Virtual Sensors for Vehicle Dynamics Applications

Virtual Sensors for Vehicle Dynamics Applications

U. Forssell, S. Ahlqvist, N. Persson, F. Gustafsson*

NIRA Dynamics AB

Teknikringen 1F

58330 Linköping, Sweden

Phone: +46/13/329800 Fax: +46/13/329829

Email:

*Dept. of Electrical Engineering

Linköping University

58183 Linköping, Sweden.

Phone: +46/13/282706 Fax: +46/13/282622

Email:

Keywords: adaptive filter, inertial sensors, sensor fusion, signal processing

Abstract

This paper discusses sensor fusion as a means to compute virtual sensor signals for certain vehicle attitude quantities, in particular vehicle yaw rate. It is shown how sensor fusion can be used to increase the performance and availability of standard sensors commonly available in a modern car. Test results from tests performed with a real vehicle are presented.

1 Introduction

NIRA Dynamics is a research and development company specialising in signal processing for vehicle dynamics applications. This paper presents some on-going activities within our company directed at creating virtual sensors using advanced sensor fusion software.

The sensor fusion idea is quite general and has many different application areas, see e.g. [1] and the references therein. As the name indicates, sensor fusion is about fusing information from several different physical sensors. The goal is to compute new virtual sensor signals using information from the existing, physical sensors. The virtual sensors can in principle be of two different types:

1.  High-precision and self-calibrating sensors, i.e. improved versions of the physical sensors. The goal is either to achieve higher performance using existing sensors or to reduce system cost by replacing expensive sensors by cheaper ones and using sensor fusion to restore signal quality.

2.  Soft sensors, i.e. sensors that have no direct physical counterpart among the sensors used but can be created using intelligent software solutions.

Sensor fusion is used in, for example, navigation, target tracking, aircraft attitude estimation and various other military applications to achieve exactly these goals. Our primary aim in our research and development efforts is to develop unique sensor fusion based systems for vehicles - in particular for vehicle dynamics applications – and the challenge is to utilise the potential to both improve performance and reduce the system cost.

Fig. 1. Sensor fusion in vehicles

Figure 1 contains a schematic picture of how the sensor fusion ideas may be applied to vehicles. To the left we have different types of sensors available in a modern high-end car: wheel speed sensors (ABS), yaw and/or roll rate gyros, accelerometers, and various engine (and powertrain) related signals. These signals are fed into a sensor integration unit, which merges the information from the different sensors and allows the computation of the virtual sensor signals. These, in turn, may be used as inputs to various control systems, such as anti-spin systems and adaptive cruise control systems, or in some Human/Machine Interface (HMI), for example a display on the dashboard.

The possibility to compute virtual sensor signals is of course very appealing, but sensor fusion also gives us tools to improve fault diagnosis of the physical sensors. The reason for this is that, by using sensor fusion, we introduce analytical redundancy, which can be used to detect and isolate different sensor faults. The redundancy also implies that we can reconfigure the system if one or more sensors brake down to achieve so-called degraded, or “limp home”, functionality. Classical designs rely on hardware redundancy to achieve these goals, which is a very expensive solution compared to using sensor fusion software.

The objective of this paper is to discuss sensor fusion algorithms in general and sensor fusion algorithms for vehicle attitude estimation problems in particular. See also the accompanying paper [2]. A number of active safety systems can benefit from higher quality state information about vehicle attitude (speed, position, orientation, etc.):

·  Anti-lock braking and anti-spin systems need accurate velocity information to compute the slip.

·  Anti-spin systems for AWD vehicles need absolute vehicle velocity information for computing the optimal slip.

·  Dynamic stability systems need an accurate and high-bandwidth yaw rate signal to control the body slip angle (i.e. the difference in angle between the steering wheel and the wheel's velocity vector).

·  Adaptive cruise control systems need accurate yaw rate information for its situation awareness.

