A method and a control arrangement of a vehicle

Abstract

A method (200) and a control arrangement (120) of a vehicle (100) on which one or more resistance forces act are presented. The method (200) comprises: - defining (210) a resistance model M as: Far = av2 + bv + c; wherein - Far is a combined aerodynamic and rolling resistance force; - v is a velocity of the vehicle (100); and - a, b, c are resistance model parameters; - determining (220) three or more n ≥3 distinct measurements of each one of: - a mass mvehicle of the vehicle (100); - a velocity v of the vehicle (100); - a traction force Ft acting on the vehicle (100); and - a gravitational force Fg acting on the vehicle (100); and - determining (230) the resistance model parameters a, b, c based on the three or more n ≥ 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg.

Description

[0001] A METHOD AND A CONTROL ARRANGEMENT OF A VEHICLE

[0002] Technical field

[0003] The present invention relates to a method and a control arrangement of a vehicle on which one or more resistance forces act, and in particular to a method and a control arrangement determining and utilizing a resistance model for the vehicle, for example for determining a distance to empty value. The present invention also relates to a computer program and a computer-readable medium that implement the method according to the invention.

[0004] Background

[0005] The following background description constitutes a description of the background to the present invention, which does not, however, necessarily have to constitute prior art.

[0006] Vehicles of today are driven by an internal combustion engine and / or at least one electric machine. The internal combustion engine is driven by fuel from a fuel tank in the vehicle. The fuel tank has a limited volume. The at least one electric machine is driven by electric energy from an energy storage. The at least one energy storage can store a limited amount of electric energy.

[0007] It is important for a driver of a vehicle to know the current range of the vehicle, i.e. to know how far the vehicle can be propelled by the fuel in the fuel tank and / or by the electric energy stored in the energy storage, also called the distance to empty for the vehicle. Based on the knowledge of the range / reach of the vehicle from the current position, it is possible for the driver to plan a route to be driven, including planning stops for filling the fuel tank, charging the energy storage and / or making other stops, such as resting pauses.

[0008] Brief description of the invention

[0009] In conventional solutions for determining a distance to empty, only the history of the fuel and / or energy consumption for the vehicle are used as a basis for the determination. For static driving conditions, the conventional solutions may provide an acceptable accuracy for the distance to empty determination.However, for changing driving conditions during an upcoming road section, for example future variations in the ambient temperature, the tire temperature, the tire pressure, the tire slip, the number of stops, the weight of the vehicle and / or the length of the vehicle, the conditions for the range of the vehicle also changes. Since the conventional solutions are generally based on historic fuel and / or energy consumption for the vehicle, they become inaccurate when the upcoming driving conditions are changing. Therefore, the sensitivity an inaccuracy due to changing or alternating driving conditions is a problem for conventional solutions.

[0010] It is therefore an objective of the present invention to provide a method and control arrangement for determining a resistance model for the vehicle, which may be utilized for adapting to changing driving conditions and which may be utilized as a basis for distance to empty determinations.

[0011] According to an aspect of the present invention, this objective is achieved through the above-mentioned method of a vehicle on which one or more resistance forces act;

[0012] the method comprising:

[0013] - defining a resistance model M as:

[0014] Far= av2+ bv + c wherein

[0015] -- Faris a combined aerodynamic and rolling resistance force;

[0016] -- v is a velocity of the vehicle; and

[0017] -- a, b, c are resistance model parameters;

[0018] - determining three or more n > 3 distinct measurements of each one of:

[0019] -- a mass mvehicleof the vehicle;

[0020] -- a velocity v of the vehicle;

[0021] -- a traction force Ftacting on the vehicle; and

[0022] -- a gravitational force Fgacting on the vehicle; and

[0023] - determining the resistance model parameters a,b,c based on the three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg.

[0024] The resistance model parameters a, b and c are determined and possibly calibrated by using online estimation under different load, road slope and / or speed conditionsfor the vehicle. The measurements being distinct means that the values are measured during varying driving conditions. Three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fgare used as basis for determining the resistance model parameters a,b,c, which makes the resistance model M being properly based on the actual physics of the vehicle. Three distinct measurements are enough to get unique solutions for the resistance model parameters a, b, c, and thus a proper determination of the resistance model parameters a, b, c. It should be noted, however, that the more distinct measurements being used as basis for the determination, the higher the rank of the below described matrix of velocities used for the determination will be, and thus the more accurate the determination of the resistance model parameters a, b, c becomes. Thus, if a higher number of measurements are made under varying conditions, the accuracy of the resistance model M is improved. A high rank is provided by many linearly independent rows in the matrix, which is achieved by gathering data from many different driving conditions.

[0025] Generally, the higher the variance of the distinct measurements is, the better and more exact, the outcome will be. In practice, this means that measurements should be performed for varying driving conditions, i.e. for different velocities of the vehicle, for different wind conditions, for different slope angles, and so on. As non-limiting examples, suitable time intervals between the measurements, having a length between 10 seconds and 10 minutes, may be used. Alternatively, the intervals between the measurements may be dynamically determined, based for example on a deviation of so far measured values.

[0026] A digital twin of the vehicle propelling system may be created as or based on the resistance model M, which may be utilized together with simulated future driving conditions for the vehicle in an upcoming road section in the calculation of a distance to empty for fuel driven vehicles, for battery electric vehicles, and / or for hybrid vehicles, which is hereby improved.

[0027] Accurate estimations of futuristics scenarios for the vehicle are made possible when being made based on the determined resistance model M, also for varying driving or vehicle conditions. This is possible since the resistance model M is physics-based, isbased on the physical characteristics of the vehicle, and for example takes into consideration a tire pressure, and a friction co-efficient dependency on temperature. The determined resistance model M may be utilized for simulating driving conditions, by estimating a set of physics-based parameters through calibration based on a set of different scenarios that affects energy consumption, including but not being limited to slope angle of the road, vehicle speed, tire temperature, and / or ambient temperature. These simulated driving conditions may have an influence on which route of a number of possible routes being the most energy efficient, and may be used in the distance to empty determination.

[0028] The solution is based on the physics of the vehicle, and is hence more accurate than conventional solutions being based only on historic data, i.e. being unrelated to the actual physics of the vehicle.

[0029] According to an embodiment of the present invention, the determination of the resistance model parameters a,b,c comprises:

[0030] - estimating the resistance model parameters a,b,c based on a vehicle force equation, the vehicle force equation being overdetermined by the three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg.

[0031] Since the vehicle force equation is overdetermined by the three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg, the estimation of the resistance model parameters a, b, c based on a vehicle force equation provides for an acceptable accuracy. The more distinct measurements being made, the higher the rank of the matrix of velocities will be, due to its then multiple linearly independent rows and columns, and thus the more accurate the determination of the resistance model parameters a, b, c, and thus also the determination of the resistance model M, will become.

[0032] According to an embodiment of the present invention, the vehicle force equation is defined as:v±1 ■a ■

[0033] = b

[0034]

[0035] -mvehiclev̇n+ Ft_n− Fg_n

[0036] where:

[0037] ^■vehicle^l + Ft _1 Fg ±

[0038] is a matrix of forces Aforces;

[0039] ~^-vchiclc ^’n + Ft_n ~ Fg_n

[0040] is a matrix of velocities Bvelocity;

[0041]

[0042] -a

[0043] b is a matrix of the resistance model parameters; and

[0044] c

[0045] - vkis an acceleration for the vehicle; k = 1, 2,...n,n > 3.

