Classifications

• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
  • B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
  • B60T8/17—Using electrical or electronic regulation means to control braking
  • B60T8/1701—Braking or traction control means specially adapted for particular types of vehicles
  • B60T8/1706—Braking or traction control means specially adapted for particular types of vehicles for single-track vehicles, e.g. motorcycles
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
  • B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
  • B60T8/17—Using electrical or electronic regulation means to control braking
  • B60T8/172—Determining control parameters used in the regulation, e.g. by calculations involving measured or detected parameters
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
  • B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
  • B60T8/32—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force responsive to a speed condition, e.g. acceleration or deceleration
  • B60T8/321—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force responsive to a speed condition, e.g. acceleration or deceleration deceleration
  • B60T8/3225—Systems specially adapted for single-track vehicles, e.g. motorcycles
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
  • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
  • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
  • B60W40/11—Pitch movement
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
  • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
  • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
  • B60W40/112—Roll movement
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B60—VEHICLES IN GENERAL
  • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
  • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
  • B60W2050/0001—Details of the control system
  • B60W2050/0043—Signal treatments, identification of variables or parameters, parameter estimation or state estimation
  • B60W2050/0052—Filtering, filters

Definitions

• the present invention refers generally to a system and a method for determining the roll angle of a two-wheeled vehicle, and more particularly to such a system and method for determining the roll angle of a motorcycle.
• the general object of the present invention is to provide a roll angle two-wheeled vehicles indicator that has an improved accuracy and is possible to implement to a moderate cost. Aspects of the object is to provide a method, an apparatus and a computer program product for accurately estimating the roll angle or the pitch angle of a motorcycle.
• the inventive concept comprises an estimation of the roll angle by measuring the angle between a vertical axis of the vehicle and the direction of the gravitational field.
• the gravitation is utilised by arranging a lateral acceleration sensor such that it generates a lateral acceleration signal based on the detection of an acceleration comprising a component dependent on the lateral movement of the vehicle and a component dependent on the gravitational effect.
• the invention is based on dynamic parameters detected by means of inertial sensors, for example accelerometers and rate gyros.
• the sensor signals are processed in a sensor fusion structure comprising an adaptive filter based on a model on the vehicle dynamics.
• the general sensor fusion approach allows different sensor configurations but requires a parameter that indicates the lateral acceleration of the vehicle.
• the lateral acceleration parameter is combined with a parameter indicating the velocity of the vehicle.
• Advantageous embodiments of the invention comprises an adaptive filter in the shape of a Kalman filter.
• the Kalman filter enables similar implementation for different sensor combinations, for example a velocity sensor and a lateral accelerometer combined with a vertical accelerometer and or a longitudinal rate gyro.
• Embodiments apt for achieving even higher performance comprise an extra gyro for generating an additional sensor signal such as the yaw rate.
• the invention is applicable on all two-wheeled vehicles and operates only a rolling vehicle.
• the invention generally requires a minimum speed for example in the range of 10 km/h. All the examples in this text are however described in relation to a motorcycle.
• the method according to an aspect of the invention comprises the steps of: - determining the vertical acceleration a z of the motorcycle;
• Another embodiment of the invention includes a method for determining the roll angle. of a motorcycle, which method comprises the steps of:
• the strength of the invention presented in this document is that the roll angle estimate can be made more accurate since estimation of the sensor offsets are straightforward using adaptive filtering techniques.
• the inertial frame (I) system is, as the name implies, fixed in the inertial space. Thus, Newton's equations must be expressed relatively this system.
• the inertial frame system is an orthogonal right-handed coordinate system, wherein the axes are denoted X, ⁇ and z . In this system the earth is assumed to be flat which allows Z to be chosen parallel to the gravitational field.
• the body frame (B) is also an orthogonal and right-handed coordinate system.
• the system is attached to the motorcycle according to figure 1 A.
• x is the axis in the longitudinal (forward) direction
• y the axis in the lateral (left) direction
• z is the axis in the vertical (upwards) direction.
