. That is, the vehicle  120  is not experiencing large inclines, declines, or other changes in elevation. The predetermined conditions may also include the speed of the vehicle  120  being greater than a predetermined speed threshold. For example, the speed of the vehicle  120  may be required to be greater than 5 m/s. The predetermined conditions may also include the effective gear of the vehicle  120  being less than a predetermined gear ratio threshold. For example, the effective gear of the vehicle  120  may be required to be less than 1. 
     Referring now to  FIGS.  6 A and  6 B , there is shown example speed data  600  and torque data  650 . As shown, portions of the speed data (i.e., measured speed profiles)  602  and torque data (i.e., measured torque profiles)  652  can be identified as vehicle maneuvers. In the illustrated example, the vehicle maneuvers correspond to portions of the vehicle data when the vehicle  120  was in acceleration (i.e., being actively propelled or driven). As shown, various measured speed profiles  602  and measured torque profiles  652  that satisfy this condition can be identified as vehicle maneuvers. 
     Referring back to  FIG.  4   , at  406 , a plurality of simulated torque profiles can be generated for each vehicle maneuver. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can generate the simulated torque profiles. Each simulated torque profile can be generated using a vehicle dynamics model. The vehicle dynamics model can be any suitable model for simulating the operation of the vehicle  120 . For example, the vehicle dynamics model may be a model generated using various modeling/simulation software, such as, but not limited to, MapleSim™, Simulink™, SystemModeler™, Dymola™, and/or SimulationX™. In various embodiments, the vehicle dynamics model can be a FMU (functional mock-up unit) and/or FMI (functional mock-up interface) that can interface with other software. 
     The vehicle dynamics model can generate the simulated torque profiles based on various input data. The input data can include various vehicle and/or other data. For example, the input data for each vehicle maneuver can include at least some of the portion of the vehicle data  500  associated that vehicle maneuver. For example, the input data can include the measured speed profile associated with the corresponding vehicle maneuver. The input data for each vehicle maneuver can also include a plurality of candidate vehicle weights. Each candidate vehicle weight can represent a presumed or putative weight of the vehicle  120 . Each simulated torque profile can correspond to one of the candidate vehicle weights. Accordingly, each simulated torque profile can represent a simulation or prediction of the torque data (i.e., torque profile) that could be measured during the vehicle maneuver if the vehicle  120  weight was the candidate vehicle weight. 
     Referring to  FIG.  8 B , there is shown an example of a plurality of simulated torque profiles  800 B. The plurality of simulated torque profiles  800 B can correspond to a particular vehicle maneuver. The plurality of simulated torque profiles  800 B can also correspond to a plurality of candidate vehicle weights (m 1 , m 2 , m 3 ). Each simulated torque profile  800 B can correspond to a different one of the candidate vehicle weights. For instance, in the illustrated example, a first simulated torque profile  802 B corresponds to a first candidate vehicle weight (m 1 ), a second simulated torque profile  804 B corresponds to a second candidate vehicle weight (m 2 ), and a third simulated torque profile  806 B corresponds to a third candidate vehicle weight (m 3 ). The simulated torque profiles  800 B can represent wheel torque and/or engine torque and may be in units of torque and/or a percentage of maximum torque. 
     Referring now to  FIG.  7   , there is shown an example vehicle dynamics model  700 . As shown, the vehicle dynamics model can receive various input data  702  and generate simulated torque profiles  704  based on the input data  702 . In the illustrated example, the input data  702  includes candidate vehicle weights, vehicle data, physical constants, and other model parameters. As described herein, the candidate vehicle weights can represent presumed or putative weights of the vehicle  120 . The vehicle data can include various vehicle data associated with the corresponding vehicle maneuvers, such as, but not limited to, measured speed profiles. The physical constants can include various physical coefficients, parameters, and/or constants that can be used by the vehicle dynamics model  700 , such as, but not limited to, wheel radii, vehicle cross-sectional dimensions, drag coefficients, roll coefficients, etc. The other model parameters can include auxiliary or secondary parameters that are specific to the vehicle dynamics model  700 . For example, the other model parameters may include PID (proportional integral derivative) controller parameters that can be used to adjust the sensitivity of the vehicle dynamics model  700 . 
