WO2024099534A1

WO2024099534A1 - Joint estimation of tyre radius and accelerometer bias

Info

Publication number: WO2024099534A1
Application number: PCT/EP2022/080999
Authority: WO
Inventors: Mats Jonasson; Mats RYDSTRÖM; Adithya ARIKERE
Original assignee: Volvo Truck Corporation
Priority date: 2022-11-07
Filing date: 2022-11-07
Publication date: 2024-05-16

Abstract

A computer-implemented method, for controlling a heavy-duty vehicle (100) based on determined tyre radii (RE1, RE2) associated with wheels (102) on the heavy-duty vehicle (100) and an accelerometer bias (b) associated with an inertial measurement unit, IMU, of the heavy- duty vehicle (100), the method comprising obtaining, (SI), by a processor device of a computer system, vehicle data comprising data indicative of axle inertias (J1,J2) associated with the wheels (102) on the heavy-duty vehicle (100), data indicative of a mass (m) of the heavy-duty vehicle (100), and data indicative of a motion resistance (Fres) of the heavy-duty vehicle (100), obtaining, (S2), by the processor device, measurement data comprising torque data indicative of respective applied torques (T1,T2) associated with the wheels (102) on the heavy-duty vehicle (100), wheel speed data indicative of respective angular accelerations (ω1, ω2) associated with the wheels (102) on the heavy-duty vehicle (100), and accelerometer data (axm) indicative of an acceleration by the vehicle (100), and obtaining (S3), by the processor device, a relationship between the tyre radii (RE1, RE2), the accelerometer bias (b), the vehicle data, the measurement data, the method further comprising determining (S4), by the processor device, the tyre radii (RE1, RE2) and the accelerometer bias (b) based on the vehicle data and on the pre-determined relationship, as function of the measurement data, and controlling (S5) the vehicle (100), by the processor device, based on the tyre radii (RE1,RE2) and the accelerometer bias (b).

Description

Docket No.: P2022-0878WO01 (P449615PC00) JOINT ESTIMATION OF TYRE RADIUS AND ACCELEROMETER BIAS TECHNICAL FIELD This disclosure relates generally to control of heavy-duty vehicles such as trucks, busses and construction equipment. In particular aspects, the disclosure relates to computer-implemented methods for joint estimation of tyre radius and accelerometer bias. Although the disclosure may be described with respect to a particular vehicle, the disclosure is not restricted to any particular vehicle. BACKGROUND Modern heavy-duty vehicles often comprise advanced vehicle motion management (VMM) systems that manage control of the different actuators of the vehicle, such as propulsion devices, steering arrangements, and braking devices, to obtain a desired vehicle motion in a safe and power conserving manner. To do this dependably and efficiently, the vehicle control systems need accurate and reliable data upon which control decisions can be based. An inertial measurement unit (IMU) measures vehicle acceleration and is an important real- time source of information about the motion of the vehicle. All IMUs are, however, associated with measurement error that complicate vehicle control. It is desired to correct for such errors. The vehicle control systems also need accurate data regarding vehicle properties in order to control actuators in the correct way to obtain the desired motion by the vehicle. Examples of important vehicle properties are wheelbase length, vehicle mass and tyre radii. Some such data items (like the wheelbase of the vehicle) are not time varying and thus pre-configurable. However, other data items vary over time and between different use cases. The effective rolling radius of a tyre, for instance, changes with vehicle load, temperature, tyre nominal inflation pressure, and also with tyre wear. It is desired to maintain an accurate and up-to-date record of these vehicle properties. There is a general desire to improve the quality of the data available for vehicle motion management involving heavy-duty vehicles. There is also a desire to provide redundant methods for obtaining vehicle motion state data. Docket No.: P2022-0878WO01 (P449615PC00) SUMMARY There is disclosed a computer-implemented method for controlling a heavy-duty vehicle based on determined tyre radii associated with wheels on the heavy-duty vehicle and an accelerometer bias associated with at least one IMU of the heavy-duty vehicle. The method, which can be performed by a processor device of a computer system, comprises obtaining vehicle data comprising data indicative of axle inertias associated with the wheels on the heavy-duty vehicle, data indicative of a mass of the heavy-duty vehicle, and data indicative of a motion resistance of the heavy-duty vehicle. The method also comprises obtaining measurement data comprising torque data indicative of respective applied torques associated with the wheels on the heavy-duty vehicle, wheel speed data indicative of respective angular accelerations associated with the wheels on the heavy-duty vehicle, and accelerometer data indicative of an acceleration by the vehicle, and also obtaining a relationship between the tyre radii, the accelerometer bias, the vehicle data, and the measurement data. The method further comprises determining the tyre radii and the accelerometer bias based on the vehicle data and on the pre- determined relationship, as function of the measurement data, and controlling the vehicle based on the tyre radii and the accelerometer bias. Aspects of the disclosure may seek to provide more accurate data regarding tyre radii and accelerometer bias, such that overall VMM operations involving the heavy-duty vehicle can be improved. Other aspects may seek to provide reference data against which data from other sources can be compared, in order to determine if the data from the other sources appear correct or if erroneous data is obtained from the other sources. A technical benefit of this may include a safer vehicle operation. In some examples, the method comprises obtaining the mass of the heavy-duty vehicle at least partly as a pre-configured mass and/or at least partly based on an output signal from a load sensor of the heavy-duty vehicle. Either of these sources or a combination can be used to increase the reliability of the data obtained from executing the method. It is appreciated, however, that the method can be performed based on any method or sensor system which provides vehicle mass data. Valuable information can also be obtained if a predetermined fixed value for the vehicle mass is used in the method. Docket No.: P2022-0878WO01 (P449615PC00) In some examples, the method comprises obtaining the torque data at least partly as an applied torque by an electric machine, where the applied torque is estimated based on a motor current associated with the electric machine. Electric machines are often able to provide very accurate torque data with low latency, which is an advantage. The methods proposed herein are particularly suitable for electrically driven or hybrid electric vehicles. In some examples, the method comprises obtaining the torque data at least partly as an applied torque by a service brake, where the applied torque is estimated based on an applied brake pressure by the service brake. A technical benefit of this is that the method can be applied in many different types of vehicles since most vehicles comprise service brake systems capable of providing applied brake pressure. In some examples, the method comprises obtaining the torque data at least partly based on an output from a torque sensor, such as a strain-force sensor. Such sensors may provide reliable torque data, which is an advantage. It is noted that the method may be based on a plurality of different torque data sources, for increased robustness. In some examples, the method comprises obtaining the torque data at least partly based on a predetermined electric machine wind-up characteristic ^^_^^^. A technical benefit may include improvements in the accuracy of the obtained torque data. In some examples, the method comprises obtaining the wheel speed data from wheel speed sensors connected to the wheels in combination with timing data from a timing device. This allows for reliably determining wheel angular acceleration, which is an advantage. In some examples, the method comprises obtaining the pre-determined relationship as ^ ^ = _^ _^^ 2^^̇_^ ^ ^ _^ _^^ = 2^^̇_^ 2^^ ^ = _^^ − ^_^^^ 2^ ^ = ^^{^} − 4^ ^^̇^ + 4^ ^̇ − 4^ ^ ^ ^{^} _{^^^ ^ ^ ^ ^ ^}^^̇_^ + 4^_^^̇_^ − ^_^^^ Docket No.: P2022-0878WO01 (P449615PC00) where ^_^^, ^_^^ are the tyre radii, ^ is the vehicle mass, ^̇_^, ^̇_^ are the angular accelerations, ^ is the accelerometer bias, ^_^^ is the accelerometer data, ^_^^^ is the motion resistance, ^_^, ^_^ are the axle inertias, and