• the local rotations ⁇ , ⁇ , ⁇ are defined as those a rate gyro would measure, thus ⁇ is the angular velocity around the x axis, ⁇ is the angular velocity around the y axis and ⁇ is the angular velocity around the z axis.
• the body frame coordinate system B must be related relatively the inertial frame system I.
• the rotation of B relative to / is expressed using the roll angle ⁇ , the slope/pitch angle ⁇ , and the yaw angle ⁇ . Further, the coordinate systems are related to each other using the transformation matrix Cf .
• Fig 1 A shows the body fixed coordinate system
• Fig IB shows accelerometers on a motorcycle in an exemplifying implementation of the invention
• Fig 1C shows a schematically a functional block diagram of the stages comprised in an embodiment of a pre-processing stage in accordance with the invention
• Fig ID shows the relation between two coordinate systems used in some embodiments of the invention
• FIG. 2 A and 2B show schematically a functional block diagram of the stages comprised in embodiments the invention
• Fig. 3 shows inter alia the forces acting on the centre of gravity and the torque around the origin
• Fig. 4 shows a flowchart of the estimation of sensor variance
• Fig 5 shows a notation for a mechanical gyroscope. used in embodiments of the invention
• Fig 6A and 6B shows a simple motorcycle model
• Fig 7 illustrates the balancing forces on a motorcycle
• Fig 8 shows a schematic block diagram of embodiments of the invention having different sensor configurations
• Fig 9-12 show diagrams of roll angle indications measured plotted against a reference from experimental test driving with the invention.
• Fig IB acceleration sensors for detecting lateral acceleration, vertical acceleration and longitudinal acceleration are placed in a suitable position on the vehicle.
• the inventive system allows a variety of positions for the sensors on the vehicle, however the sensors should be protected against disturbances and noise, h the embodiment of Fig IB, an accelerometer component 101 comprising a lateral accelerometer 104, a vertical accelerometer 106 and a longitudinal accelerometer 108 are placed under the saddle.
• a further development of this embodiment comprises an additional longitudinal accelerometer used to improve an estimation of the vehicle velocity or to detect hills.
• the system according to the present invention will be described with reference to the example according to Fig IB having a selection or a combination of sensors for accelerometers and possible rate gyros.
• Embodiments of the inventive concept therefore further comprises a pre-processing stage devised to enhance the sensor signal quality or to adapt the sensor signal to the actual estimation stages.
• a pre-processing stage devised to enhance the sensor signal quality or to adapt the sensor signal to the actual estimation stages.
• the information delivered by sensors detecting a parameter related to the roll angle typically has a low frequency during driving, e.g. in the range of 10 Hz.
• h a normal motorcycle the disturbances typically occur above 10 Hz, and because only the roll angle information is used the disturbances above the range of 10 Hz are suppressed.
• the invention is conveniently realised by means of a digital signal or data processing system, such as a computer.
• Fig 1 C shows a functional block diagram of an embodiment of the pre-processing stages in a pre-processor 110.
• the pre-processor 110 comprises processing in four stages, viz. a continuous time stage 112, a sampling stage 114, a discrete time stage 116 and one or more down-sampling stage(s) 118.
• the signal from a sensor 120 is filtered in an ideal low pass (LP) filter 122.
• the LP filter would at least comprise a design to attenuate frequencies above half the sampling frequency in order to minimise alias effects.
• the LP filter would also comprise a design to suppress high frequency disturbances for example with higher frequencies than about 10 Hz.
• a simple low order analogue filter is used in cased where the sampling rate is sufficiently high, in order to avoid difficulties arising for high order filters in the continuous time domain.
• the sampling stage 114 samples the analogue signal for example by means of an A/D converter and outputs a digital signal in the discrete time domain.
• the discrete time stage 116 preferably comprises a data rate or sample rate reduction mechanism devised to reduce the data rate and hence the computational load.
• the data reduction mechanism preferably comprises a low pass filter 126 devised to attenuate frequencies above half the sampling frequency of the decimated signal. Decimation of the data rate by a factor k is carried in a decimation stage 128 out by selecting every k:th sample in the discrete signal and discarding the rest of the samples.
