Doppler Radar and MEMS Gyro Augmented DGPS

for Large Vehicle Navigation

Jussi Parviainen∗, Martti Kirkko-Jaakkola∗, Pavel Davidson∗, Manuel A. Vazquez Lopez†, and Jussi Collin∗

∗ Department of Computer Systems

Tampere University of Technology, Tampere, Finland

Email: firstname.lastname@tut.fi† Department of Signal and Communications Theory

Carlos III University, Madrid, Spain

Email: mvazquez@tsc.uc3m.es

Abstract— This paper presents the development of a land vehi-cle navigation system that provides accurate and uninterruptedpositioning. A ground speed Doppler radar and one MEMSgyroscope are used to augment differential GPS (DGPS) andprovide accurate navigation during GPS outages. The goal is tomaintain a position accuracy of 2 meters or better for 15 secondswhen an accurate GPS solution is not available. The Dopplerradar and gyro are calibrated when DGPS is available, and aloosely coupled Kalman filter gives an optimally tuned navigationsolution. Field tests were carried out in a harbor environmentusing straddle carriers.

I. INTRODUCTION

Accurate navigation is a key task for automated ground

vehicle control. Using code based differential GPS (DGPS)

and real time kinematic (RTK) DGPS satellite navigation,

the position of a receiver can be determined with sub meter

or even with centimeter-level accuracy. However, there are

some instances when GPS performance can be worse than

expected. The satellite signals can be masked by buildings

and other reflecting surfaces. GPS performance degradation

may also occur because of multipath. In order to overcome

these difficulties some additional sensors that are not affected

by the external disturbances can be used. During GPS out-

ages or unreliable position fixes, the vehicle position can be

estimated using heading and velocity measurements. In our

system ground speed from the Doppler radar and heading rate

from the gyro are used to perform the dead reckoning (DR)

computations.

There are different sensors such as accelerometers, wheel

encoders, Doppler radars that give information about a vehicle

translational motion. The conventional 6 degrees of freedom

inertial navigation system (INS) consists of three gyros and

three accelerometers. The description of INS and its perfor-

mance can be found in numerous works, for example [1]–

[5]. The cost of INS depends significantly on the required

navigation performance during GPS outages. If we wanted to

use INS for our application, we would need a tactical grade

INS with the gyro of approximately 10 deg/h accuracy. A DR

implementation using a single gyro and a ground speed sensor

can significantly lower the cost of positioning system.

The possible choice for ground speed sensor is a wheel

encoder or Doppler radar. A wheel encoder measures the

distance traveled by a vehicle by counting the number of full

and fractional rotations of a wheel [6]. This is mainly done

by an encoder that outputs an integer number of pulses for

each revolution of the wheel. The number of pulses during a

certain time period is then converted to the traveled distance

through multiplication with a scale factor depending on the

wheel radius. Many previous works used wheel encoders

to measure ground speed [7]. However, there are several

sources of inaccuracy in the translation of the wheel encoder

readings to traveled distance or velocity of the vehicle. They

are [8], [9]: wheel slips, uneven road surfaces, skidding, and

changes in wheel diameter due to variations in temperature,

pressure, tread wear and speed. The first three error sources

are terrain dependent and occur in a non-systematic way.

This makes it difficult to predict and limit their detrimental

effect on the accuracy of the estimated traveled distance and

velocity. A non-contact speed sensor, such as a Doppler radar,

can overcome these difficulties. Its output is not affected by

wheel slip and the device is easy to maintain. However, the

Doppler radar is not completely independent of environmental

conditions; for instance, depending on the placement of the

radar, splashing water may cause errors in the system.

By combining the aforementioned gyroscope and Doppler

radar, we have developed a low-cost DR system to accurately

position a vehicle during short DGPS outages. Previously, a

DR system including Doppler radar and gyro was proposed

in [10] for agricultural devices. The previous work of au-

thors containing same sensors, gyro and Doppler radar, is

presented in [11]. The basic navigation algorithm is quite

similar compared to our previous work. However, there are

some differences when the similar sensors are applied to large

land vehicles. In this paper those differences are introduced.

In addition, we show the results of actual straddle carrier tests

in a harbor area using our integrated DGPS/DR system that

provides accurate and uninterrupted navigation even during

DGPS outages.

Paper continues with Section II giving a brief overview

of the Doppler radar, the gyroscope, and the DGPS receiver

used in our system. The algorithms are explained in detail in

Section III. Finally, experimental results with straddle carriers

are shown in Section IV.

978-1-61284-4577-0188-7/11/$26.00 c©2011 IEEE140

II. INSTRUMENTATION

A. Doppler Radar as Speed Sensor

Conventionally, the ground speed of a land vehicle is mea-

sured based on wheels rotation using wheel encoders. In these

cases measured speed is sensitive to wheel slip and pressure

of the tires. Moreover, maintenance of wheel encoders can be

difficult and expensive. Therefore Doppler radar was used to

measure the speed of the vehicle. In our tests we used Dickey

John III radar [12]. The dynamic range of this radar is from

0.5 km/h to 107 km/h. Output of the Doppler radar is always

positive. Therefore the direction of vehicle movement cannot

be determined based on Doppler radar output. In addition

to this the Doppler radar is also insensitive to speed below

0.5 km/h. Fig. 1 illustrates the insensitivity zone. Some studies

have been carried out to detect the direction as in [13], but

this kind of radar is still not commonly used and is expensive.