     Referring back to  FIG.  4   , at  408 , a plurality of error profiles can be generated. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can generate the error profiles. An error profile can be generated for each vehicle maneuver based on differences between the plurality of simulated torque profiles and the measured torque profile corresponding to that vehicle maneuver. 
     Referring to  FIGS.  8 A and  8 B , there is shown an example measured torque profile  800 A and an example of a plurality of simulated torque profiles  800 B. In the illustrated example, the measured torque profile  800 A and simulated torque profiles  800 B correspond to the same vehicle maneuver. Accordingly, an error profile can be generated based on differences between the measured torque profile  800 A and each of the simulated torque profiles  800 B. Since each simulated torque profile  800 B corresponds to a different candidate vehicle weight (m 1 , m 2 , m 3 ), each error profile can represent the error of each candidate vehicle weight. 
     Referring to  FIG.  9   , there is shown a plurality of example error profiles  900 . As shown, each error profile can correspond to a particular vehicle maneuver. For instance, in the illustrated example, a first error profile  910  corresponds to a first vehicle maneuver (maneuver 1), a second error profile  920  corresponds to a second vehicle maneuver (maneuver 2), a third error profile  930  corresponds to a third vehicle maneuver (maneuver 3). Each error profile  900  can represent the error between the measured torque profile  800 A and the simulated torque profiles  800 B for the corresponding vehicle maneuver. Since each simulated torque profile  800 B can correspond to a particular candidate vehicle weight, each error profile  900  can represent the error of each candidate vehicle weight for a particular vehicle maneuver. 
     The differences between the simulated torque profiles  800 B and the measured torque profiles  800 A can be determined in various ways. In some embodiments, the differences can correspond to differences between the area under the curve of each of the simulated torque profiles  800 B and the area under of the curve of the measured torque profile  800 A. The differences may be the mean square error of the differences of the respective areas under the curves. An advantage of determining the differences in this manner is that noise and/or other errors in the torque profiles may have less of an effect on the area under the curve as compared to the torque profile itself. 
     Referring back to  FIG.  4   , at  410 , the estimated weight of the vehicle  120  can be determined based on the plurality of error profiles  900 . For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can determine the estimated weight of the vehicle  120 . This may involve minimizing and/or averaging the error profiles  900 . For example, referring back to  FIG.  9   , each error profile  900  can have a minimum that corresponds to a particular candidate vehicle weight. In the illustrated example, the first error profile  910  has a minimum  912 , the second error profile  920  has a minimum  922 , and the third error profile  930  has a minimum  932 . The candidate vehicle weights that minimize the error profiles  900  can be identified and used to determine the estimated weight of the vehicle  120 . In the illustrated example, the candidate vehicle weights corresponding to the minimums  912 ,  922 , and  932  can be used to determine the estimated weight of the vehicle  120 . Hence, each error profile  900  can represent a grid search for a candidate vehicle weight that minimizes the error between the simulated torque profiles  800 B and the measured torque profiles  800 A. 
     In various embodiments, the estimated weight of the vehicle  120  can be determined based on an average of the candidate vehicle weights that minimize the error profiles  910 . For instance, in the illustrated example, the candidate vehicle weights corresponding the minimums  912 ,  922 , and  932  can be averaged to determine the estimated weight of the vehicle  120 . In some embodiments, the average of the candidate vehicle weights can be a weighted average. The candidate vehicle weights can be assigned different weights based on the corresponding error profile  900 . For example, the candidate vehicle weights can be weighted based on a sensitivity of the corresponding error profiles  910 . The sensitivity of an error