• the steps for reducing the sampling frequency of a discrete signal for example from 100 Hz to 50 Hz comprises the steps of designing a suitable LP-filter attenuating frequencies above 25 Hz, applying the LP-filter to the signal and removing every second sample from the filtered signal.
• the data reduction mechanism in Fig 1C also comprises a down sampling mechanism having another LP -filter 130 and a sample decimation stage 132 for example operating in a manner similar to first data reduction stages.
• the technique for roll angle estimation by model based sensor fusion in accordance with the invention requires a good sensor model, i.e. the model of the vehicle dynamics as indicated by the parameters detected by the sensors.
• Different embodiments of the invention employs various models.
• One embodiment is based on a simple approach wherein the signals from a lateral and a vertical accelerometer is processed in a model using a static mathematics formula.
• the estimation of model parameters are determined by means of an adaptive filter, preferably a Kalman filter based on the model.
• the Kalman filter embodiment is advanced enough to estimate not only the roll angle but also parameters such as yaw rate and sensor offsets, thus creating a very versatile and useful system.
• the system comprises several versions of the adaptive filter. The choice of filter depends on how the features of the system are modelled and the sensors used.
• Fig 2 A shows an embodiment of a the stages and the functional units of a roll estimation method and apparatus in accordance with the invention.
• Signals or data from a number m of inertial sensors such as accelerometers ace l...acc m, possibly a number n of gyros gyro 1...gyro n and the angular velocities ⁇ front and ⁇ rear of the front and rear wheels are input to a pre-processing stage 201.
• a velocity estimation is made either as a part of the pre-processing or in a separate stage before the Kalman filter possibly using a combination of the front and rear angular velocity signals.
• the pre-processed sensor signals thus indicating different parameters relating to the vehicle dynamics are input into an adaptive filter 202, here in the shape of a Kalman filter.
• the adaptive filter 202 is based on a selected and predetermined model of the vehicle dynamics and is devised to generate and output an estimation of a number 1...k parameter values 204 dependent on the input sensor signals.
• one of the output parameters is the roll angle indicator signal.
• the output parameter value 204 is possibly input into a calculating stage or vehicle roll angle calculator 206 devised to calculate, dependent on said parameter value from the adaptive filter, a further processed, e.g. low pass filtered, roll angle indication value RAI 208 that is dependent on and indicative of the roll angle of the vehicle or other .
• This general structure is usable for different configurations of sensors, for example one, two or three accelerators possibly combined with one longitudinal gyro or a veliicle velocity signal from at least one of the front or rear wheels.
• Fig 2B shows an even more general structure of the invention taking as an input a lateral acceleration signal 210, a vertical acceleration signal 211, pre-processing 212 and an estimation model calculator 214 devised to calculate a signal or a parameter 216 RAI indicative of roll angle of the vehicle.
• the calculator 214 comprises the a selected simple or advanced model of the vehicle dynamics.
• Models of Vehicle Dynamics The invention is implementable by means of different models of vehicle dynamics and some embodiments may even comprise several selectable models used dependent on different driving situations or other requirements. A number of different models and model varieties comprised in the invention are described in the following sections.
• the estimation of the roll angle is based on inertial sensor signals, in particular accelerometer signals which requires the most modelling effort. It is generally preferred to operate with a accurate model having relatively few states.
• the following section describes examples of the derivation of models for ideal accelerometers.
• the inputs to these expressions are the orientation, velocity and acceleration of the body fixed system.
• the first step is to model acceleration on a point on the motorcycle.
• two coordinate systems are used viz. one that is fixed in the inertial space (I) and one that is fixed to the motorcycle (B).
• the point on the motorcycle where acceleration is calculated is denoted P.
• 7 B is the position of coordinate system B in /and r PI B is the coordinate expressed in B.
• This is illustrated in Fig ID and is valid for cases or vehicles wherein a first coordinate system moves in relation to a fixed coordinate system.
• Accelerator Model Derivation 1 Using the expressions derived as shown in the definitions section is the acceleration calculated as:
• the accelerometers are also influenced by the gravitational field.