^_^ are the applied torques. In some examples, the method comprises obtaining the pre-determined relationship as a machine learning structure configured based on the vehicle data and taking the measurement data as input. A technical benefit may include more accurate results tailored for a specific vehicle or operating scenario, e.g., since the machine learning structure can be trained to be more relevant for a given vehicle type and/or use case. In some examples, the method comprises obtaining the pre-determined relationship as the solution to an optimization problem involving the vehicle data and the measurement data. The optimization problem can be formulated in dependence of use case and vehicle type, which is an advantage. The optimization problem solution can also be iteratively refined over time, which is an advantage since then the results become better over time as more and more data become available. Thus, in some examples, the method comprises determining the tyre radii and the accelerometer bias iteratively over time. A technical benefit may include more accurate results. The optimization problem can for instance be formulated as a least-squares type optimization problem having an objective function ^ given by

where ^ and ^ are weights,

^ = [^_^ , ^, ^_^^, … , ^_^^ , ^_^, ^_^^, … , ^_^^]^ and where ^⁽^⁾ is given by the relationships ^_^^ = ^_^ + ^ ^_^ = ^_^^̇_^+^_^^_^,^ ^ ^̇ _^ _^ = ^_^^ Docket No.: P2022-0878WO01 (P449615PC00) In some examples, the method comprises determining the tyre radii and the accelerometer bias conditioned on that a state of the vehicle meets predetermined acceptance criteria comprising any of wheel slip, pitch angle, and vehicle acceleration. A technical benefit of adding such features to the proposed method is that singularities can more easily be avoided, and performance thus improved. In some examples, the method comprises determining the tyre radii and the accelerometer bias conditioned on that an environment of the vehicle meets predetermined acceptance criteria comprising any of road slope and road banking. A technical benefit of adding such features to the proposed method is that the effects of road slope and road banking are mitigated, which could otherwise lead to at least a temporary reduction in estimation performance. In some examples, the method comprises determining an accuracy metric associated with the vehicle data and determining the tyre radii and the accelerometer bias conditioned on that the vehicle data accuracy metric meets predetermined acceptance criteria. A technical benefit of adding such features to the proposed method is that the effects of inaccurate vehicle data are mitigated. The above aspects, accompanying claims, and/or examples disclosed herein above and later below may be suitably combined with each other as would be apparent to anyone of ordinary skill in the art. Additional features and advantages are disclosed in the following description, claims, and drawings, and in part will be readily apparent therefrom to those skilled in the art or recognized by practicing the disclosure as described herein. There are also disclosed herein control units, computer systems, computer readable media, and computer program products associated with the above discussed technical benefits. BRIEF DESCRIPTION OF THE DRAWINGS With reference to the appended drawings, below follows a more detailed description of aspects of the disclosure cited as examples. Figure 1 illustrates an example heavy-duty vehicle, Figure 2 schematically illustrates a wheel comprising a tyre, Docket No.: P2022-0878WO01 (P449615PC00) Figure 3A illustrate examples of directly measurable vehicle state variables, Figure 3B show some example non-measurable state variables on a heavy-duty vehicle, Figure 4 schematically illustrates a vehicle control system, Figure 5 schematically illustrates a machine learning based control system, Figure 6 is a schematic diagram of an exemplary computer system, Figure 7 is a flow chart illustrating methods, and Figure 8 shows an example computer program product. DETAILED DESCRIPTION The present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments are shown. The disclosure may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided for thoroughness and completeness. Like reference character refer to like elements throughout the description. Aspects set forth below represent the necessary information to enable those skilled in the art to practice the disclosure. Figure 1 illustrates an example heavy-duty vehicle 100, here in the form of a truck comprising a tractor 110 and a trailer 120. The vehicle 100 is supported on the road surface 101 by a plurality of wheels 102, wherein at least a subset of the wheels 102 comprise one or more motion support devices (MSD) 104, such as a service brake, an electric machine, a power steering arrangement, active suspension, and/or a power transmission that connects the wheel to a motor such as a combustion engine or central electric machine. It should be readily understood that one or more pairs of wheels may be arranged without an MSD. Also, an MSD may be arranged connected to more than one wheel, e.g., via a differential drive arrangement. It is appreciated that the herein disclosed methods, computer systems and computer- implemented control units can be applied with advantage also in other types of heavy-duty vehicles, such as trucks with drawbar connections, construction equipment, buses, and the like. Docket No.: P2022-0878WO01 (P449615PC00) The vehicle 100 may also comprise more than two vehicle units, i.e., a dolly vehicle unit may be used to tow more than one trailer. The vehicle 100 comprises a computer-implemented control system arranged to control vehicle motion, among other things. This control system may comprise one or more control units 130, 140 distributed over the vehicle or centralized at one place. Each vehicle control unit 130, 140 may comprise one or more processor devices and/or computer systems. A processor device and/or computer system may be distributed over several spatially separated units or centralized in one place. The control system, or parts thereof, may be arranged to communicate via wireless link 150 to a wireless access point 160, such as a radio base station 160 of a cellular access network or the like. Thus, the vehicle control system may communicate with one or more remote servers 170, data repositories, and remote processing resources, in order to exchange data and perform various computation tasks. The vehicle control system 130, 140 may be referred to as a system for vehicle motion management (VMM). An example computer system 600 that can be used for vehicle control purposes will be discussed in more detail below in connection to Figure 6. At least some of the wheels 102 on the vehicle 100 are equipped with wheel speed sensors. A wheel speed sensor is a sensor which measures the rotation speed ^ and angular acceleration ^̇ of the wheel, e.g., based on a Hall effect sensor, a rotary encoder, or the like. A wheel speed sensor can also be used to determine the number of rotations a wheel undergoes in a given period of time. Wheel speed sensors are generally known and will therefore not be discussed in more detail herein. A modern heavy-duty vehicle, such as the truck 100, normally comprises sensors to estimate vehicle motion and to monitor the environment in vicinity of the vehicle. Global positioning system (GPS) sensors may be used to position the vehicle and to determine a traveled distance of the vehicle. Electronic maps may also be used for determining a travelled distance, for instance based on a known starting position and destination. Electronic maps may also comprise information about road geometry at a given location, such as the road slope and/or road banking. An inertial measurement unit (IMU) can be configured to provide information about vehicle motion, such as accelerations in different directions, yaw motion, pitch motion, Docket No.: P2022-0878WO01 (P449615PC00) and vehicle roll. An IMU can be centrally arranged in the vehicle or mounted close to a wheel to determine accelerations specific for that wheel in a reliable and robust manner. Longitudinal wheel slip ^_^ may, in accordance with SAE J670 (SAE Vehicle Dynamics Standards Committee January 24, 2008) be defined as