profile  910  can correspond to the slope or rate of change of that error profile  910 . An error profile with a greater slope can be considered more sensitive than an error profile having a lower slope because a greater slope can represent a large change in error in response to a small change in candidate vehicle weight. Candidate vehicle weights corresponding to error profiles  910  having greater sensitivity can be given more weight than candidate vehicle weights corresponding to error profiles  910  having lower sensitivity. For example, the candidate vehicle weight identified from error profile  920  may be assigned greater weight than the candidate vehicle weights identified from error profiles  910  and  930 . 
     Subsequent to  410 , the estimated weight of the vehicle  120  can be used in various ways. For example, the fuel economy of the vehicle  120  can be determined based on the estimated weight of the vehicle  120 . That is, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can determine the fuel economy of the vehicle  120 . 
     Additionally, or alternatively, the load state of the vehicle  120  can be determined based on the estimated weight of the vehicle  120 . For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can determine the load state of the vehicle  120 . The load state of a vehicle  120  can indicate whether the vehicle  120  is loaded with cargo. The load state of a vehicle  120  may also indicate whether the vehicle  120  is excessively loaded. The load state of a vehicle  120  can be used to determine the utilization rate of the vehicle  120 . In various embodiments, the load state of the vehicle  120  can be determined based on a predetermined threshold. For example, the vehicle  120  can be determined to be in a loaded state if the estimated weight of the vehicle  120  satisfies a predetermined vehicle weight threshold. If the estimated weight of the vehicle  120  does not satisfy the predetermined vehicle weight threshold, the vehicle  120  can be determined to be in an unloaded state. In some embodiments, the predetermined vehicle weight threshold may be a first predetermined weight threshold, and the vehicle  120  may be determined to be in an overloaded state if the estimated weight of the vehicle  120  satisfies a second predetermined vehicle weight threshold. The second predetermined weight threshold may be greater than the first predetermined weight threshold. 
     Referring to  FIG.  10   , there is shown another example method  1000  for determining an estimated weight of a vehicle  120 . In contrast with the approach described with reference to  FIG.  4   , method  1000  can use pre-generated simulated torque profiles. That is, the vehicle dynamics model need not be used during execution of method  1000 . An advantage of this approach is the amount of data processing by method  1000  can be reduced. At scale, for example, when estimating the weight of hundreds, thousands, or even millions of vehicles  120 , this can significantly improve the efficiency of method  1000 . 
     Like method  400 , method  1000  can be implemented by the fleet management system  110 , one or more telematics devices  130 , or a combination thereof. That is, method  1000  can be implemented by operating at least one processor of the fleet management system  110  and/or one or more telematics devices  130 . For example, method  1000  can be implemented by the processor  112  and/or the processor  132  executing instructions stored on the data storage  114  and/or the data storage  134 . 
     At  1002 , vehicle data associated with the vehicle  120  can be received. For example, the telematics device  130  may receive vehicle data from the sensor  138  and/or vehicle components  122 . Alternatively, or additionally, the fleet management system  110  may receive vehicle data from a telematics device  130 . Alternatively, or additionally, the processor  112  and/or processor  132  may receive vehicle data from the data storage  114  and/or data storage  134 . 
     The vehicle data can include a plurality of vehicle parameters collected during operation of the vehicle  120 . As described herein, the vehicle data may include any information, parameters, attributes, characteristics, and/or features associated with the vehicles  120 . For example, the vehicle data may include speed data  502 , torque data  504 , gear ratio data  506 , rotation data  508 , elevation data  510 , and/or acceleration data  512 . The vehicle data can include various time series of data points, with each data point representing the value of a particular vehicle parameter at a given time. The vehicle data may vary depending on a vehicle dynamics model. 