• the acceleration of a point in space can be calculated from the measured acceleration according to: f
• ⁇ ⁇ cos ⁇ - ⁇ sin ⁇ ⁇ _ ycos ⁇ +gsin ⁇ cos ⁇ (6)
• ⁇ ⁇ + tan ⁇ ⁇ cos ⁇ + ⁇ sin ⁇ J
• accelerometers are also influenced by gravity. Extending the derived model to model gravity is done by adding how the longitudinal, the lateral and the vertical accelerometer are affected when rotated in a field of gravity. The accelerometer models are therefore dependent of the two roll angle ⁇ and tilt angle ⁇ . This dependence of the roll angle is the feature required in order to use the sensor to estimate the roll angle. Unfortunately, the tilt angle, seen as disturbance, complicates the problem. For normal hill slopes, the error is small though.
• a Bx it + w ⁇ -v ⁇ + z ⁇ - y ⁇ - x ⁇ 2 + ⁇ 2 )+y ⁇ + z ⁇ - gsin ⁇ + ⁇ x a
• Bz w+v ⁇ -u ⁇ + y ⁇ - x ⁇ + x ⁇ + y ⁇ - z ⁇ 2 + ⁇ 2 )+ g cos ⁇ cos ⁇ + ⁇ ⁇ z
• the sensors are usually influenced by a scaling error as well. This error is partly absorbed by the sensor offsets and is not modelled. Implementing such sensor errors in the models is straightforward but can result in other problems.
• the complexity of the models 5 makes estimation of all interesting parameters using very few sensors impossible because of divergence problems.
• Figure 3 shows a force diagram, hi figure 3, R is the curve radius, z the height ground to CoG (centre of gravity) in the local coordinate system, M ⁇ is the torque excerted by the wheels, ⁇ is the roll angle, ⁇ the local yawrate, ⁇ the global yawrate, F ⁇ is the virtual force due to acceleration (the centripetal force), and F 2 is the force due to gravity.
• the first is the connection between the sign of the lateral acceleration a y and the second is a new model of the measurement of the lateral acceleration.
• Adaptive Vehicle Dynamics Model A more advance embodiment employing an adaptive filter, here exemplified by means of a Kalman filter will now be described.
• the angular velocity is preferably taken from the front wheel but the rear wheel signal can be used to support the system.
• k is greater than 1.
• f, g and h are non-linear functions of the states x k
• z k are the measurements from the sensors.
• the extended Kalman filter equations are x klk ⁇ x klk-l + Lk L z k ⁇ hk ⁇ x k/k-l )i
• the extended Kalman filter can thus be implemented using (10), (11) and (12).
• H' may thus be expressed as gcosx j +zx (l + tan 2 x) u + 2zx 3 tan x, 0 1 0
• the discrete time equivalent to B is G, and G is easily derived from B using standard theory for sampled systems.
• ⁇ 5z MyHan ⁇ + cos ⁇ cos ⁇ + o z cos ⁇ h the expression above ⁇ x is the offset in the longitudinal accelerometer, ⁇ y the offset in the lateral accelerometer and ⁇ z the offset in the vertical accelerometer.
• Selectable Adaptive Filter hi an embodiment employing selectable adaptive filter the Kalman filter approach described above allows sensor fusion from many different kinds of sensors. Provided that a good model for the sensor is known, the new sensor information is used to improve the performance, hi cases when the accuracy of the roll angle estimate using accelerometers is inadequate, the system can be supported by additional sensors in form of rate gyros.
• a one axis rate gyro measures the angular velocity around an axis. If the purpose is to measure ⁇ , ⁇ or ⁇ in the positive direction the gyro can be located in three different orientations. Other orientations of the gyro will also work but then the measurements are a linear combination of ⁇ , ⁇ an ⁇ , which will mcrease the complexity of the system.
• the velocity wis estimated using the ABS-signals is the angular velocity of the wheel delivered.
• the angular velocity measured on non-driven wheel front wheel on motorcycles
• the signal from the driven wheel is also noisier due to the engine.
• the slope angle ⁇ can be estimated as:
• a sensor noise level estimation is provided.