[0046] Hereby, an efficient and accurate determination of the resistance model parameters a, b, c and the resistance model M based on a number of individual measurements is provided. Generally, a higher rank of the matrix of velocities Bvelocity, which is provided by a higher number of linearly independent rows and columns of the matrix of velocities Bvelocity, provides for a more accurate determination of the resistance model parameters a, b, c. A high rank is generally provided by many linearly independent rows in the matrix velocities Bvelocity, which is achieved by measuring data at many different driving conditions. It should be noted that the matrix of velocities Bvelocitywill have full rank thanks to the three or more n > 3 distinct measurement values determined for each of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg. Therefore, there are unique solutions for the resistance model parameters a, b, c.

[0047] According to an embodiment of the present invention, a determinant of the matrix of velocities Bvelocityis non-zero.

[0048] The accuracy of the determination of the resistance model parameters a,b,c and the resistance model M is increased with an increasing number of individual measurements, i.e. with increasing rank of the matrix of velocities Bvelocity. Basically, the determinant of the matrix of velocities Bvelocitybeing non-zero results in an at least acceptable accuracy for the determination of the resistance model parameters a, b, c and the resistance model M. For maximal accuracy, the rank of matrix ofvelocities Bvelocityshould be as high as possible. It should be noted that the matrix of velocities Bvelocityhaving a non-zero determinant according to this embodiment also implies that the matrix of velocities Bvelocityis a square matrix, since non-square matrices do not comprise determinants.

[0049] According to an embodiment of the present invention, the values of the matrix of velocities Bvelocityare weighted such that values associated with more recent velocity measurements are given higher importance than values associated with older measurements.

[0050] Hereby, the accuracy of the determination of the resistance model parameters a, b, c and the resistance model M is further improved, because older and thus less important measurement values are given less weight / importance in the determination.

[0051] According to an embodiment of the present invention, the method further comprises: - predicting at least one future traction force Ft_future_k; k > 1; for a road section ahead of the vehicle based on:

[0052] -- at least one future combined aerodynamic and rolling resistance force

[0053] Farfuture k> k > 1; which is determined based on the resistance model M;

[0054] -- at least one future gravitational force on the vehicle Fg future k; k > 1;

[0055] -- at least one future vehicle mass mvehiclefuture k; k > 1; and

[0056] -- at least one future acceleration of the vehicle v̇future k; k > 1.

[0057] Thus, the accurately determined resistance model M may be used together with some predicted future vehicle characteristics as a basis for the prediction of the at least one future traction force Ft future kfor the road section ahead of the vehicle. Hereby, an accurate and efficient prediction of the at least one future traction force Ft future k is provided. The high quality at least one future traction force Ft_future_kmay then be utilized as a basis for an accurate determination of the distance to empty for the vehicle.According to an embodiment of the present invention, the at least one future traction force FtfUture fe; k > 1; is predicted as:

[0058] Pt_future_l P ar_future_l Pg_future_l VT-vehicle_future_l * ^’ / uture_l = + +

[0059]

[0060] P t_future_n P ar_future_n P g_future_n VT-vehicle_future_n * Vfuture nHereby, an efficient and accurate prediction the at least one future traction force Pt_future_k is provided.

[0061] According to an embodiment of the present invention, the method further comprises - predicting a future speed and direction vdir distof a wind for a road section ahead of the vehicle;

[0062] - predicting the at least one future combined aerodynamic and rolling resistance force Par future k> k > 1 based on the future speed and direction vdir distof the wind, and on the resistance model M.

[0063] To predict the at least one future combined aerodynamic and rolling resistance force Par future k based on the future wind conditions improves both the accuracy and the efficiency of the predictions.

[0064] According to an embodiment of the present invention,

[0065] - it is predicted that a speed of the future wind to be experienced by the vehicle will be non-zero and varying; and

[0066] - the at least one future combined aerodynamic and rolling resistance force

[0067] Par future k; & > 1 is then predicted as:

[0068] Par_future_k P * Af * Cd+ * ^dist_k T (■*•!—P * Af * Cd* ^dir_dist) *

[0069]

[0070] Vdistjt + P * Af * Q * Vdir dist T ^o)> where:

[0071] - p is a density of air;

[0072] - Afis a frontal area of the vehicle;

[0073] - cdis a coefficient for a rolling resistance of the vehicle;

[0074] - x2, x1, x0are combined vehicle resistance model parameters;

[0075] - vdist_kis at least one future vehicle speed;

[0076] - vdir_dist_kis at least one future wind speed and direction;1

[0077] - -p * Af* cd+ x2correspond to resistance model parameter a;

[0078] - x - p * Af* cd* vdir kcorrespond to resistance model parameter b; and

[0079] - -p * Af * cd* vdir k2+ xQcorrespond to resistance model parameter c.

[0080] By predicting the future wind conditions in the upcoming road section ahead of the vehicle, the prediction of the at least one future combined aerodynamic and rolling resistance force FarfUture kmay utilize this model for the at least one future combined aerodynamic and rolling resistance force Farjuture_k, which takes the wind condition predictions being adapted to changing wind conditions into consideration. Hereby, an accurate and reliable prediction of the at least one future combined aerodynamic and rolling resistance force FarfUture kis facilitated.

[0081] According to an aspect of the present invention, the method further comprises: - determining the combined vehicle resistance model parameters x2, x1, x0as:

[0082] i

[0083] - x2= a - ½ρ * Af* cd,

[0084] - x1= b + p * Af* cd* vdir dist k; and

[0085] 14o

[0086] “

[0087]

[0088] *0 ~ C2P * Af * * Vdir_dist_k ■

[0089] Hereby, the combined vehicle resistance model parameters x2, x1, x0, and thus the model for the at least one future combined aerodynamic and rolling resistance force Far_future_kis efficiently and reliably determined based on the previously determined resistance model parameters a,b,c.

[0090] According to an aspect of the present invention,

[0091] - it is predicted that a speed of the future wind to be experienced by the vehicle will be zero and / or constant; and

[0092] - the at least one future combined aerodynamic and rolling resistance force

[0093] Farfuture k>' k > 1 is then predicted as:

[0094] F

[0095]

[0096] ar_future_k ~ (2P * Af * ^cl "h -^2) * ^dist_k + * ^dist_k "h -^0> where:

[0097] - p is a density of air;

[0098] - A is a frontal area of the vehicle;- cdis a coefficient for a rolling resistance of the vehicle;

[0099] - x2, x1, x0are combined vehicle resistance model parameters;

[0100] - vdist_kis at least one future vehicle speed;

[0101] - -p * Af* cd+ x2corresponds to resistance model parameter a;

[0102] - xtcorresponds to resistance model parameter b; and

[0103] - x0corresponds to resistance model parameter c.

[0104] When there will be no wind or a constant wind in the upcoming road section, the model for the future combined aerodynamic and rolling resistance force Far future kmay be simplified this way, which reduces the computational complexity.