     At  1004 , a plurality of vehicle maneuvers can be identified based on the vehicle data. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can identify the vehicle maneuvers. As described herein, the criteria used to identify the vehicle maneuvers can depend on a vehicle dynamics model. For example, the vehicle maneuvers may be identified by identifying portions of the vehicle data that satisfy one or more predetermined conditions associated with the vehicle dynamics model. The predetermined conditions may be related to underlying assumptions, rules, and/or requirements of the vehicle dynamics model. 
     Each vehicle maneuver can be associated with a portion of the vehicle data. For example, a vehicle maneuver may be associated with a portion of the speed data  502 , torque data  504 , gear ratio data  506 , rotation data  508 , elevation data  510 , and/or acceleration data  512 . As described herein, a portion of the vehicle data  500  corresponding to a vehicle maneuver can be referred to as a profile. For example, a portion of the speed data  502  associated with a vehicle maneuver may be referred to as a measured speed profile. Similarly, a portion of the torque data  504  associated with a vehicle maneuver may be referred to as a measured torque profile. In various embodiments, each vehicle maneuver may be associated with a portion of the vehicle data  500  that includes a measured torque profile. 
     Each vehicle maneuver can be associated with a portion of the vehicle data that includes an identifying profile. The identifying profile can include any type or combinations of types of vehicle data. For example, the identifying profile may include an acceleration profile containing acceleration data  512 . As another example, the identifying profile may include an elevation profile containing elevation data  510 . As a further example, the identifying profile may include a normalized concatenation of an acceleration profile and an elevation profile. The identifying profile can be used to identify other vehicle maneuvers that are comparable or similar to the vehicle maneuver. 
     At  1006 , a plurality of previous comparable vehicle maneuvers can be identified. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can identify the plurality of previous comparable vehicle maneuvers. A previous comparable vehicle maneuver can be identified for each vehicle maneuver. 
     The previous comparable vehicle maneuvers can be identified by comparing each identifying profile with a plurality of previous representative identifying profiles associated with a plurality of previous representative vehicle maneuvers. The previous representative identifying profiles can include the same type or types of vehicle data as the identifying profiles. For example, the previous representative identifying profiles may include previous representative elevation profiles. As another example, the previous representative identifying profiles may include previous representative elevation profiles. As a further example, the previous representative identifying profiles may include normalized concatenations of previous representative acceleration profiles and previous representative elevation profiles. 
     The identifying profiles can be compared in various ways. In some cases, the identifying profiles can be compared by determining a similarity score between the identifying profile and each previous representative identifying profile. For example, a dynamic time warping algorithm can be used to determine a cumulative distance between the identifying profile and each previous representative identifying profile. 
     Referring now to  FIGS.  12 A and  12 B , there is shown an example implementation of a dynamic time warping algorithm. In the illustrated example, there are two time series or temporal sequences  1210 ,  1220  having varying speeds. As shown, dynamic time warping can be used to measure a similarity between the first and second time series  1210 ,  1220 . More specifically, dynamic time warping can be used to compute local stretches or compressions  1212  to apply to the time axis of the first time series  1210  to optimally match the second time series  1220 . This can form a cumulative distance that can represent the similarity between the time series  1210 ,  1220 . 
     As shown, dynamic time warping can be implemented using a cost matrix  1230 . The cost matrix  1230  can be an (N+1)×(M+1) matrix, where N is the number of data points in the first time series  1210  and M is the number of data points in the second time series  1220 . The cost matrix  1230  can be initialized by setting elements i=1 to N, j=0 and i=0, j=1 to M to infinity, and element i=0, j=0 to zero. The remaining elements in the cost matrix (i.e., i=1 to N, j=1 to M) can be determined by the following equation: 
     