• the diagonal in the Covariance matrix R in the state space model in the Kalman filter describes the variance of the noise on the measurements.
• the noise levels on the sensors are not certain to be constant but can be dependent on engine rpm (rotation per minute), gear, velocity, temperature, driver, type of motorcycle etc. order to make a robust system, one option is to estimate the variances and feed it forward into the filter.
• the embodiment is illustrated in figure 4, thus comprising an input of lateral and vertical accelerometer signals ay and az into an estimate- model stage 402, coupled to an estimate variance stage 404 that generates a variance estimation that is input into an adaptive filter 406, here in the shape of a Kalman filter.
• the function of the Estimate model block is to estimate a simple signal model from which the residuals can be analyzed.
• a specific model for the lateral accelerometer is directed to the conditions necessary to balance the motorcycle during steady state cornering.
• M ⁇ xp
• the torque ⁇ x is calculated as
• ⁇ r -z, jU ⁇ mgz G cos ⁇ sin ⁇ ⁇
• the angular velocities of both the wheels are required in an embodiment devised to detect skidding or spinning during braking and acceleration. Otherwise the velocity is easily estimated using the angular velocity of one wheel and scaling with the wheel radius.
• the velocity estimate can also be improved if an additional accelerometer in the longitudinal direction is available.
• the actual velocity is estimated in any per se known manner the selection of which not being crucial for the function of the inventive system, since the sensitivity to errors in the velocity estimate is small.
• the general system relies on M accelerometers and N rate gyros. All systems of this kind comprises at least one accelerometer and a velocity estimate.
• a rate gyro alone cannot be used to estimate the roll angle because of the unknown sensor offset.
• Estimating the accelerometer offset for a single lateral accelerometer is also difficult and requires a slightly different approach than the other systems.
• rate gyro offset and accelerometer offset is straightforward.
• the rate gyro have in the experiments been located measuring the roll rate along the longitudinal axis. The gyro can be aligned in any direction and if several gyros are used and aligned in different directions could the performance be improved further.
• Fig 8 shows schematically four different embodiments 808,809,810,812 each having sensors 802 in specific configurations, a possible pre-filtering stage 804 and an adaptive filter 806, here in the shape of an extended Kalman filter, outputting a roll angle indication signal RAI.
• the functionality of each sensor and filter configuration is illustrated using diagrams of plotted measurements shown in Fig 9-12 of the roll angle from an experimental test driving on a test track similar to an ordinary road containing hills, crests and valleys. All plots are made from the same test-drive.
• the complexity of the kalman filter increases with the number of states and measurements.
• the rule of thumb is that the computational load increases with the number of states squared, h the description below of each system the states used in the current implementation on the motorcycle will be presented. These set of states are not chosen in order to minimize the computational load of the system but rather to make slightly different version of the Kalman filter easy to implement during development.
• the one accelerometer system 808 of Fig 8 is the least advanced of the embodiments.
• the required signals are a velocity estimate and an lateral accelerometer which is illustrated in the block diagram in Figure 8.
• the states used in the current implementation on the motorbike are x ⁇ : ⁇ , roll angle x 2 : ⁇ , angular velocity roll angle ⁇ 3 : , angular acceleration roll angle x 4 : ⁇ , yaw rate x 5 : ⁇ , angular acceleration yaw angle x 6 : ⁇ v , sensor offset lateral accelerometer
• the applied model using the presented set of states are the matrices
• the matrix G can be chosen in several ways and two variants are presented here. The difference is how the process noise is modelled. Depending on application and which are different matrices the best choise.
• Alternative I
• the first two are from the two lateral accelerometer models and the last is an assumption that the roll angle is measured using a virtual sensor measuring the roll angle. This last measurement is modelled to be zero but with a large uncertainty.
• the purpose of the virtual measurement is to eliminate divergence problems emerging when only the two accelerometer models are used.
• the virtual measurement introduces an assumption about the road because the model is poor if driving in circles.
• This implementation has approximately the same performance as the six state system. By using this simplified version, the number of calculations are drastically reduced since the number of states are halved.