·  Smart airbag systems need accurate velocity and acceleration information to control the release of the airbag during e.g. vehicle roll over.

A problem in many vehicle projects, however, is that the high-precision sensors that are needed in order to meet the functional specifications typically have to be replaced by less accurate sensors due to cost considerations. Hence, there is a huge potential for using sensor fusion technology to create high-precision virtual sensors at a very modest cost in this area. To examplifyexemplify our ideas we will in this paper concentrate on the problem of estimating a high precision yaw rate signal from a standard, low-cost gyro using sensor fusion.

The rest of the paper is organised as follows. Next, in Section 2, we review some basic algebraic relations, which reveal much of the core ideas of the sensor fusion approach. Then, we go on to discuss the details for how to estimate a high-precision yaw rate signal in Section 3. Section 4 contains some test results and, finally, Section 5 summarises the paper.

2 Theoretical Foundation

The core idea behind our sensor fusion solution can be highlighted using the following example. Consider two different sensors measuring the same varying physical parameter gives separate measurements yi(t) of a the parameter x, where each measurement has an offset bi with an offset scaling ci(t) according to a known function of time. The measurements can be expressed algebraically as the equations:

y1(t) = x(t) + c1(t)b1

y2(1) = x(t) + c2(t)b2

These two equations have three unknowns and is therefore insoluble, and the offsets cannot be directly eliminated. When two measurements y1(1),y2(1) and y1(2),y2(2) are available, there are two more equations and only one more unknown, i.e. four equations and four unknowns. Thus, the offsets and the variable parameter values x(1),x(2) can be solved under the condition that there is no linear dependency in data. In this example, the linear independency condition is:

c1(1)/c1(2) ¹ c2(1)/c2(2)

If, for example, c1 is constant and c2(t) is the velocity vx(t), linear independency occurs when the velocity has changed between two measurements. This leads to observability, and under these conditions we can resolve all unknowns and hence also determine the sought parameter x without error.

In practice there is a measurement noise added to each of the observations. In order to eliminate the noise, a number of observation samples large enough to constitute an overdetermined equation system is collected and solved using a least squares solution. In a real-time application, this should be implemented using a recursive filter, preferably a Kalman filter, into which the sampled observations are input. Under certain identifiability assumptions (like persistence of excitation), the Kalman filter gives consistent estimates of the sought quantity (quantities). As always in adaptive filtering, there is a trade-off between noise suppression and tracking ability, which must be handled with care for optimal performance of the adaptive filter [1]. Here we will not go into details on this for sake of conciseness. Next we will see how these basics translate into a more explicit form when discussing high precision yaw rate signal estimation.

3 High Precision Yaw Rate Sensor

Our ideas for how to compute a high precision yaw rate sensor signal will be described in this section. As indicated in figure 2, the idea is to utilise available information from existing sensors in a modern car and to use sensor fusion to compute an improved yaw rate signal.

The idea of our patent pending [2,3] system is to compute a bias and scale factor free yaw rate signal using an adaptive filter that estimates the error in the yaw rate signal from the yaw rate gyro and removes that from the original signal by means of a simple subtraction operation, cf. figure 2. A feature of this solution is that the bandwidth of the original signal is preserved and, in case of limited computational power, the adaptive filter can run at a very moderate rate (it should be high enough to capture the most important temperature drifts etc. of the sensor, though).

Fig. 2. Computation of the high precision yaw rate signal

The details of our solution are as follows. For the sake of simplicity of the explanation, we are here assuming that there is no lateral movement of the vehicle. In the relations:

is the yaw rate from a gyro; vx is the velocity of the vehicle in the x-direction; ay is the acceleration in the y-direction. The curve radius R is computed according to the following relation, where R is defined as the distance to the centre of the rear wheel axle (of length L):

The angular wheel velocities w for each of the respective wheels are received from an ABS and the inverse R-1 of R is solved for in order to avoid numerical problems when driving straight ahead. The wheel radii ratio is subject to an offset:

The influence of the offset on the denominator is negligible, which results in the following expression for inverse curve radius:

wherein the computable quantity

is used for the inverse curve radius. Finally, the velocity at the centre of the rear wheel axle is

where r denotes the nominal wheel radius.