where ^_^ is an effective tyre rolling radius in meters, ^ is the angular velocity of the wheel, and ^_^ is the longitudinal speed of the wheel (in the coordinate system of the wheel). Thus, ^_^ is bounded between -1 and 1 and quantifies how much the wheel is slipping with respect to the road surface. Wheel slip is, in essence, a speed difference measured between the wheel and the vehicle. Figure 2 schematically illustrates a wheel 102 suitable for use on a heavy-duty vehicle 100. The wheel has an unloaded tyre radius ^_^ and a loaded tyre radius ^_^, where the loaded tyre radius ^_^ is generally smaller than the unloaded tyre radius ^_^. The unloaded tyre radius may vary some in dependence of tyre nominal inflation pressure, temperature, and other tyre properties, but it is normally possible to determine it at least approximately in a reliable manner from tyre specification alone, although tyre wear does have an effect which can be hard to determine without manual inspection. The loaded tyre radius ^_^ is more difficult to determine, since it depends on the weight of the vehicle, i.e., the normal force ^_^ acting on the tyre and also on the temperature of the tyre (which affects both tyre material properties and tyre inflation pressure). The effective rolling radius ^_^ of the wheel 102 is somewhere inbetween the unloaded and the loaded tyre radius. This is the tyre radius which relates wheel angular speed ^ to wheel hub longitudinal speed ^_^ when there is no wheel slip. A problem encountered when executing advanced VMM methods involving a heavy-duty vehicle 100 is that the tyre radii (^_^, ^_^, and/or ^_^) may not be accurately known for all wheels of the heavy-duty vehicle 100. This makes it difficult to translate wheel angular speed ^ into vehicle speed ^_^, and also to determine wheel slip ^_^ in an accurate manner. It is possible to measure or estimate the effective rolling radius ^_^ of a wheel. This can be done, e.g., by recording a travelled distance by a vehicle in a time period (using a GPS system Docket No.: P2022-0878WO01 (P449615PC00) or a map) and comparing this distance to the number of rotations of a wheel during the same time period. Suppose that a travelled distance ^ (in meters) is measured using a map or some form of GPS-based sensor system, and that the number of wheel rotations ^ is recorded for some wheel on the vehicle as it travels the distance ^. Assuming no wheel slip, these two quantities can be used to determine effective rolling radius for wheel, by the relationship ^ ^_^ ≈ 2^^ The relation between tyre effective rolling radius ^_^ and travelled distance ^ above assumes no wheel slip. If wheel slip is present N will change. This effect can, however, at least partly be reduced if slip is estimated and taken into account by the travelled distance-based tyre radius estimator. The longer the distance travelled, the more accurate the estimate of effective rolling radius will be since measurement noise and other transient disturbances will be averaged out. However, travelling a longer distance also takes a longer time, which means that it will take time to generate a reliable estimate of effective rolling radius ^_^. Thus, an accurate rolling radius measurement can be at least temporarily offset from its true value if the vehicle load changes, or if the tyre temperature changes faster than the tyre radius estimation algorithm can adapt. Faster methods are required which can be used both for monitoring the slower travelled distance-based tyre radius estimator and for providing tyre radius data for the VMM system when the travelled distance-based tyre radius estimator is not sufficiently accurate. The effective rolling radius ^_^ of a wheel can also be obtained from a comparison of vehicle acceleration ^̇_^ (the time derivative of the vehicle longitudinal speed ^_^) parallel to the road surface and the angular acceleration ^̇ of the wheel 102 (the time derivative of the angular speed ^ of the wheel). If wheel slip is sufficiently small to be neglected, ^̇_^ ≈ ^_^^̇ If there is wheel slip, then ^_^ ≈ ^_^^⁽1 − ^_^ ⁾ which gives that ^ ^ ≈ _^ _^ ^⁽1 − ^_^ ⁾ Docket No.: P2022-0878WO01 (P449615PC00) If ^_^ is small (which is normally is) a Taylor series expansion gives that

Taking the time derivative and neglecting time-variation in wheel slip, the following approximate relationship is obtained