[0105] According to an aspect of the present invention, the method further comprises:

[0106] - determining the combined vehicle resistance model parameters x2, x1, x0as:

[0107] i

[0108] - x2= a - ½ρ * Af* cd,

[0109]

[0110] - Xi = / ?; and

[0111] - x0= c.

[0112] Hereby, the combined vehicle resistance model parameters x2, xt, x0, and thus the model for the at least one future combined aerodynamic and rolling resistance force Par future k is efficiently and reliably determined based on the previously determined resistance model parameters a,b,c.

[0113] According to an aspect of the present invention, the prediction of the future speed and direction vdir distof the wind for the road section ahead of the vehicle is based on one or more in the group of:

[0114] - sensor data;

[0115] - weather data;

[0116] - positioning information;

[0117] - vehicle-to-everything information; and

[0118] - map data.

[0119] The prediction of the future speed and direction vdir distof the wind for the road section ahead may thus be based on essentially any information comprising anyindications on how the wind may vary over time and / or along the road section ahead, such that a reliable and accurate prediction is facilitated.

[0120] According to an aspect of the present invention, the method further comprises:

[0121] - predicting the at least one future gravitational force on the vehicle Fg future k; k > 1 based on an upcoming road slope adistfora road section ahead of the vehicle;

[0122]

[0123] kg f uture k ^vehicle future k * 9 *sin— 1- Hereby, the influence of the inclination adistof the road to be travelled by the vehicle has on the at least one future gravitational force on the vehicle Fg future kis taken into consideration to provide an accurate and reliable prediction.

[0124] According to an aspect of the present invention, the upcoming road slope adistis predicted based on positioning information and map data.

[0125] Digital maps of today comprise detailed road slope information, which is hereby easily utilized for providing high quality predictions of the at least one future gravitational force on the vehicle Fg future k.

[0126] According to an aspect of the present invention, the method further comprises:

[0127] - predicting the at least one future vehicle mass mvehicie future kk > 1 based on one of more in the group of:

[0128] -- a current weight of the vehicle; and

[0129] -- a load and delivery scheme, positioning information and map data.

[0130] The weight of the vehicle may change considerably during a route, mainly due to loading and / or unloading of cargo. Such changes of the cargo weight, and thereby also changes of the vehicle weight, may easily be taken into account if the load and delivery scheme is used as a basis. Thus, an accurate prediction of the future vehicle mass mvehicle_future_kis hereby provided.

[0131] According to an aspect of the present invention, the method further comprises:

[0132] - predicting the at least one future acceleration of the vehicle vfuture k, k > 1 based on one or more in the group of:

[0133] -- a current speed of the vehicle;

[0134] -- positioning information, and map data comprising speed limit information for theroad section ahead of the vehicle; and

[0135] - vehicle-to-everything information comprising speed limit information for the road section ahead of the vehicle.

[0136] By taking the current speed and also the speed limits for the road section ahead of the vehicle into account, a more accurate and reliable prediction of the future acceleration of the vehicle vfuture kis provided. Such speed limit information is available in the detailed digital maps of today.

[0137] According to an aspect of the present invention, the method further comprises:

[0138] - determining a distance to empty for the vehicle based on the at least one future traction force Ft future kk > 1.

[0139] Since the at least one future traction force FtfUture kis accurately and efficiently predicted as herein described, the distance to empty determination for internal combustion engine vehicles, for battery electric vehicles, and / or for hybrid vehicles may also be accurately and efficiently determined. The distance to empty determination is based on the physics-based digital twin of the vehicle propelling system, providing for a better estimation of the energy consumption, which is vital for distance to empty functions. The digital twin is here utilized together with simulated future driving conditions for the vehicle in the upcoming road section, such that an accurate distance to empty determination is facilitated, also for varying conditions in the upcoming road section. The distance to empty determination is here based on the physics of the vehicle, and is hence more accurate than conventional solutions being based only on historic data, i.e. being unrelated to the actual physics of the vehicle and the possible future driving scenarios.

[0140] According to an aspect of the present invention, the distance to empty for the vehicle is determined based also on one or more in the group of:

[0141] - positioning information, and map data comprising tank station information for the road section ahead of the vehicle;

[0142] - vehicle-to-everything information comprising tank station information for the road section ahead of the vehicle;

[0143] - positioning information, and map data comprising charging station information forthe road section ahead of the vehicle; and

[0144] - vehicle-to-everything information comprising charging station information for the road section ahead of the vehicle.

[0145] A fuel tank may be filled and / or an energy storage may be charged in the upcoming road section, which obviously increases the distance to empty. To take also a presence or non-presence of tank stations and / or charging stations into consideration when determining the distance to empty provides for a more complete information regarding the distance to empty being presented for the driver. Hereby, the driver may more efficiently and intelligently plan the route, including deciding when to stop for filling / charging and when to make other pauses.

[0146] According to an aspect of the present invention, the distance to empty for the vehicle is determined as one or more in the group of:

[0147] - a distance reachable by the vehicle when consuming an amount of fuel in a fuel tank of the vehicle; and

[0148] - a distance reachable by the vehicle when consuming an amount of energy stored in an energy storage of the vehicle.

[0149] Thus, the herein presented solution is generally applicable to vehicles having an internal combustion engine powertrain, an electric machine powertrain, ora hybrid combustion and electric powertrain.

[0150] According to an aspect of the present invention, the three or more n > 3 distinct measurements are instantaneous measurement values.

[0151] The measurements values being instantaneous means that they are measured simultaneously for a specific driving condition. Thus, the three or more n > 3 distinct measurements have been measured instantaneously for various different driving situations and under various different driving conditions. Hereby, the determination of the resistance model parameters a, b, c may be performed with high accuracy. The more distinct measurement values being available to be taken into consideration in the determination, the higher the quality of the determination of the resistance model parameters a, b, c will become.According to an aspect of the present invention, the objective is achieved through a control arrangement of a vehicle configured for determining resistance model parameters a, b, c for a vehicle on which one or more resistance forces act.

[0152] The control arrangement is configured to:

[0153] - define a resistance model M as:

[0154] Far= av2+ bv + c; wherein

[0155] -- Faris a combined aerodynamic and rolling resistance force;

[0156] -- v is a velocity of the vehicle; and

[0157] -- a, b, c are resistance model parameters;

[0158] - determine three or more n > 3 distinct measurements of each one of:

[0159] -- a mass mvehicleof the vehicle;

[0160] -- a velocity v of the vehicle;

[0161] -- a traction force Ftacting on the vehicle; and

[0162] -- a gravitational force Fgacting on the vehicle; and

[0163] - determine the resistance model parameters a, b, c based on the three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg.

[0164] According to an aspect of the present invention, the objective is achieved through a vehicle comprising a herein described control arrangement.

[0165] It will be appreciated that all the embodiments described for the method aspect of the invention are applicable also to the control arrangement aspect and the vehicle aspect of the invention. Thus, all the embodiments described for the method aspect of the invention may be performed by the control arrangement, which may also be a control unit or device, i.e. a device, and / or by the vehicle. The control arrangement and the vehicle, and their embodiments have advantages corresponding to the advantages mentioned above for the method and its embodiments.