       
         
           
             
               d 
               ⁡ 
               ( 
               
                 
                   x 
                   i 
                 
                 , 
                 
                   y 
                   j 
                 
               
               ) 
             
             + 
             
               min 
               ⁢ 
               
                 { 
                 
                   
                     
                       
                         D 
                         
                           
                             i 
                             - 
                             1 
                           
                           , 
                           
                             j 
                             - 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         D 
                         
                           
                             i 
                             - 
                             1 
                           
                           , 
                           j 
                         
                       
                     
                   
                   
                     
                       
                         D 
                         
                           i 
                           , 
                           
                             j 
                             - 
                             1 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     where x is the first time series  1210 , y is the second time series  1220 , D is the cost matrix  1230 , and d(x i , y j )=|x i −y j | 
     The optimal alignment of the time series  1210 ,  1220  can be determined by tracing back the path from element i=N, j=M to element i=0, j=0. Each element can trace back to another element based on the previous element D i-1,j-1  (match), D i-1,j  (insertion), or D i,j-1  (deletion) that was used calculate the current element. 
     Although dynamic time warping may be used to determine similarity between identifying profiles, it should be appreciated that various other matching algorithms or models can also be used. In some cases, machine learning and other techniques may be used to match the identifying profiles of the vehicle maneuvers to the previous representative identifying profiles of previous representative vehicle maneuvers. 
     Referring back to  FIG.  10   , at  1008 , a plurality of simulated torque profiles for each previous comparable vehicle maneuver can be received. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can receive each plurality of simulated torque profiles (e.g., from data storage  114  and/or data storage  134 ). Each plurality of simulated torque profiles can have been previously generated using a vehicle dynamics model, as described herein. In this manner, the vehicle dynamics model need not be used during the execution of method  1000 . This can greatly reduce the amount of data processing required when performing weight estimations for large numbers of vehicles  120 . 
     At  1010 , a plurality of error profiles can be generated. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can generate the error profiles. As descried herein, an error profile can be generated for each vehicle maneuver based on differences between the plurality of simulated torque profiles and the measured torque profile corresponding to that vehicle maneuver. For example, the differences may correspond to differences between the area under the curve of each of the simulated torque profiles and the area under of the curve of the measured torque profile. In some cases, the differences may be the mean square error of the differences of the respective areas under the curves. 
     At  1012 , the estimated weight of the vehicle  120  can be determined based on the plurality of error profiles. The estimated weight of the vehicle  120  can be determined by minimizing the plurality of error profiles. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can determine the estimated weight of the vehicle  120 . As described herein, this may involve minimizing and/or averaging the error profiles. For example, the estimated weight of the vehicle  120  can be determined based on an average of the candidate vehicle weights that minimize the error profiles. As described herein, the candidate vehicle weights can be assigned different weights based on the corresponding error profile. For example, the candidate vehicle weights can be weighted based on a sensitivity of the corresponding error profiles. The sensitivity of an error profile can correspond to the slope or rate of change of that error profile. 
     Referring to  FIG.  11   , there is shown an example method  1100  for preprocessing vehicle weight estimations. Method  1100  can be used to pre-generate the simulated torque profiles used in method  1000 . In this manner, the vehicle dynamics model need not be used during execution of method  1000 . An advantage of this approach is the amount of data processing during execution of method  1000  can be reduced. At scale, for example, when estimating the weight of hundreds, thousands, or even millions of vehicles  120 , this can significantly improve the efficiency of method  1000 . 
     Like methods  400  and  1000 , method  1100  can be implemented by the fleet management system  110 , one or more telematics devices  130 , or a combination thereof. That is, method  1100  can be implemented by operating at least one processor of the fleet management system  110  and/or one or more telematics devices  130 . For example, method  1100  can be implemented by the processor  112  and/or the processor  132  executing instructions stored on the data storage  114  and/or the data storage  134 . 
     At  1102 , vehicle data associated with a plurality of vehicles  120  can be received. For example, a plurality of telematics devices  130  may receive vehicle data from sensors  138  and/or vehicle components  122 . Alternatively, or additionally, the fleet management system  110  may receive vehicle data from a plurality of telematics devices  130 . Alternatively, or additionally, the processor  112  and/or processor  132  may receive vehicle data from the data storage  114  and/or data storage  134 . 