So, if ^_^=0.01, ^_^ will be about 1% too large. It is a reasonable assumption that slip can be maintained at values less than 3%. For normal driving (acceleration less than 2 m/s2 and high friction) slip seldomly exceeds 3%. Measurement noise and other disturbances may need to be suppressed by averaging, which again introduces significant latency in the process for estimating effective rolling radius. In addition, an unknown bias ^ in the longitudinal acceleration ^̇_^ could result in an erroneous estimate of tyre radius. Suppose that the longitudinal acceleration output ^_^^ from an IMU can be modelled as ^_^^ = ^̇_^ + ^ − ^ ⋅ sin(^_^) ≈ ^_^ + ^ where ^ is the gravitational acceleration and ^_^ is the road slope, then ^ obviously has a negative effect on the accuracy of the acceleration data, even if road slope ^_^ can be neglected. In case road slope cannot be neglected, it can be compensated for in some cases. Map data can, for instance, be used to obtain a current road slope ^_^. An inclinometer can also be used to obtain an estimate of the road slope ^_^, at least if the vehicle is not accelerating (which can be inferred from actuator controls and environment sensors such as a vision-based sensor or a ground speed radar sensor system) The effective rolling radius ^_^ of the wheel 102 can also be obtained from a comparison of vehicle speed ^_^ with a corresponding wheel angular velocity ^, as the two are related according to ^_^ ≈ ^_^^ Docket No.: P2022-0878WO01 (P449615PC00) The tyre’s angular speed ^ can be measured by a wheel speed sensor and the longitudinal speed ^_^ of the vehicle hub can be measured by a GPS receiver, by a radar sensor, by a vision-based sensor, or some other form of vehicle speed sensor known in the art. The main problem with this method is that it requires the vehicle speed data to be available and of high integrity. This is, for instance, not the case if GPS is relied upon and the vehicle enters a tunnel or an urban canyon environment where the GPS system is inaccurate. The effective rolling radius of a wheel can be defined by using the kinematic relation ^̇ ^ _^ _^ = ^̇ or by using the kinetic relation ^ ^_^ = ^_^ where ^ is an applied wheel torque and ^_^ is a generated tyre force at the wheel having the tyre radius ^_^. It has been realized that the former expression can be extended using the latter, in case the vehicle control system has access to data indicative of an applied wheel torque. Regarding the details of determining the torque ^, it is noted that there are several methods known in the art for estimating an applied torque by an electric machine. Such methods are outside of the scope of the present disclosure and will therefore only be briefly discussed herein. For instance, in case of a permanent magnet synchronous machine (PMSM), the following relationship holds at least approximately in many cases

where ^ is the number of pole pairs of the PMSM, ψ_^ is the flux linkage of the permanent magnet, ^_^ and ^_^ are the d- and q-axis inductances of the PMSM, and ^_^ and ^_^ are the d- and q-axis currents of the PMSM. Docket No.: P2022-0878WO01 (P449615PC00) In "Accurate Torque Estimation for Induction Motors by Utilizing Globally Optimized Flux Observers," 2020 International Symposium on Power Electronics, Electrical Drives, Automation and Motion SPEEDAM, 2020, pp. 219-226, M. Stender, O. Wallscheid and J. Bocker discuss torque estimation for induction motors. US8080956B2 provides an example of how applied torque can be estimated in practice. Torque applied to an axle can of course also be measured by a mechanical or an electric torque sensor. A torque sensor, also known as a torque transducer or torquemeter, is a device for measuring and sometimes also recording the torque on a rotating system, such as a drive axle of a wheel. Static torque is relatively easy to measure. Dynamic torque, on the other hand, is not easy to measure since it generally requires transfer of some effect electric or magnetic from the shaft being measured to a static system. One way to achieve this is to condition the shaft or a member attached to the shaft with a series of permanent magnetic domains. The magnetic characteristics of these domains will vary according to the applied torque, and thus can be measured using non-contact sensors. Commonly, torque sensors or torque transducers use strain gauges applied to a rotating shaft or axle. With this method, a means to power the strain gauge bridge is necessary, as well as a means to receive the signal from the rotating shaft. This can be accomplished using slip rings, wireless telemetry, or rotary transformers. Newer types of torque transducers add conditioning electronics and an A/D converter to the rotating shaft. Stator electronics then read the digital signals and convert those signals to a high-level analog output signal. Yet another way to measure torque is by way of twist angle measurement or phase shift measurement, whereby the angle of twist resulting from applied torque is measured by using two angular position sensors and measuring the phase angle between them. The estimated applied torque ^ is preferably compensated for one or more predetermined wheel and/or driveline properties, such as an inertia value and/or a stiffness value. The estimated applied torque T can also be determined at least in part based on a predetermined electric machine wind-up characteristic. According to an example, the control unit 130, 140 can be arranged to estimate an applied torque as ^ = ^_^^^^^ − ^_^^^^^^ − ^⁽ _^^^^^ ⁾ Docket No.: P2022-0878WO01 (P449615PC00) where ^_^^^^^ is a determined or estimated motor torque, ^_^^^^^^ is a moment related to a motor inertia, and ^(^^_^^^) is a wind-up effect of the electric machine, which can be pre-determined by, e.g., laboratory experimentation or by computer simulation. Consider the simplified vehicle models 300, 310 in Figures 3A and 3B. These simplified vehicle models only comprise two wheels each. A two-wheeled model of this kind may be referred to as a bicycle model of a heavy-duty vehicle such as the vehicle 100 in Figure 1 and can be used in at least some control operations involving actuators of the heavy-duty vehicle 100. Thus, even if no real heavy-duty vehicle only comprises two wheels, a model of this kind can still be valuable in controlling a multi-wheel heavy-duty vehicle. Assume that wheel torques, angular wheel accelerations, and longitudinal vehicle (hub) acceleration are measured as illustrated in Figure 3A, where

are the applied torques and the measured angular accelerations at the i-th wheel, and ^_^^ is the potentially biased output from the IMU. Wheel torques are reported by the actuators and/or measured by torque sensors, angular accelerations are computed based on the output from the wheel speed sensors. It is also assumed that wheel slips ^_^ and pitch angles of the vehicle are negligible. The variables which are not directly measurable in this example are illustrated in Figure 3B. These are the tyre radii ^_^^ , the true (unbiased) acceleration ^_^ of the vehicle, and the longitudinal tyre forces ^_^^, where again index i denotes the i-th wheel on the vehicle. Assume that the accelerometer output can be modelled as above, i.e.,

Where ^_^^ is the output of the accelerometer, ^_^ = ^̇_^ is the true acceleration, ^ is the unknown accelerometer bias and ^_^ is the longitudinal road slope angle. As mentioned earlier, it is assumed that the slope angle is small and hence we remove the slope contamination of the accelerometer output. In practice, the accelerometer has a noise term, which is normally small and therefore neglected here. In case road slope data is available, it can be used to improve the accuracy of the accelerometer output model. The kinematic relation between angular wheel speed and translational acceleration is, assuming negligible wheel slip, ^_^ = ^_^^^̇_^ Docket No.: P2022-0878WO01 (P449615PC00) ^_^ = ^_^^^̇_^ The axle dynamics are approximated by the equalities ^_^ ⋅ ^̇_^ = ^_^ − ^_^^^_^^