[0166] According to an aspect of the present invention, the above-mentioned computer program and computer-readable medium are configured to implement the method and its embodiments described herein. The mentioned computer program and computer-readable medium and their respective embodiments have advantagescorresponding to the advantages mentioned above for the method aspect and its embodiments.

[0167] Brief list of figures

[0168] Embodiments of the invention will be illustrated in more detail below, along with the enclosed drawings, where similar references are used for similar parts, and where:

[0169] Figure 1 shows an example vehicle, in which aspects and embodiments of the present invention may be implemented,

[0170] Figure 2 schematically illustrates a vehicle travelling on a road section and some forces acting on the vehicle,

[0171] Figure 3 shows a flow chart for a method according to some aspects and embodiments of the present the invention,

[0172] Figure 4 schematically illustrates an example driving situation, and

[0173] Figure 5 shows a control unit, in which a method according to any one of the herein described aspect and embodiments may be implemented.

[0174] Description of preferred embodiments

[0175] Figure 1 schematically illustrates an example vehicle 100 according to some aspects and embodiments of the herein presented invention. The vehicle 100 is illustrated as a tractor vehicle. However, for other embodiments, the vehicle 100 may, for example, be of any other kind of heavy vehicle, such as a bus or a truck. The vehicle may also, e.g., be a passenger car. The vehicle may also be another type of vehicle. Although not illustrated in figure 1, the vehicle 100 may be equipped with a trailer. The vehicle 100 comprises a powertrain which may comprise at least one power source 101 in form of an internal combustion engine and / or at least one electric machine. The powertrain may thus be configured as classic internal combustion engine (ICE) powertrain, as an electric vehicle (EV) powertrain, such as a battery electric vehicle (BEV) powertrain, or as a hybrid electric vehicle (HEV) powertrain.The vehicle 100 may further, as schematically illustrated, comprise multiple wheels 102, of which only wheels 102 of the left-hand side of the vehicle 100 are visible in figure 1. It is to be understood that the vehicle 100 may have fewer or more wheels than what is shown in figure 1.

[0176] The powertrain comprises the above mentioned at least one power source 101, such as an internal combustion engine and / or one or more electrical machines, configured to apply a propulsive power and / or a braking power to one or more of the wheels 102 of the vehicle 100. The at least one power source 101 may be arranged essentially anywhere in the vehicle, as long as power from the at least one power source 101 is provided to one or more of the wheels 102 of the vehicle 100. Various applicable examples exist in the art.

[0177] The vehicle 100 may comprise one or more electric energy storages 103, configured to provide electric energy to one or more electric machines of the vehicle 100. The vehicle 100 may further comprise a fuel tank 104 configured to provide fuel to an internal combustion engine of the vehicle.

[0178] The components of the powertrain of the vehicle 100, possibly as well as other components in the vehicle, may be controlled by a vehicle control system forming part of a vehicle electrical system via a control arrangement 120. The control arrangement 120 may be distributed on several control units configured to control different parts of the vehicle 100. The control arrangement 120 may, e.g., include a control unit for controlling the applying of a propulsive power and / or regenerative brake power of the power source 101. The control arrangement 120 may also comprise a control unit for executing the herein presented method steps. The vehicle may further comprise one or more sensors 106, being connected to the control arrangement 120, and being configured to sense / detect various conditions, characteristics or values, and to provide indications associated with those various conditions, characteristics or values to the control arrangement 120. The control arrangement 120 may comprise, or may be connected to, at least one below described communication device 105.As is known in the art, the vehicle 100 may comprise a large number of control units and sensors for controlling various part of the vehicle and / or for measuring various parameters.

[0179] Figure 1, only illustrates units / devices / entities of the vehicle that may be required for a general understanding of the herein presented solution. The presented solution does, however, not perse rely on use of such illustrated units / devices / entities.

[0180] Further, as understood by a skilled person, the vehicle 100 may also comprise a large number of other devices, components and / or system than the ones shown in figure 1.

[0181] As a basic force model of the vehicle 100, the following forces acting on the vehicle and being schematically illustrated in figure 2 may be mentioned:

[0182] mv̇ = Ft− Far− Fg; (eq. 1)

[0183] where

[0184] - mv̇ is the resulting longitudinal dynamics acting on the vehicle 100;

[0185] - Ftis the traction force acting on the vehicle 100;

[0186] - Faris the combined forces of rolling and aerodynamic resistance;

[0187] - Fgis the gravitational component acting downward from the vehicle, which depends on the road slope angle a.

[0188] Figure 3 shows a flow chart for a method 200 of a vehicle 100, according to an aspect and some embodiments of the present invention. The method 200, and its embodiments, may be performed by the control arrangement 120, e.g. comprising one or more control units, as is explained in detail in this document.

[0189] It should be noted that the method steps illustrated in figure 3 and described herein do not necessarily have to be executed in the order illustrated in figure 3. The steps may essentially be executed in any suitable order, as long as the physical requirements and the information needed to execute each step is available when the step is executed.

[0190] In a first step 210 of the method 200, since it is typically difficult to differentiate the individual aerodynamic and rolling resistances, a combined aerodynamic and rollingresistance force Faracting on the vehicle may be approximated as a resistance model M for the one or more resistance forces acting on the vehicle 100 illustrated in figure 2. The Faris is defined as:

[0191] Far= av2+ bv + c; wherein (eq. 2)

[0192] - Faris a combined aerodynamic and rolling resistance force acting on the vehicle; - v is a velocity of the vehicle 100; and

[0193] - a,b, c are resistance model parameters for the model M.

[0194] In a second step 220 of the method 200, three or more n > 3 distinct measurements are determined for each one of:

[0195] - a mass mvehicleof the vehicle 100;

[0196] - a velocity v of the vehicle 100;

[0197] - a traction force Ftacting on the vehicle 100, i.e. the force between the tires and underlying surface that generates a forward motion of the vehicle; and

[0198] - a gravitational force component Fgacting downwards on the vehicle 100, which in this document is the gravitational force component acting downward from the vehicle, which is dependent on the slope angle a of the road.

[0199] Thus, three or more n > 3 distinct measurement values are determined for each of the mass mvehicie, the velocity v, the traction force Ft, and the gravitational force Fg. The measurement values may be obtained from or based on measurements made by one or more mass, speed, traction force and / or slope data sensors 106 in the vehicle. A traction force sensor may obtain the traction force Ftfrom the torque provided to the drive wheels by the engine / machine, which is normally zero if a gearbox of the vehicle is in neutral.

[0200] As mentioned above, figure 2 schematically illustrates some of the forces acting on the vehicle 100. According to an embodiment, the three or more n > 3 distinct measurements are instantaneous measurement values, i.e. are immediate / instant / momentary values that may change overtime when the vehicle100 travels on a road. Thus, the three or more n > 3 distinct measurements may therefore result in three or more n > 3 different respective values for each parameter.

[0201] In a third step 230, the resistance model parameters a, b, c of the resistance model M in eq. 1 above are determined based on the three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg.

[0202] According to an embodiment, the resistance model parameters a,b,c of the resistance model M are estimated 231 based on a vehicle force equation for the vehicle. The force equation is overdetermined by the three or more n > 3 distinct measurements of each one of the mass mvehicie, the velocity v, the traction force Ft, and the gravitational force Fg.