     The vehicle data can include a plurality of vehicle parameters collected during operation of the vehicles  120 . As described herein, the vehicle data may include any information, parameters, attributes, characteristics, and/or features associated with the vehicles  120 . For example, the vehicle data may include speed data  502 , torque data  504 , gear ratio data  506 , rotation data  508 , elevation data  510 , and/or acceleration data  512 . The vehicle data can include various time series of data points, with each data point representing the value of a particular vehicle parameter at a given time. The vehicle data may vary depending on the vehicle dynamics model. 
     At  1104 , a plurality of vehicle maneuvers can be identified based on the vehicle data. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can identify the vehicle maneuvers. As described herein, the criteria used to identify the vehicle maneuvers can depend on the vehicle dynamics model used by method  1100 . For example, the vehicle maneuvers may be identified by identifying portions of the vehicle data that satisfy one or more predetermined conditions associated with the vehicle dynamics model. The predetermined conditions may be related to underlying assumptions, rules, and/or requirements of the vehicle dynamics model. 
     Each vehicle maneuver can be associated with a portion of the vehicle data. For example, a vehicle maneuver may be associated with a portion of the speed data  502 , torque data  504 , gear ratio data  506 , rotation data  508 , elevation data  510 , and/or acceleration data  512 . As described herein, a portion of the vehicle data  500  corresponding to a vehicle maneuver can be referred to as a profile. For example, a portion of the speed data  502  associated with a vehicle maneuver may be referred to as a measured speed profile. Similarly, a portion of the torque data  504  associated with a vehicle maneuver may be referred to as a measured torque profile. In some embodiments, each vehicle maneuver may be associated with a portion of the vehicle data  500  that includes a measured speed profile. 
     Each vehicle maneuver can be associated with a portion of the vehicle data that includes an identifying profile. As described herein, the identifying profile can include any type or combinations of types of vehicle data. For example, the identifying profile may include an acceleration profile containing acceleration data  512 . As another example, the identifying profile may include an elevation profile containing elevation data  510 . As a further example, the identifying profile may include a normalized concatenation of an acceleration profile and an elevation profile. The identifying profile can be used to identify other vehicle maneuvers that are comparable or similar to the vehicle maneuver. 
     At  1106 , a plurality of representative vehicle maneuvers can be identified based on the identifying profile associated with each vehicle maneuver. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can identify the representative vehicle maneuvers. 
     The plurality of representative vehicle maneuvers can be identified by comparing each identifying profile with each other identifying profile. In this manner vehicle maneuvers that are sufficiently similar to each other (i.e., have similar identifying profiles) can be simplified to a single representative vehicle maneuver. This can greatly reduce the number of simulated torque profiles that are generated by the vehicle dynamics model. As a result, the number of comparisons executed when identifying previous comparable vehicle maneuvers in method  1000  can also be reduced. 
     The identifying profiles can be compared in various ways. In some cases, the identifying profiles can be compared by determining a similarity score between each identifying profile and eliminating at least some of the vehicle maneuvers from being identified as representative vehicle maneuvers based on the similarity scores. As described herein, a dynamic time warping algorithm can be used to determine the similarity scores by determining a cumulative distance between each identifying profile. 
     At  1108 , a plurality of simulated torque profiles can be generated for each representative vehicle maneuver. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can generate the simulated torque profiles. r dynamics model may be a model generated using various modeling/simulation software, such as, but not limited to, MapleSim™, Simulink™, SystemModeler™, Dymola™, and/or SimulationX™. In various embodiments, the vehicle dynamics model can be a FMU (functional mock-up unit) and/or FMI (functional mock-up interface) that can interface with other software. 
     The vehicle dynamics model can generate the simulated torque profiles based on various input data. The input data can include various vehicle and/or other data. For example, the input data for each representative vehicle maneuver can include at least some of the portion of the vehicle data  500  associated that representative vehicle maneuver. For example, the input data can include the measured speed profile associated with the corresponding representative vehicle maneuver. The input data for each vehicle maneuver can also include a plurality of candidate vehicle weights. Each candidate vehicle weight can represent a presumed or putative weight of the vehicle  120 . Each simulated torque profile can correspond to one of the candidate vehicle weights. Accordingly, each simulated torque profile can represent a simulation or prediction of the torque data (i.e., torque profile) that could be measured during the vehicle maneuver if the vehicle  120  weight was the candidate vehicle weight. 
     At  1110 , each plurality of simulated torque profiles can be stored in association with the identifying profile for each representative vehicle maneuver. For example, the fleet management system  110  (e.g., processor  112 ) and/or telematics device  130  (e.g., processor  132 ) can store each plurality of simulated torque profiles in data storage  134  and/or data storage  114 . In this manner, the simulated torque profiles can be available without further use of the vehicle dynamics model, for example, by matching a vehicle maneuver to one of the representative maneuvers using method  1000 . This can greatly reduce the amount of data processing required to perform weight estimations for large numbers of vehicles  120 . 