where ^_^and ^_^ are the axle inertias. Newtons second law on the complete vehicle combination gives the relationship ^ ⋅ ^_^ = ^_^^ + ^_^^ − ^_^^^ where ^ is the vehicle mass and ^_^^^ is the motion resistance that mainly comprises effects of air drag and rolling resistance. The vehicle mass ^ can be estimated, e.g., by using bellow pressure measurements from a suspension system of the vehicle 100, which with a known bellow area, gives the normal load. Summing up the normal loads and also adding the vertical load of the axles, the total normal load of the vehicle can be determined. Finally, by dividing the total normal load with the gravity constant ^, the total mass of the vehicle is obtained. A second similar method to obtain the vehicle mass ^ is to use suspension height measurement devices at each axle and apply Hooks law to get the vertical force across the suspension. A third method is to apply Newtons second law in the longitudinal direction where longitudinal acceleration is measured, the total drag force is obtained by summing up all wheel torques from reported torque from the actuators. The mass ^ is then obtained by dividing the drag force with the acceleration. If the third method is applied, the longitudinal accelerometer will be influenced by accelerometer bias, which in fact is the topic of this disclosure. To limit the estimation error of the mass, due to the accelerometer bias, the estimation could just be allowed for large acceleration. The motion resistance ^_^^^ can be pre-determined, e.g., in dependence of vehicle type by laboratory experiments, computer simulation, and/or by field trials. Methods for determining air drag by computer simulation are known. Rolling resistance for a given vehicle type and tyre set-up can be determined based on computer simulation and/or by practical experimentation involving one or more test vehicles. The simplified two-wheel model and the above expressions generate six equations in total and with six unknown variables (^_^ , ^, ^_^^, ^_^^ , ^_^^, ^_^^). This means that, for each time instant, it Docket No.: P2022-0878WO01 (P449615PC00) is possible to solve the algebraic equation system. The solution can also be found analytically, as

Thus, for the two-wheel model in Figures 3A and 3B, it is possible to compute tyre radii and also the accelerometer bias. Note also there is a singularity when wheel accelerations become zero. This singularity is, however, easily avoidable to not performing the calculations unless there is significant vehicle acceleration. The above equations can be extended to vehicle models with more than two wheels in a straight-forward manner. Thus, it is appreciated that the concept can be extended to determining tyre radii for any number of wheels on a vehicle. Suppose that a vehicle comprises ^ wheels with respective tyre radii ^_^^, ^_^^ , … , ^_^^ , where index ^ again denotes wheel number, then the wheel radii and also a number of IMU biases can be determined according to the principles discussed above. Another option is to instead collect data over a time period, such as samples ^ = 1 … ^ and then use the above relationships in an objective function forming part of an optimization problem, such as a least-squares type of objective function. It is then preferred to introduce weights for each “update”, since the input data is likely to differ in reliability. A very small acceleration for instance is not likely to yield accurate results. An example objective function which has been shown to yield good results is a non-linear least squares objective function

^ = [^_^ , ^, ^_^^, … , ^_^^ , ^_^^, … , ^_^^]^{^} are treated as unknown parameters, Docket No.: P2022-0878WO01 (P449615PC00) and the function ^(^) is determined based on the following relationships:

represents motion resistance. The matrix ^ and the scalar ^ are weights which reflect the relative accuracies of the different components of the optimization problem. An advisable principle here is to collect data only when the assumptions made can be trusted. This can be done, e.g., by monitoring slip and pitch angle to ensure they are within predefined bounds. Methods for determining suitable weights comprise practical experimentation and statistical analysis. It is for instance possible to determine ranges for vehicle state variables such as wheel slip, pitch angle, and vehicle acceleration that map onto pre-determined sets of weights. The weights can be continuous or discrete. The weights (such as the ^ and ^ weights discussed above) can be pre-determined as function of time (new measurement data is given precedence over older measurement data). The weights can also be pre-determined as function of vehicle mass reliability. The mass of the vehicle can be estimated using one of the above methods. A monitor can be implemented which detects when mass changes. This monitor can be implemented in any number of ways known in the art. The weight as function of vehicle mass reliability can be configured based on a convergence time of a mass estimator, where the convergence time is counted from a time instant of weight estimator reset. Different vehicle mass estimators have different convergence properties, and the suitable weight as function of mass estimator convergence rate can be determined by practical experimentation, computer simulation, and/or during field trials involving physical vehicles. The acceleration of the vehicle can also be accounted for when determining the weights (such as the ^ and ^ weights discussed above). A suitable mapping between weights and acceleration reliability can be determined by practical experimentation, Docket No.: P2022-0878WO01 (P449615PC00) computer simulation, and/or during field trials involving physical vehicles. The higher the reliability the larger the weight, and vice versa. Figure 4 illustrates an example vehicle control system 400 configured to determine tyre radii and IMU bias in a reliable manner according to the principles discussed herein. A vehicle state monitor 410 measures or estimates current vehicle wheel slip, pitch angle, and vehicle acceleration. The vehicle state monitor then compares the vehicle state variables to pre- determined acceptance criteria, which can be thresholds or ranges where the method has been found to give satisfactory results during testing. The module 410 determines whether proper condition exists to perform the joint estimation of tyre radii and accelerometer bias. If any of these are outside predetermined ranges, then the tyre radii and accelerometer bias estimates will not be updated, or the contribution from present data will at least heavily downweighted. Too small wheel acceleration will also halt the learning. If the vehicle state satisfies the pre-determined vehicle state acceptance criteria, then a vehicle environment monitor 420 compares estimated road slope to vehicle environment acceptance criteria. If this test is also passed, then a weight determination module 430 determines a set of suitable weights using a pre-determined mapping from vehicle mass data reliability and accelerometer data reliability to a set of weights. The module 430 may, e.g., determine the ^ and ^ weights discussed above for use in the optimization routine. The weights will generally be high only if the confidence of the vehicle’s mass estimate is high and confidence from the accelerometer is high. The weights are then input to an optimization routine 440 which attempts to minimize an objective function over a state space comprising effective tyre rolling radii and IMU biases (there can be more than one IMU, here there are ^ unknown IMU biases). Figure 5 illustrates an implementation 500 of the concepts discussed herein based on machine learning. A machine learning structure 510 is initialized based on vehicle data 520, such as vehicle type. The vehicle data generally comprises data indicative of axle inertias associated with the wheels 102 on the heavy-duty vehicle 100, data indicative of a mass of the heavy-duty vehicle, and data indicative of a motion resistance of the heavy-duty vehicle. The machine learning structure initialization may comprise setting up a neural network or some other type of suitable machine learning structure known in the art. A convolutional neural network has Docket No.: P2022-0878WO01 (P449615PC00) been shown to provide satisfactory results. According to one example, machine learning structure initialization operation may comprise training the structure using the set of equations discussed above, or a converged optimization function. Thus, a theoretical relationship given, e.g., by Newtons second law in combination with the kinetic and kinematic relations involving the effective tyre rolling radius discussed above can be used to initialize the structure, and the structure can then be tailored to a given vehicle, having a certain set of tyres and a specific sensor system set-up by training. The training is preferably preferred using some sort of ground truth system where both effective tyre radii and true vehicle acceleration is provided. The machine learning structure is then trained using training data 530, until a suitable convergence criterion is reached. The training data may comprise data from field trials using different types of vehicles, having different IMUs with varying error characteristics. The training data preferably also comprises vehicles with different types of tyres. During training a ground truth system may be used, such as an accurate satellite positioning system that determines both vehicle speed and acceleration in a reliable manner, as well as travelled distance, from which both effective tyre rolling radius and accelerometer bias can be determined. A ground truth system is preferably comprised in the training phase, which accurately measures the relevant parameters, such as unbiased acceleration, true tyre rolling radius, and also the actual vehicle properties involved. Once the machine learning structure has been initialized and trained, it can be fed by measurement data, whereupon the jointly estimated tyre radii and accelerometer bias are output from the structure. Figure 6 is a schematic diagram of a computer system 600 for implementing examples disclosed herein. The computer system 600 is adapted to execute instructions from a computer- readable medium to perform these and/or any of the functions or processing described herein. The computer system 600 may be connected (e.g., networked) to other machines in a LAN, an intranet, an extranet, or the Internet. While only a single device is illustrated, the computer system 600 may include any collection of devices that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. Accordingly, any reference in the disclosure and/or claims to a computer system, computing system, computer device, computing device, control system, control unit, electronic control Docket No.: P2022-0878WO01 (P449615PC00) unit (ECU), processor device, etc., includes reference to one or more such devices to individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. For example, control system may include a single control unit, or a plurality of control units connected or otherwise communicatively coupled to each other, such that any performed function may be distributed between the control units as desired. Further, such devices may communicate with each other or other devices by various system architectures, such as directly or via a Controller Area Network (CAN) bus, etc. The computer system 600 may comprise at least one computing device or electronic device capable of including firmware, hardware, and/or executing software instructions to implement the functionality described herein. The computer system 600 may include a processor device 602 (may also be referred to as a control unit), a memory 604, and a system bus 606. The computer system 600 may include at least one computing device having the processor device 602. The system bus 606 provides an interface for system components including, but not limited to, the memory 604 and the processor device 602. The processor device 602 may include any number of hardware components for conducting data or signal processing or for executing computer code stored in memory 604. The processor device 602 (e.g., control unit) may, for example, include a general-purpose processor, an application specific processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a circuit containing processing components, a group of distributed processing components, a group of distributed computers configured for processing, or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The processor device may further include computer executable code that controls operation of the programmable device. The system bus 606 may be any of several types of bus structures that may further interconnect to a memory bus (with or without a memory controller), a peripheral bus, and/or a local bus using any of a variety of bus architectures. The memory 604 may be one or more devices for storing data and/or computer code for completing or facilitating methods described herein. The memory 604 may include database components, object code components, script components, or other types of information structure for supporting the various activities herein. Any distributed or local memory device may be utilized with the systems and methods of this Docket No.: P2022-0878WO01 (P449615PC00) description. The memory 604 may be communicably connected to the processor device 602 (e.g., via a circuit or any other wired, wireless, or network connection) and may include computer code for executing one or more processes described herein. The memory 604 may include non-volatile memory 608 (e.g., read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.), and volatile memory 610 (e.g., random-access memory (RAM)), or any other medium which can be used to carry or store desired program code in the form of machine- executable instructions or data structures and which can be accessed by a computer or other machine with a processor device 602. A basic input/output system (BIOS) 612 may be stored in the non-volatile memory 608 and can include the basic routines that help to transfer information between elements within the computer system 600. The computer system 600 may further include or be coupled to a non-transitory computer- readable storage medium such as the storage device 614, which may comprise, for example, an internal or external hard disk drive (HDD) (e.g., enhanced integrated drive electronics (EIDE) or serial advanced technology attachment (SATA)), HDD (e.g., EIDE or SATA) for storage, flash memory, or the like. The storage device 614 and other drives associated with computer- readable media and computer-usable media may provide non-volatile storage of data, data structures, computer-executable instructions, and the like. A number of modules can be implemented as software and/or hard coded in circuitry to implement the functionality described herein in whole or in part. The modules may be stored in the storage device 614 and/or in the volatile memory 610, which may include an operating system 616 and/or one or more program modules 618. All or a portion of the examples disclosed herein may be implemented as a computer program product 620 stored on a transitory or non-transitory computer-usable or computer-readable storage medium (e.g., single medium or multiple media), such as the storage device 614, which includes complex programming instructions (e.g., complex computer-readable program code) to cause the processor device 602 to carry out the steps described herein. Thus, the computer-readable program code can comprise software instructions for implementing the functionality of the examples described herein when executed by the processor device 602. The processor device 602 may serve as a controller or control system for the computer system 600 that is to implement the functionality described herein. Docket No.: P2022-0878WO01 (P449615PC00) The computer system 600 also may include an input device interface 622 (e.g., input device interface and/or output device interface). The input device interface 622 may be configured to receive input and selections to be communicated to the computer system 600 when executing instructions, such as from a keyboard, mouse, touch-sensitive surface, etc. Such input devices may be connected to the processor device 602 through the input device interface 622 coupled to the system bus 606 but can be connected through other interfaces such as a parallel port, an Institute of Electrical and Electronic Engineers (IEEE) 1394 serial port, a Universal Serial Bus (USB) port, an IR interface, and the like. The computer system 600 may include an output device interface 624 configured to forward output, such as to a display, a video display unit (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)). The computer system 600 may also include a communications interface 626 suitable for communicating with a network as appropriate or desired. Figure 7 is a flow chart illustrating methods which summarize at least some of the discussion herein. The flow chart illustrates aspects of a computer-implemented method for controlling a heavy-duty vehicle 100 based on determined tyre radii ^_^^ , ^_^^ associated with wheels 102 on the heavy-duty vehicle 100 and an accelerometer bias ^ associated with at least one IMU of the heavy-duty vehicle 100. The method comprises obtaining, S1, by a processor device of a computer system such as that discussed below in connection to Figure 6 or some other control circuit, vehicle data comprising data indicative of axle inertias ^_^, ^_^ associated with the wheels 102 on the heavy- duty vehicle 100, data indicative of a mass ^ of the heavy-duty vehicle 100, and data indicative of a motion resistance ^_^^^ of the heavy-duty vehicle 100. The mass ^ of the heavy-duty vehicle 100 may be obtained S11, at least partly as a pre-configured mass and/or at least partly based on an output signal from a load sensor of the heavy-duty vehicle 100. Other methods of inferring vehicle mass are also known in the art. The method also comprises obtaining, S2, by the processor device, measurement data comprising torque data indicative of respective applied torques