[0203] The vehicle force equation may be defined as:

[0204] mvehicle_1* v̇1+ Ft_1− Fg_1

[0205]

[0206] mvehicle_n* v̇n+ Ft_n− Fg_n

[0207] where:

[0208] mvehicle_1* v̇1+ Ft_1− Fg_1is a matrix of forces Aforces; mvehicle_n* v̇n+ Ft_n− Fg_n

[0209] 2

[0210] is a matrix of velocities Bvelocity;

[0211] 2

[0212]

[0213] vnvn

[0214] -a

[0215] b is a matrix of the resistance model parameters; and

[0216] c

[0217] - v̇kis an acceleration for the vehicle 100; k = 1,2,...n, n > 3.

[0218] According to an embodiment, the determinant of the matrix of velocities Bvelocityis non-zero, i.e. det( Bvelocity) #= 0. Thus, according to this embodiment, matrix of velocities Bvelocityis a square matrix, since non-square matrices do not comprise determinants.According to an embodiment, the values of the matrix of velocities Bvelocityare weighted such that values associated with more recent velocity measurements are given higher importance / weight than values associated with older measurements. Hereby, the estimation of the resistance model parameters a,b,c becomes more up-to-date and / or accurate for the current conditions experienced in the present and upcoming situations.

[0219] According to an embodiment, at least one future traction force FtfUture k; k > 1; is predicted for an upcoming road section ahead of the vehicle 100 in a fourth step 240 of the method 200. The at least one future traction force Ft future k; k > 1 is here predicted 240 based on:

[0220] - at least one future combined aerodynamic and rolling resistance force Far_future_k>' k > 1 which is determined based on the resistance model M, i.e. is based on the expression Far= av2+ bv + c being transformed for the future;

[0221] - at least one future gravitational force on the vehicle 100 Fg_future_k, k > 1; - at least one future vehicle mass mvehicle_future, k > 1; and - at least one future acceleration of the vehicle 100 v̇future_k; k > 1.

[0222] The at least one future traction force FtfUture, k > 1; is, according to an embodiment, predicted 240 as:

[0223] Ft_future_l F ar_future_l Fg_future_l V^-vehicle_future_l * ^’ / uture_l = + +

[0224]

[0225] F t_future_n F ar_future_n F g_future_n Vl^vehicle_future_n * Vfuture_n

[0226] (eg. 4) According to an embodiment, a future speed and direction vdir distof a wind for a road section ahead of the vehicle 100 are predicted in a fifth step 250 of the method 200. According to an embodiment, the prediction 250 of the future speed and direction vdirdist of the wind for the road section ahead of the vehicle 100 is based on essentially any sensed, obtained and / or provide information being useful for indicating future wind conditions, such as sensor data, weather data, positioning information, vehicle-to-everything information and / or map data.Then, the at least one future combined aerodynamic and rolling resistance force Farfuture k>' k > 1 is predicted in a sixth step 260 of the method. The prediction 260 is here based on the predicted future speed and direction vdir distof the wind, and on the resistance model M.

[0227] There are various ways to predict at least one future combined aerodynamic and rolling resistance force Far Uture k; k > 1, depending on the wind conditions that will be experienced by the vehicle. Thus, depending on the characteristics of a future wind acting on the vehicle 100, a suitable prediction of the at least one future combined aerodynamic and rolling resistance force Farjuture_, k > 1 may be chosen.

[0228] When it is predicted 251 that a speed of the future wind to be experienced by the vehicle 100 will be non-zero and varying, then the at least one future combined aerodynamic and rolling resistance force Far Uture k; k > 1 is, according to an embodiment, predicted 261 as:

[0229] Far_future_k P * Af * ^d T -T?) * ^dist_k T (T1—P * Af * ^d * V dir dist) *

[0230]

[0231] Vdist_k T * ^d * Vdirjlist T ^o)> (®Q- 5)

[0232] where:

[0233] - ρ is a density of air; - Afis a frontal area of the vehicle; - cdis a coefficient for a rolling resistance of the vehicle 100;

[0234] - x2, x1, x0are combined vehicle resistance model parameters;

[0235] - vdist_kis at least one future vehicle speed;

[0236] -vdir dist k is at least one future wind speed and direction;

[0237] - −ρ * Af* cd+ x2correspond to resistance model parameter a;

[0238] - x1− ρ * Af* cd* vdir_kcorrespond to resistance model parameter b; and - −ρ * Af* cd* vdir_k2+ x0correspond to resistance model parameter c.The expression in equation 5 above may be seen as a model for the future combined aerodynamic and rolling resistance force Farfuturek. The combined vehicle resistance model parameter x2may then, i.e. if the future wind will be non-zero and varying, be determined 262 as x2= a - ½ρ * Af* cd,

[0239]

[0240] the combined vehicle resistance model parameter x may be determined 262 as x1= b + ρ * Af* cd* vdir_dist_k, and the combined vehicle resistance model parameter x0may be determined 262 as x0= c - ½ρ * Af* cd* vdir_dist_k2HEIGHT="26" WIDTH="171" SRC="imgf000021_0002.tif" / > ~2P * * Q * Vdir_dist_k ■

[0241] When the future wind is predicted to be non-zero and varying, a future aerodynamic resistance force FafUture kmay further be defined as:

[0242] Fa_future_k= ½ρ * Af* cd* (v − vdir_dist_k)². (eq. 6)

[0243] It should be noted that the future aerodynamic resistance force Fafuturekis dependent on a future ambient temperature Tambient future, because the density of air p is temperature dependent. Such a future ambient temperature Tambient futuremay be determined based on one or more temperature measurements. The determination of the future ambient temperature Tambientfuture may also be based on weather and / or ambient temperature predictions and / or based on weather reports for an upcoming road section ahead of the vehicle 100. Also, vehicle-to-everything information may provide information of ambient temperature conditions in the upcoming road section.

[0244] Further, when the future wind is predicted to be non-zero and varying, a future rolling resistance force Fr future kmay be defined as:

[0245] P

[0246]

[0247] Fr_future_k= x2* vdist_k2+ x1* vdist_k+ x0. (eq. 7) It should be noted that the future rolling resistance force Fr future kmay be dependent on a future tire temperature Ttire future. Such a future tire temperature TtirefUtUre may be determined based on a suitable tire temperature model and / or may be determined based on one or more temperature measurements. Thedetermination of the future tire temperature TtirefUturemay also be based on ambient temperature predictions and / or weather reports for an upcoming road section ahead of the vehicle 100. Vehicle-to-everything information may for example provide information regarding temperature conditions in the upcoming road section.

[0248] However, when is predicted 252 that a speed of the future wind to be experienced by the vehicle 100 in the upcoming road section will be zero and / or constant, then prediction 263 of the at least one future combined aerodynamic and rolling resistance force FarfUture k; k > 1 may be slightly simplified as:

[0249] P

[0250]

[0251] Far_future_k= (½ρ * Af* cd+ x2) * vdist_k2+ x1* vdist_k+ x0; (eq. 8) where:

[0252] - p is a density of air;

[0253] - Afis a frontal area of the vehicle 100;

[0254] - cdis a coefficient for a rolling resistance of the vehicle;

[0255] - x2, x1, x0are combined vehicle resistance model parameters;

[0256] - vdist_kis at least one future vehicle speed;

[0257] - ½ρ * Af* cd+ x2corresponds to resistance model parameter a;

[0258] - corresponds to resistance model parameter b; and

[0259] - x0corresponds to resistance model parameter c.