Thus, in a practical implementation of the system depicted in figure 2, the sensor measurements are:

1.  y1(t) from a yaw rate sensor, i.e. gyro signal;

2.  y2(t) = , from ABS sensors, is computed as above; and possibly

3.  y3(t) from a lateral acceleration sensor.

All these sensor measurements are subject to an offset and measurement noise given by the relations:

where dABS is an offset that depends on relative tire radius between left and right wheels. In this model, the offsets may be estimated on-line using e.g. a recursive least squares method or a Kalman filter. We prefer the latter due to the Kalman filter’s advantageous tuning flexibility in multi-parameter estimation problems.

Remarks

1. 
The important question of identifiability, that is, under what conditions are the offsets possible to estimate, is answered by studying the rank of the matrix to be inverted in the least squares solution. For the accelerometer sensor, the matrix is given by:

and, in short, this matrix has full rank if and only if the velocity changes during the time horizon. Furthermore, the more variation, the better estimate. Similarly, the offsets are identifiable from yaw rate and ABS sensors if the velocity or the curve radius changes anytime.

2.  Another problem to consider in a practical implementation of the system is that of wheel spin and other abnormal driving conditions, which must be considered separately. Due to space limitations, we do not go into the details of this here. In general, these kinds of problems must be handled by turning off or slowing down the adaptation for some (or all) of the parameters during these conditions.

4 Test Results

To demonstrate the performance of the high precision yaw rate function we now show the results of two different tests:

1.  A 105 second drive on public road, with rapid lane changing forth and back on first part, then an aggressively taken roundabout and then a drive through the same bend, with hard ABS-braking to complete the stop. The results are plotted in figures 3-6.

2.  A test drive comprising of four laps in a large roundabout where the improvement in long-term drift is clearly visible, cf. figure 7.

Test Drive Number 1

A map of the measurement drive is shown in figure 3. From the measurements we can see an instant following of the correct yaw rate but a noisy estimate in the solid line (HPY Direct), shown in figures 4 and 5. A filtered version is also distinguishable from figure 4, which is highly noise attenuated but lags approximately 40 ms in time, which gives an effective bandwidth limit of 25 Hz. However, it should be pointed out that there exists no theoretical limit for this bandwidth with our implementation. The filter effect is a mere compromise between acceptable time lag and acceptably good noise attenuation. The zoomed part (Fig. 4) is taken at a high rate of yaw (the roundabout part). For these measurements the temperature gradient is close to zero as the gyro is left on a long time before collection is started. The offset estimate is stable (Fig. 6), however some influence of the aggressive drive style is shown in the estimate.

Fig. 3. Test drive 1

Fig. 4. High precision estimate direct and low-pass filtered

Fig. 5. Zoom filtered estimate

Fig. 6. Offset estimate

Test Drive Number 2

To demonstrate the performance improvements achieved in terms of yaw rate drift we performed a test where a standard Volvo S80 with a production-type yaw rate gyro was fitted with our high precision yaw rate system and driven four laps in a large roundabout. Figure 7 contains trace plots from our inertial navigation system using the raw yaw rate signal (red) and using our system (blue).

Fig. 7. Navigation performance with and without our system

The performance improvement is huge: the drift is decreased by a factor 10 in this test (the standard gyro has a drift of about 2 degrees per second, our system less than 0.2 degrees per second). In figure 7 one should notice that using the raw yaw rate signal (red) we think we leave the roundabout with approximately 180 degrees wrong heading (top right instead of bottom left). For the blue trace the plot almost exactly represents the true vehicle path. It should also be noted that in this test the vehicle speed was computed without knowledge of exact tire radius.