• the roll angle estimate using the one accelerometer system is plotted in figure 9 showing the performance. It is obvious that there is a clear correlation between the estimate and the reference angle. The largest error originates in the sensor offset estimate.
• the advantages of this embodiment is that it has few sensors, entails a small computational load and embodies an automatic sensor calibration. Possible drawbacks that are relieved in the other embodiments are a relative sensitivity to disturbances, a somewhat noisy estimate, relatively slow speed in computation, fairly large errors and a relatively slow tracking of sensor error.
• Two Accelerometer System Fig 10 shows in a similar way the performance of a two accelerator system.
• the diagram is self explaning and it is obvious that the roll angle estimate closely follows the reference.
• the following states are used ] : ⁇ , roll angle ⁇ 2 . ⁇ , roll velocity ⁇ 3 : ⁇ , roll acceleration x 4 : ⁇ , yaw rate ⁇ 5 : ⁇ , yaw acceleration x 6 : ⁇ y , sensor offset lateral accelerometer x 7 : ⁇ . , sensor offset vertical accelerometer
• the applied model using the presented set of states are the matrices
• the matrix G can be chosen in several ways and two variants are presented here. The difference is how the process noise is modelled. Depending on application different matrices seems to be the best choice.
• Alternative I
• Fig 11 shows again in a similar way the performance of a one accelerator and one rate gyro system.
• the diagram is self explaning and it is obvious that the roll angle estimate closely follows the reference even more closely.
• the used states are x j : ⁇ , roll angle x 2 : ⁇ , roll velocity x 3 : ⁇ , roll acceleration x 4 : ⁇ , yaw rate x 5 : ⁇ , yaw acceleration x 6 : ⁇ y , sensor offset lateral accelerometer x 7 : ⁇ gj , ro , sensor offset longitudinal gyro
• the matrix G can be chosen in several ways and two variants are presented here. The difference is how the process noise is modelled. Depending on application are different matrices the best choice. Alternative I
• the number of states can be reduced to four if the computational load is to be reduced.
• the states are then chosen as xf. ⁇ , roll angle x 2 : ⁇ , yaw rate x 3 : ⁇ y , sensor offset lateral accelerometer x 4 : ⁇ , sensor offset longitudinal gyro and the alternative implementation is straightforward using the information from the presented implementation.
• This implementation will have the same performance as the seven state system when matrix G is chosen as in the second variant.
• Two Accelerometers and one Rate Gyro Fig 1 shows again in a similar way the performance of a two accelerator and one rate gyro system.
• the diagram is self explaning and it is obvious that the roll angle estimate closely follows the reference even more closely.
• the used states are x y : ⁇ , roll angle x 2 : ⁇ , roll velocity x 3 : , roll acceleration x 4 : ⁇ , yaw rate ⁇ 5 : ⁇ , yaw acceleration ⁇ 6 : ⁇ y , sensor offset lateral accelerometer ⁇ n : ⁇ z , sensor offset vertical accelerometer x 8 : ⁇ syro , sensor offset longitudinal gyro
• the applied model using the presented set of states are the matrices
• the matrix G can be chosen in several ways and two variants are presented here. The difference is how the process noise is modelled. Depending on application different matrices are the best choice.
• Alternative I
• the model for the measurements is then ux 4 — z y x 3 + z y x 4 tan x l + g sin x ⁇ + x 6
• the number of states can be reduced to four if the computational load is to be reduced.
• the states are then chosen as ⁇ ⁇ : ⁇ , roll angle x 2 : ⁇ , yaw rate ⁇ 3 : ⁇ y , sensor offset lateral accelerometer ⁇ 4 : ⁇ z , sensor offset vertical accelerometer and the alternative implementation is straightforward using the information from the presented implementation.
• This implementation will have the same performance as the seven state system when matrix G is chosen as in the second variant.
• the system according to the present invention further includes a computer program product comprising means devised to direct data in a data processing system to perform the steps and the functions of the previously described methods and apparatuses.
• a computer program product comprising means devised to direct data in a data processing system to perform the steps and the functions of the previously described methods and apparatuses.

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