     It will be appreciated that for simplicity and clarity of illustration, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. In addition, numerous specific details are set forth in order to provide a thorough understanding of the embodiments described herein. However, it will be understood by those of ordinary skill in the art that the embodiments described herein may be practiced without these specific details. In other instances, well-known methods, procedures and components have not been described in detail so as not to obscure the embodiments described herein. Also, the description is not to be considered as limiting the scope of the embodiments described herein. 
     It should also be noted that the terms “coupled” or “coupling” as used herein can have several different meanings depending in the context in which these terms are used. For example, the terms coupled or coupling may be used to indicate that an element or device can electrically, optically, or wirelessly send data to another element or device as well as receive data from another element or device. Furthermore, the term “coupled” may indicate that two elements can be directly coupled to one another or coupled to one another through one or more intermediate elements. 
     It should be noted that terms of degree such as “substantially”, “about” and “approximately” as used herein mean a reasonable amount of deviation of the modified term such that the end result is not significantly changed. These terms of degree may also be construed as including a deviation of the modified term if this deviation would not negate the meaning of the term it modifies. 
     In addition, as used herein, the wording “and/or” is intended to represent an inclusive-or. That is, “X and/or Y” is intended to mean X or Y or both, for example. As a further example, “X, Y, and/or Z” is intended to mean X or Y or Z or any combination thereof. 
     Furthermore, any recitation of numerical ranges by endpoints herein includes all numbers and fractions subsumed within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.90, 4, and 5). It is also to be understood that all numbers and fractions thereof are presumed to be modified by the term “about” which means a variation of up to a certain amount of the number to which reference is being made if the end result is not significantly changed. 
     The terms “an embodiment,” “embodiment,” “embodiments,” “the embodiment,” “the embodiments,” “one or more embodiments,” “some embodiments,” and “one embodiment” mean “one or more (but not all) embodiments of the present invention(s),” unless expressly specified otherwise. 
     The terms “including,” “comprising” and variations thereof mean “including but not limited to,” unless expressly specified otherwise. A listing of items does not imply that any or all of the items are mutually exclusive, unless expressly specified otherwise. The terms “a,” “an” and “the” mean “one or more,” unless expressly specified otherwise. 
     The example embodiments of the systems and methods described herein may be implemented as a combination of hardware or software. In some cases, the example embodiments described herein may be implemented, at least in part, by using one or more computer programs, executing on one or more programmable devices comprising at least one processing element, and a data storage element (including volatile memory, non-volatile memory, storage elements, or any combination thereof). Programmable hardware such as FPGA can also be used as standalone or in combination with other devices. These devices may also have at least one input device (e.g., a pushbutton keyboard, mouse, a touchscreen, and the like), and at least one output device (e.g., a display screen, a printer, a wireless radio, and the like) depending on the nature of the device. The devices may also have at least one communication device (e.g., a network interface). 
     It should also be noted that there may be some elements that are used to implement at least part of one of the embodiments described herein that may be implemented via software that is written in a high-level computer programming language such as object-oriented programming. Accordingly, the program code may be written in C, C++ or any other suitable programming language and may comprise modules or classes, as is known to those skilled in object-oriented programming. Alternatively, or in addition thereto, some of these elements implemented via software may be written in assembly language, machine language or firmware as needed. In either case, the language may be a compiled or interpreted language. 
     At least some of these software programs may be stored on a storage media (e.g., a computer readable medium such as, but not limited to, ROM, magnetic disk, optical disc) or a device that is readable by a general or special purpose programmable device. The software program code, when read by the programmable device, configures the programmable device to operate in a new, specific and predefined manner in order to perform at least one of the methods described herein. 
     Furthermore, at least some of the programs associated with the systems and methods of the embodiments described herein may be capable of being distributed in a computer program product comprising a computer readable medium that bears computer usable instructions for one or more processors. The medium may be provided in various forms, including non-transitory forms such as, but not limited to, one or more diskettes, compact disks, tapes, chips, and magnetic and electronic storage. 
     The present invention has been described here by way of example only, while numerous specific details are set forth herein in order to provide a thorough understanding of the exemplary embodiments described herein. However, it will be understood by those of ordinary skill in the art that these embodiments may, in some cases, be practiced without these specific details. In other instances, well-known methods, procedures and components have not been described in detail so as not to obscure the description of the embodiments. Various modification and variations may be made to these exemplary embodiments without departing from the spirit and scope of the invention, which is limited only by the appended claims.