associated with the wheels 102 on the heavy-duty vehicle 100, wheel speed data indicative of respective angular accelerations ^̇_^, ^̇_^ associated with the wheels 102 on the heavy-duty vehicle 100, and accelerometer data ^_^^ indicative of an acceleration by the vehicle 100. Methods of obtaining Docket No.: P2022-0878WO01 (P449615PC00) accurate real-time the torque data was discussed above. Some examples comprise obtaining S21 the torque data at least partly as an applied torque by an electric machine, where the applied torque is estimated based on a motor current associated with the electric machine, obtaining S22 the torque data at least partly as an applied torque by a service brake, where the applied torque is estimated based on an applied brake pressure by the service brake, obtaining S23 the torque data at least partly based on an output from a torque sensor, such as a strain-force sensor, and obtaining S24 the torque data at least partly based on a predetermined electric machine wind-up characteristic ^^_^^^. The wheel speed data is most conveniently obtained S25 from wheel speed sensors connected to the wheels 102 in combination with timing data from a timing device. A relationship can, as discussed above, be obtained S3, by the processor device, which models a mapping between the tyre radii ^_^^, ^_^^, the accelerometer bias ^, the vehicle data, and the measurement data. This enables the processor device to determine S4 the tyre radii ^_^^, ^_^^ and the accelerometer bias ^ based on the vehicle data and on the pre-determined relationship, as function of the measurement data. Thus, the vehicle 100 can be controlled S5, by the processor device, based on the tyre radii ^_^^ , ^_^^ and the accelerometer bias ^. This control may, e.g., involve actuator control and vehicle state estimation facilitating actuator control by other vehicle control modules. According to some aspects, the method comprises obtaining S31 the pre-determined relationship as ^ ^ = _^ _^^ 2^^̇_^ ^ ^ = _^ _^^ 2^^̇_^ 2^^_^^ − ^ ^ = _^^^ 2^ ^ = ^^{^} − 4^ ^^̇^ + 4^ ^̇ − 4^ ^^ ^ ^ ^{^} _{^^^ ^ ^ ^ ^ ^} ̇_^ + 4^_^^̇_^ − ^_^^^ Docket No.: P2022-0878WO01 (P449615PC00) where ^_^^, ^_^^ are the tyre radii, ^ is the vehicle mass, ^̇_^, ^̇_^ are the angular accelerations, ^ is the accelerometer bias, ^_^^ is the accelerometer data, ^_^^^ is the motion resistance, ^_^, ^_^ are the axle inertias, and

^_^ are the applied torques. According to some other aspects, the method comprises obtaining S32 the pre-determined relationship as a machine learning structure configured based on the vehicle data and taking the measurement data as input. The method may also comprise obtaining S33 the pre-determined relationship as the solution to an optimization problem involving the vehicle data and the measurement data. This optimization problem may, for instance, be formulated as a least-squares type optimization problem having an objective function ^ given by

where ^ and ^ are weights, the determination of which was discussed above,

and where ^⁽^⁾ is given by the relationships ^_^^ = ^_^ + ^ ^_^ = ^_^^̇_^+^_^^_^,^ ^ ^̇ _^ _^ = ^_^^ The method preferably comprises determining S41 the tyre radii ^_^^, ^_^^ and the accelerometer bias ^ iteratively over time, which means that the estimates are successively refined as more and more data becomes available. According to some aspects, the method comprises determining S42 the tyre radii ^_^^, ^_^^ and the accelerometer bias ^, conditioned on that a state of the vehicle 100 meets predetermined acceptance criteria comprising any of wheel slip, pitch angle, and vehicle acceleration. An example of such method features was discussed above in connection to Figure 4. Of particular Docket No.: P2022-0878WO01 (P449615PC00) importance is the vehicle mass data and presence of a non-zero acceleration by the vehicle. Wheel slip and pitch angle may also be of interest. According to some other aspects, also discussed above in connection to Figure 4, the method comprises determining S43 the tyre radii ^_^^, ^_^^ and the accelerometer bias ^ conditioned on that an environment of the vehicle 100 meets predetermined acceptance criteria comprising any of road slope and road banking. According to some further aspects, the method comprises determining S44 an accuracy metric associated with the vehicle data and determining the tyre radii ^_^^ , ^_^^ and the accelerometer bias ^ conditioned on that the vehicle data accuracy metric meets predetermined acceptance criteria. The vehicle data may comprise various data items. If one or more such items are found inaccurate, the update can be avoided or at least down-weighted heavily such that the inaccurate data does not contaminate the output. Figure 8 illustrates a computer readable medium 810 carrying a computer program comprising program code means 820 for performing the methods illustrated in Figure 7 and the techniques discussed herein, when said program product is run on a computer. The computer readable medium and the code means may together form a computer program product 800. The operational steps described in any of the exemplary aspects herein are described to provide examples and discussion. The steps may be performed by hardware components, may be embodied in machine-executable instructions to cause a processor to perform the steps, or may be performed by a combination of hardware and software. Although a specific order of method steps may be shown or described, the order of the steps may differ. In addition, two or more steps may be performed concurrently or with partial concurrence. The terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting of the disclosure. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items. It will be further understood that the terms "comprises," "comprising," "includes," and/or "including" when used herein specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or Docket No.: P2022-0878WO01 (P449615PC00) addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that, although the terms first, second, etc., may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element without departing from the scope of the present disclosure. Relative terms such as "below" or "above" or "upper" or "lower" or "horizontal" or "vertical" may be used herein to describe a relationship of one element to another element as illustrated in the Figures. It will be understood that these terms and those discussed above are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element, or intervening elements may be present. In contrast, when an element is referred to as being "directly connected" or "directly coupled" to another element, there are no intervening elements present. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. It is to be understood that the present disclosure is not limited to the aspects described above and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the present disclosure and appended claims. In the drawings and specification, there have been disclosed aspects for purposes of illustration only and not for purposes of limitation, the scope of the inventive concepts being set forth in the following claims.