[0260] Here, i.e. if the future wind will be zero and / or constant, the combined vehicle resistance model parameter x2may then be determined 264 as x2= a - ½ρ * Af* cd, the combined vehicle resistance model parameter x may be determined 264 as x = b, and the combined vehicle resistance model parameter x0may be determined 264 as x0= c.

[0261] According to various embodiments, the method 200 comprises a prediction step 270, in which the at least one future gravitational force on the vehicle 100 Fg future kk > 1 is predicted 271 based on an upcoming road slope adistfor a road section ahead of the vehicle 100 as:

[0262]

[0263] Fg_future_k= mvehicle_future_k* g * sin(αdist); k ≥ 1. (eq. 6)The upcoming road slope adistmay here be predicted 271 based on positioning information and map data comprising topology information, and / or based on measurements of a current road slope.

[0264] According to an embodiment, the prediction step 270 comprises predicting 272 the at least one future vehicle mass mvehicle_future_k; k ≥ 1 based on one of more in the group of:

[0265] - a current weight of the vehicle 100; and

[0266] - a load and delivery scheme, positioning information and map data. Thus, it may be predicted how the cargo weight being carried by the vehicle 100 will change over time as the vehicle travels along the road section ahead, possibly due to loading and unloading cargo.

[0267] According to an embodiment, the prediction step 270 comprises predicting 273 the at least one future acceleration of the vehicle 100 vfuture kk > 1 based on one or more in the group of:

[0268] -- a current speed of the vehicle ();

[0269] -- positioning information, and map data comprising speed limits for the upcoming road; and

[0270] - vehicle-to-everything information comprising speed limit information for the upcoming road.

[0271] Essentially any information providing an indication associated with a possible acceleration or retardation of the vehicle may be utilized for the prediction 273.

[0272] In an eighth step 280 of the method 200, a distance to empty for the vehicle is, according to an embodiment, determined based on the at least one future traction force Ft_future_k; k ≥ 1. Since the traction force Ft_future_kis the force between the tires and underlying surface that generates forward motion of the vehicle, the consumption of fuel and / or energy in order to propel the vehicle at a certain speed during the road section ahead may be accurately determined based on the at least one future traction force Ft future k.For a vehicle comprising an internal combustion engine, the distance to empty for the vehicle 100 may be determined 280 as a distance reachable by the vehicle 100 when consuming an amount of fuel in a fuel tank 104 of the vehicle 100. The distance to empty for the vehicle 100 may further be determined 280 based on positioning information and map data and / or on vehicle-to-everything information comprising tank station information for the upcoming road section.

[0273] For a vehicle comprising at least one electric machine, the distance to empty for the vehicle 100 may be determined 280 as a distance reachable by the vehicle 100 when consuming an amount of energy stored in an energy storage 103 of the vehicle 100. The distance to empty for the vehicle 100 may further be determined 280 based on positioning information and map data and / or vehicle-to-everything information comprising charging station information for the upcoming road section.

[0274] According to various embodiments, at least one communication device 105 may be configured for transferring information to and / or from the vehicle 100, and thus to and / or from the control arrangement 120. The at least one communication device 105 may be a vehicle-to-vehicle (V2V) communication device, a vehicle-to-infrastructure (V2I) communication device, and / or a vehicle-to-everything (V2X) communication device. Such devices are in this document commonly denoted as a vehicle-to-everything communication device 105, which is configured for receiving and / or transmitting vehicle-to-everything information from and / or to other offboard entities, such as other vehicles and / or infrastructure entities. The received vehicle-to-everything information may thus be provided by another vehicle travelling in, or having travelled, the upcoming road section, and / or by an infrastructure entity.

[0275] Figure 4 schematically illustrates a non-limiting example of a driving situation for the vehicle 100. The vehicle 100 is here illustrated in a first position 610. Before reaching the first position 610, the vehicle 100 has travelled a previous road section 605, for which the above mentioned three or more n > 3 distinct measurements of each one of the mass mvehi eof the vehicle 100, the velocity v of the vehicle 100, the traction force Ftacting on the vehicle 100, and the gravitational force Fgacting on the vehicle 100 have been determined 220.Thus, when the vehicle 100 is in the first position 610, it is possible to determine 230, or to already have determined 230, the resistance model parameters a,b,c of the resistance model M, i.e. Far= av2+ bv + c, as described above. For example, the values of the matrix of velocities Bvelocitymay here have been weighted by utilizing a forgetting factor, such that recent velocity measurements are given higher importance than older velocity measurements are given.

[0276] As described herein, at least one future traction force Ft future kk > 1; for an upcoming road section 620 may then be predicted 240. The prediction 240 may be based e.g. on predictions of at least one future combined aerodynamic and rolling resistance force Farfuturek; k > 1, at least one future gravitational force on the vehicle 100 Fg future k; k > 1, at least one future vehicle mass mvehiclefuturek; k > 1, and at least one future acceleration of the vehicle 100 VfUture kk > 1.

[0277] These predictions may take into consideration one or more conditions and / or parameters that will be present for and / or experienced by the vehicle 100 in the upcoming road section 620. Such conditions and / or parameters may comprise a presence or non-presence of wind acting on the vehicle 100 in the upcoming road section 620, an upcoming road slope adistfor the upcoming road section 620, at least one future vehicle mass mvehicle future k, k > 1 of the vehicle in the upcoming road section 620, and / or at least one future acceleration of the vehicle 100 VfUture kk > 1 in the upcoming road section 620. Such conditions and / or parameters may be determined based on for example sensor measurements, positioning information, map data, upcoming road slope adistinformation, vehicle-to-everything information, load and delivery schemes, speed limit information and / or other relevant information.

[0278] According to some embodiments, the future ambient temperature Tambient futuremay be predicted and taken into consideration as well by these predictions, because the density of air p is temperature dependent, and thus influences the future aerodynamic resistance force Fa future k. Further, the future tire temperature TtirefUturemay also be taken into consideration by the predictions, because the future tire temperature Ttfrefuture may influence future rolling resistance force Fr_future_k.Based on the at least one future traction force FtfUture kk ≥ 1, a distance to empty 630 for the vehicle 100 is determined 280. Thus, it is here determined how far the vehicle 100 will get when consuming the fuel in its fuel tank 104 and / or the energy stored in the energy storage 103 of the vehicle 100. According to some embodiments, available information associated with tank stations and / or charging stations 641, 642 may be utilized as a basis for the determination of the distance to empty 630 for the vehicle 100.

[0279] Generally, the herein presented determination of the distance to empty 630, i.e. the determination of the reach / range of the vehicle 100, is based on the at least one future traction force Ft future kk > 1, which in turn is determined based on the actual physics of the vehicle 100 and also takes changing future driving conditions into consideration. The determination 280 of the distance to empty 630 thus also takes various changing characteristics, such as e.g. ambient temperatures, road slopes, speed limits and / or tank or charging stations, of the road section 620 ahead of the vehicle into consideration, such that the determination 280 becomes efficient, robust and accurate.

[0280] According to an aspect, a control arrangement 120 of a vehicle 100 is presented. The control arrangement 120, which may e.g. be or comprise at least one control unit, is configured for determining resistance model parameters a, b, c for a vehicle 100 on which one or more resistance forces act. The control arrangement 120 is therefore configured to define 210 a resistance model M as:

[0281] Far= av2+ bv + c; (eq. 9)

[0282] wherein

[0283] - Faris a combined aerodynamic and rolling resistance force;

[0284] - v is a velocity of the vehicle 100; and

[0285] - a,b, c are resistance model parameters.

[0286] The control arrangement 120 is further configured to determine 220 three or more n > 3 distinct measurements of each one of:

[0287] - a mass mvehicleof the vehicle 100;- a velocity v of the vehicle 100;

[0288] - a traction force Ftacting on the vehicle 100; and

[0289] - a gravitational force Fgacting on the vehicle 100.

[0290] The control arrangement 120 is further configured to determine 230 the resistance model parameters a, b, c based on the three or more n > 3 distinct measurements of each one of the mass mvehicle, the velocity v, the traction force Ft, and the gravitational force Fg.

[0291] According to an aspect, a vehicle 100 comprising the herein described control arrangement 120 is presented. Such a vehicle 100 is schematically illustrated e.g. in figures 1 and 2.

[0292] The person skilled in the art will appreciate that the herein described embodiments for braking a vehicle may also be implemented in a computer program, which, when it is executed in a computer, instructs the computer to execute the method. The computer program is usually constituted by a computer program product 503 stored on a non-transitory / non-volatile digital storage medium, in which the computer program is incorporated in the computer-readable medium of the computer program product. The computer-readable medium comprises a suitable memory, such as, for example: ROM (Read-Only Memory), PROM (Programmable Read-Only Memory), EPROM (Erasable PROM), Flash memory, EEPROM (Electrically Erasable PROM), a hard disk unit, etc.

[0293] Figure 5 shows in schematic representation a control unit 500 / 120. The control unit 500 / 120 comprises a computing unit 501, which can be constituted by essentially any suitable type of processor or microcomputer, for example a circuit for digital signal processing (Digital Signal Processor, DSP), or a circuit having a predetermined specific function (Application Specific Integrated Circuit, ASIC). The computing unit 501 is connected to a memory unit 502 arranged in the control unit 500 / 120, which memory unit provides the computing unit 501 with, for example, the stored program code and / or the stored data which the computing unit 501 requires to be able to perform computations. The computing unit 501 is also arranged to store partial or final results of computations in the memory unit 502.In addition, the control unit 500 / 120 is provided with devices 511, 512, 513, 514 for receiving and transmitting input and output signals. These input and output signals can contain waveforms, impulses, or other attributes which, by the devices 511, 513 for the reception of input signals, can be detected as information and can be converted into signals which can be processed by the computing unit 501. These signals are then made available to the computing unit 501. The devices 512, 514 for the transmission of output signals are arranged to convert signals received from the computing unit 501 in order to create output signals by, for example, modulating the signals, which can be transmitted to other parts of and / or systems in the vehicle.

[0294] Each of the connections to the devices for receiving and transmitting input and output signals can be constituted by one or more of a cable; a data bus, such as a CAN bus (Controller Area Network bus), a MOST bus (Media Orientated Systems Transport bus), or some other bus configuration; an ethernet connection; or by a suitable wireless connection. A person skilled in the art will appreciate that the above-stated computer can be constituted by the computing unit 501 and that the above- stated memory can be constituted by the memory unit 502.

[0295] Control systems in modern vehicles commonly comprise communication bus systems consisting of one or more communication buses for linking a number of electronic control units (ECU's), or controllers, and various components located on the vehicle. Such a control system can comprise a large number of control units and the responsibility for a specific function can be divided amongst more than one control unit. Vehicles of the shown type thus often comprise significantly more control units than are shown in figures 1 and 5, which is well known to the person skilled in the art within this technical field.

[0296] In a shown embodiment, the present invention may be implemented by the one or more herein mentioned control units or processing / control arrangements 500 / 120. The invention can also, however, be implemented wholly or partially in one or more other control units already present in the vehicle, or in some control unit dedicated to the present invention.Here and in this document, control units, control entities or processing arrangements are sometimes described as being arranged for performing the methods and / or steps 210, 220, 230, 231, 240, 250, 251, 252, 260, 261, 262, 263, 264, 270, 271, 272, 273, 280 according to the invention. This also includes that the units, entities or processing arrangements are designed to and / or configured to perform these method steps.

[0297] One or more control entities 410, 420, 430, 431, 440, 450, 451, 452, 460, 461, 462, 463, 464, 470, 471, 472, 473, 480 may be arranged for performing the methods and / or steps. Such entities 410, 420, 430, 431, 440, 450, 451, 452, 460, 461, 462, 463, 464, 470, 471, 472, 473, 480 may be arranged as separate entities, or may be logically separated but physically implemented in the same unit, or may be both logically and physically arranged together. These control entities 410, 420, 430, 431, 440, 450, 451, 452, 460, 461, 462, 463, 464, 470, 471, 472, 473, 480 may for example correspond to groups of instructions, which can be in the form of programming code, that are input into, and are utilized by a processor / computing unit 601 when the entities are active and / or are utilized for performing its method steps, respectively.

[0298] The present invention is not limited to the above described embodiments. Instead, the present invention relates to, and encompasses all different embodiments being included within the scope of the independent claims.

Claims

Claims1. A method (200) of a vehicle (100) on which one or more resistance forces act;the method (200) comprising:- defining (210) a resistance model M as:Far= av2+ bv + c wherein-- Faris a combined aerodynamic and rolling resistance force;-- v is a velocity of the vehicle (100); and-- a, b, c are resistance model parameters;- determining (220) three or more n > 3 distinct measurements of each one of:-- a mass mvehi eof the vehicle (100);-- a velocity v of the vehicle (100);-- a traction force Ftacting on the vehicle (100); and-- a gravitational force Fgacting on the vehicle (100); and- determining (230) the resistance model parameters a,b,c based on the three or more n > 3 distinct measurements of each one of the mass mvehi e, the velocity v, the traction force Ft, and the gravitational force Fg.

2. The method (200) as claimed in claim 1, wherein the determination (230) of the resistance model parameters a, b, c comprises:- estimating (231) the resistance model parameters a, b, c based on a vehicle force equation, the vehicle force equation being overdetermined by the three or more n > 3 distinct measurements of each one of the mass mvehi e, the velocity v, the traction force Ft, and the gravitational force Fg.

3. The method (200) as claimed in claim 2, wherein the vehicle force equation is defined as:-mvehiclev̇1+ Ft_1− Fg_1= b-mvehiclev̇n+ Ft_n− Fg_nwhere:mvehicle^l + Ff l Fg_ris a matrix of forces Aforces;~^-vehicle^n + Ftn— Fgn2is a matrix of velocities Bvelocity;2vn-ab is a matrix of the resistance model parameters; andc- vkis an acceleration for the vehicle (100); k = 1, 2,... n, n > 3.