Claims

Docket No.: P2022-0878WO01 (P449615PC00) CLAIMS 1. A computer-implemented method, for controlling a heavy-duty vehicle (100) based on determined tyre radii (^_^^, ^_^^) associated with wheels (102) on the heavy-duty vehicle (100) and an accelerometer bias (^) associated with at least one inertial measurement unit, IMU, of the heavy-duty vehicle (100), the method comprising obtaining, (S1), by a processor device of a computer system, vehicle data comprising data indicative of axle inertias (^_^, ^_^) associated with the wheels (102) on the heavy-duty vehicle (100), data indicative of a mass (^) of the heavy-duty vehicle (100), and data indicative of a motion resistance (^_^^^) of the heavy-duty vehicle (100), obtaining, (S2), by the processor device, measurement data comprising torque data indicative of respective applied torques (^_^, ^_^) associated with the wheels (102) on the heavy-duty vehicle (100), wheel speed data indicative of respective angular accelerations (^̇_^, ^̇_^) associated with the wheels (102) on the heavy-duty vehicle (100), and accelerometer data (^_^^) indicative of an acceleration by the vehicle (100), and obtaining (S3), by the processor device, a relationship between the tyre radii (^_^^, ^_^^), the accelerometer bias (^), the vehicle data, and the measurement data, the method further comprising determining (S4), by the processor device, the tyre radii (^_^^ , ^_^^) and the accelerometer bias (^) based on the vehicle data and on the pre-determined relationship, as function of the measurement data, and controlling (S5) the vehicle (100), by the processor device, based on the tyre radii (^_^^ , ^_^^) and the accelerometer bias (^). 2. The method according to claim 1, comprising obtaining, (S11) the mass (^) of the heavy-duty vehicle (100), at least partly as a pre-configured mass and/or at least partly based on an output signal from a load sensor of the heavy-duty vehicle (100). 3. The method according to claim 1 or 2, comprising obtaining (S21) the torque data at least partly as an applied torque by an electric machine, where the applied torque is estimated based on a motor current associated with the electric machine. Docket No.: P2022-0878WO01 (P449615PC00) 4. The method according to any previous claim, comprising obtaining (S22) the torque data at least partly as an applied torque by a service brake, where the applied torque is estimated based on an applied brake pressure by the service brake. 5. The method according to any previous claim, comprising obtaining (S23) the torque data at least partly based on an output from a torque sensor, such as a strain-force sensor. 6. The method according to any previous claim, comprising obtaining (S24) the torque data at least partly based on a predetermined electric machine wind-up characteristic (^^_^^^). 7. The method according to any previous claim, comprising obtaining, (S25) the wheel speed data from wheel speed sensors connected to the wheels (102) in combination with timing data from a timing device. 8. The method according to any previous claim, comprising obtaining (S31) the pre- determined relationship as

where ^_^^, ^_^^ are the tyre radii, ^ is the vehicle mass, ^̇_^, ^̇_^ are the angular accelerations, ^ is the accelerometer bias, ^_^^ is the accelerometer data, ^_^^^ is the motion resistance, ^_^, ^_^ are the axle inertias, and

^_^ are the applied torques. 9. The method according to any previous claim, comprising obtaining (S32) the pre- determined relationship as a machine learning structure configured based on the vehicle data and taking the measurement data as input. 10. The method according to any previous claim, comprising obtaining (S33) the pre- determined relationship as the solution to an optimization problem involving the vehicle data and the measurement data. Docket No.: P2022-0878WO01 (P449615PC00) 11. The method according to claim 10, where the optimization problem is a least-squares type optimization problem having an objective function ^ given by ^ = (^ − ^(^))^{^}^^^ − ^(^)^ + ^(^ − ^(^))^{^} where ^ and ^ are weights,

and where ^⁽^⁾ is given by the relationships ^_^^ = ^_^ + ^ ^_^ = ^_^^̇_^+^_^^_^,^

12. The method according to any previous claim, determining (S41) the tyre radii (^_^^, ^_^^) and the accelerometer bias (^) iteratively over time. 13. The method according to any previous claim, determining (S42) the tyre radii (^_^^, ^_^^) and the accelerometer bias (^), conditioned on that a state of the vehicle (100) meets predetermined acceptance criteria comprising any of wheel slip, pitch angle, and vehicle acceleration. 14. The method according to any previous claim, determining (S43) the tyre radii (^_^^, ^_^^) and the accelerometer bias (^) conditioned on that an environment of the vehicle (100) meets predetermined acceptance criteria comprising any of road slope and road banking. 15. The method according to any previous claim, determining (S44) an accuracy metric associated with the vehicle data, and determining the tyre radii (^_^^ , ^_^^) and the accelerometer bias (^) conditioned on that the vehicle data accuracy metric meets predetermined acceptance criteria. Docket No.: P2022-0878WO01 (P449615PC00) 16. A vehicle (100) comprising a processor device configured to perform the method of any previous claim. 17. A computer program product comprising program code for performing, when executed by the processor device, the method of any previous claim. 18. A non-transitory computer-readable storage medium comprising instructions, which when executed by a processor device, cause the processor device to perform the method of any previous claim. 19. A computer system comprising a processor device configured to control a heavy-duty vehicle (100) based on determined tyre radii (^_^^, ^_^^) associated with wheels (102) on the heavy-duty vehicle (100) and an accelerometer bias (^) associated with an inertial measurement unit, IMU, of the heavy-duty vehicle (100), where the processor device is configured to obtain vehicle data comprising data indicative of axle inertias (^_^, ^_^) associated with the wheels (102) on the heavy-duty vehicle (100), data indicative of a mass (^) of the heavy-duty vehicle (100), and data indicative of a motion resistance (^_^^^) of the heavy-duty vehicle (100), obtain measurement data comprising torque data indicative of respective applied torques (^_^, ^_^) associated with the wheels (102) on the heavy-duty vehicle (100), wheel speed data indicative of respective angular accelerations (^̇_^, ^̇_^) associated with the wheels (102) on the heavy-duty vehicle (100), and accelerometer data (^_^^) indicative of an acceleration by the vehicle (100), and obtain a relationship between the tyre radii (^_^^ , ^_^^), the accelerometer bias (^), the vehicle data, the measurement data, determine the tyre radii (^_^^, ^_^^) and the accelerometer bias (^) based on the vehicle data and on the pre-determined relationship, as function of the measurement data, and control the vehicle (100) based on the tyre radii (^_^^, ^_^^) and the accelerometer bias (^).