4. The method (200) as claimed in claim 3, wherein a determinant of the matrix of velocities Bvelocityis non-zero.

5. The method (200) as claimed in any one of claims 3-4, wherein the values of the matrix of velocities Bvelocityare weighted such that values associated with more recent velocity measurements are given higher importance than values associated with older measurements.

6. The method (200) as claimed in any one of claims 1-5, the method further comprising:- predicting (240) at least one future traction force Ft future kk > 1,' for a road section (620) ahead of the vehicle (100) based on:-- at least one future combined aerodynamic and rolling resistance forceFarfUture k; k > 1; which is determined based on the resistance model M;-- at least one future gravitational force on the vehicle (100) Fg future k; k > 1;-- at least one future vehicle mass mvefliciefuture k>' k > 1; and-- at least one future acceleration of the vehicle(100) v / uture k; k > 1.

7. The method (200) as claimed in claim 6, wherein the at least one future traction force FtfUtUre k, k > 1; is predicted (240) as:F t_future_l F ar_future_l Fg_future_l mve]ucle_fiiture_l * ^future_l = + +F t_future_n F ar_future_n F g_future_n mvehicle_future_n * ^future_n 8. The method (200) as claimed in any one of claims 6-7, further comprising:- predicting (250) a future speed and direction vdir distof a wind for a road section (620) ahead of the vehicle (100);- predicting (260) the at least one future combined aerodynamic and rolling resistance force FarfUture k; k > 1 based on the future speed and direction vdir distof the wind, and on the resistance model M.

9. The method (200) as claimed in claim 8, wherein- it is predicted (251 ) that a speed of the future wind to be experienced by the vehicle (100) will be non-zero and varying; and- the at least one future combined aerodynamic and rolling resistance forceFarfuture k> k > 1 is then predicted (261 ) as:Far_future_k P * * ^d T ^2^ * ^dist_k + (T1—P * Af * Cd* ^dir_dist) * -£ Vdistjc + (.2 P * Af *cd * Vdir_dist "h ^o)' where:- p is a density of air;- Af is a frontal area of the vehicle;- cdis a coefficient for a rolling resistance of the vehicle;- %2> oarecombined vehicle resistance model parameters;-vdist k isatleast °nefuture vehicle speed;-vdir dist k isatleastonefuture wind speed and direction;- −ρ * Af* cd+ x2correspond to resistance model parameter a;- - p * A * cd* vdir kcorrespond to resistance model parameter b; and- - -p * Af * cd* vdir+ x0correspond to resistance model parameter c.

10. The method (200) as claimed in claim 9, further comprising:- determining (262) the combined vehicle resistance model parameters x2, xltx0as:i- x2= a --p *Af* cd;- x1= b + p * Af* cd* vdir dist k; and14o“*0 ~ C2P * Af * ^d * Vdir_dist_k ■11. The method (200) as claimed in claim 8, wherein- it is predicted (252) that a speed of the future wind to be experienced by the vehicle (100) will be zero and / or constant; and- the at least one future combined aerodynamic and rolling resistance forceFarfuture k>' k > 1 is then predicted (263) as:Far_future_k P * * ^d T ^2^ * ^dist_k T -^1 * ^dist_k T -^0> where:- p is a density of air;- Af is a frontal area of the vehicle;- cdis a coefficient for a rolling resistance of the vehicle;- %2> 1, oarecombined vehicle resistance model parameters;-vdist k isatleast one future vehicle speed;- -p * Af* cd+ x2corresponds to resistance model parameter a;- x corresponds to resistance model parameter b; and- x0corresponds to resistance model parameter c.

12. The method (200) as claimed in claim 11, further comprising:- determining (264) the combined vehicle resistance model parameters x2, x, x0as:i-x2= a --p *Af* cd,- xt= b; and- x0= c.

13. The method (200) as claimed in any one of claims 8-12, wherein the prediction (250) of the future speed and direction vdir distof the wind for the road section (620) ahead of the vehicle (100) is based on one or more in the group of: - sensor data;- weather data;- positioning information;- vehicle-to-everything information; and- map data.

14. The method (200) as claimed in any one of claims 6-13, further comprising:- predicting (271) the at least one future gravitational force on the vehicle (100)Fafuturefe; > 1 based on an upcoming road slope adistfor a road section (620) ahead of the vehicle (100), Fg_future_k ~ ^-vehicle_future_k *9 * Sin (t^rfist), k > 1.

15. The method (200) as claimed in claim 14, wherein the upcoming road slope adistis predicted based on positioning information and map data.

16. The method (200) as claimed in any one of claims 6-15, further comprising:- predicting (272) the at least one future vehicle mass mvehiclefUture k; k > 1 based on one of more in the group of:-- a current weight of the vehicle (100); and-- a load and delivery scheme, positioning information and map data.

17. The method (200) as claimed in any one of claims 6-16, further comprising:- predicting (273) the at least one future acceleration of the vehicle (100) ^future k>' k > 1 based on one or more in the group of:-- a current speed of the vehicle (100);-- positioning information, and map data comprising speed limit information for the road section (620) ahead of the vehicle (100); and- vehicle-to-everything information comprising speed limit information for the road section (620) ahead of the vehicle (100).

18. The method (200) as claimed in any one of claims 6-17, further comprising:- determining (280) a distance to empty (630) for the vehicle (100) based on the at least one future traction force Ft future kk > 1.

19. The method (200) as claimed in claim 18, wherein the distance to empty (630) for the vehicle (100) is determined (280) based also on one or more in the group of:- positioning information, and map data comprising tank station information for the road section (620) ahead of the vehicle (100);- vehicle-to-everything information comprising tank station information for the road section (620) ahead of the vehicle (100);- positioning information, and map data comprising charging station information for the road section (620) ahead of the vehicle (100); and- vehicle-to-everything information comprising charging station information for the road section (620) ahead of the vehicle (100).

20. The method (200) as claimed in any one of claims 18-19, wherein the distance to empty (630) for the vehicle (100) is determined (280) as one or more in the group of:- a distance (630) reachable by the vehicle (100) when consuming an amount of fuel in a fuel tank (104) of the vehicle (100); and- a distance (630) reachable by the vehicle (100) when consuming an amount of energy stored in an energy storage (103) of the vehicle (100).

21. The method (200) as claimed in any one of claims 1-20, wherein the three or more n > 3 distinct measurements are instantaneous measurement values.

22. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to any one of claims 1 -21.

23. A computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the method according to any one of claims 1 -21.

24. A control arrangement (120) of a vehicle (100) configured for determining resistance model parameters a, b, c fora vehicle (100) on which one or more resistance forces act;the control arrangement (120) being configured to:- define (210) a resistance model M as:Far= av2+ bv + c wherein-- Faris a combined aerodynamic and rolling resistance force;-- v is a velocity of the vehicle (100); and-- a, b, c are resistance model parameters;- determine (220) three or more n > 3 distinct measurements of each one of:-- a mass mveflicieof the vehicle (100);-- a velocity v of the vehicle (100);-- a traction force Ftacting on the vehicle (100); and-- a gravitational force Fgacting on the vehicle (100); and- determine (230) the resistance model parameters a,b, c based on the three or more n > 3 distinct measurements of each one of the mass mvehicie, the velocity v, the traction force Ft, and the gravitational force Fg.

25. A vehicle (100) comprising:- a control arrangement (120) according to claim 24.

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