The output of Dickey John radar is a square wave whose

frequency is proportional to the speed of the vehicle. The

radar is attached to the vehicle at certain boresight angle,

which is approximately 35 degrees. The measured Doppler

shift frequency fd depends on speed as follows:

fd = 2v(f0/c) cos(θ), (1)

where v, f0, c and θ are the speed of vehicle, the transmitted

frequency of radar, speed of light and inclination angle of

radar. However, this angle θ can be slightly different from

the nominal boresight angle and that affects the calculation of

vehicle velocity. Thus the radar should be calibrated before

use. The calibration includes the estimation of unknown scale

factor (SF) error, which can be found using GPS velocity. Once

the radar is calibrated it can be used for accurate ground speed

measurement.

B. Gyroscope

Analog Devices ADIS16130 MEMS gyroscope was used

for heading rate measurements. Output of the gyro is digital

and can be read using serial peripheral interface (SPI) com-

munication. According to sensor datasheet [14] the gyro has

bias stability of 0.0016◦/s (1σ) and angle random walk is

0.56◦/√

h (1σ).

0

3

-3

True speed (km/h)

Measured speed (km/h)

0.5

0.5-0.5 3-3

Doppler radar speed

Fig. 1. Doppler radar speed measurement

The gyro was calibrated in laboratory for long term bias

and scale factor. The calibrated values for bias and SF were

found to be within specifications of data sheet.

C. DGPS receiver

In the tests, we used dual frequency Javad receiver. The

GPS antenna was mounted at the top of the vehicle close to

the center of rotation. The accuracy of this receiver is about

ten centimeters in the real time kinematic (RTK) DGPS mode,

which makes it suitable for reference position to evaluate

the accuracy of dead reckoning. The receiver can operate

in four different modes: standalone, code DGPS, RTK float

solution, and RTK fixed solution. Naturally, the RTK fixed

solution mode is the most accurate. Whenever such a solution

is available, the DGPS receiver is used to calibrate the Doppler

radar and the gyro.

III. NAVIGATION ALGORITHM

Like in our previous work [11], the data obtained from

the sensors is processed using three different Kalman filters.

One estimates the scale factor of the Doppler radar, another

calibrates the gyro, and the Extended Kalman filter (EKF)

computes the position and heading. Calibration of the Doppler

radar and the gyro was performed by two different filters to

keep the design robust, i.e. possible errors in other sensor do

not affect to the calibration of both sensors.

A. Doppler radar calibration

Because Doppler radar and GPS antenna are located in

different places of the vehicle, a lever arm compensation is

needed. The GPS antenna is located almost at the center of

rotation of the vehicle and the distance between the antenna

and the radar is known. In absence of other errors, the lever

arm correction is computed as follows:

vD = vDGPS + w ×R (2)

where R is the vector pointing from the GPS antenna to the

Doppler radar; w is the heading rate measurement (rad/s);

vD and vDGPS are the speeds of the Doppler radar and

GPS antenna, respectively.

However, before we can compensate for the lever arm, we

have to calibrate the scale factor error of the Doppler radar.

This can be done while the vehicle is driving along a straight

line. The velocity measured by the Doppler radar at time k is

modeled as

vDk =(

1 + SD)

vk + nD

k (3)

where vk

is the true (unknown) velocity at time k , SD is the

scale factor error, and nD

kis a random variable (r.v.) of additive

white Gaussian noise (AWGN) whose mean and variance are

known. The SF error is modeled as a random constant. In order

to estimate it, the horizontal velocity given by GPS is used.

This is assumed to be the true velocity distorted by AWGN,

vDGPS

k = vk + nDGPS

k , (4)

with nDGPS ∼ N(

0, σ2DGPS

)

.

141

Using (3) and (4) we calculate the difference between

Doppler radar and GPS ground speed

zDk = vDk − vDGPS

k = SDvk + nD

k − nDGPS

k . (5)

Equation (5) can be seen as the observation equation of a dy-

namic system in state-space form. Since we are assuming that

both nD

kand nDGPS

kare Gaussian and independent, Kalman

filter (KF) [15] can be applied to estimate the state SD. The

true velocity needed in (5) is not known, though, and GPS

velocity will be used as an approximation in that equation.

Once an estimate of the scale factor error is available, the

true velocity is estimated using that obtained from the Doppler

radar as

vk =vDk

1 + SD(6)

with SD being the final estimate of the Doppler radar scale

factor error given by the KF.

B. Gyroscope calibration

The output of the gyroscope at time k can be modeled as

wg

k= (1 + Sg)wk +Bg + ng

k

= wk + Sgwk +Bg + ng

k

(7)

where wk

is the angular rate at epoch k, Sg is the gyro SF

error, Bg is the bias and ng

kdenotes random noise which we

model as AWGN with variance σ2g . Modern MEMS gyros

have quite good bias stability, especially when the temperature

is constant. However, the day-to-day bias can be significant.

Therefore, initial bias calibration has to be performed before

starting navigation. The bias may also fluctuate during oper-

ation; it is particularly sensitive to the ambient temperature.

Consequently, when navigating for longer periods, the gyro-

scope bias should be recalibrated whenever possible.

The SF error is caused by gyro misalignment and sensitivity

error. If the vehicle is not doing significantly more left turns

than right turns, or vice versa, the SF error will be canceled

by opposite turns; in the extreme case of driving circles in a

single direction, even a moderate SF error may accumulate into

dozens of degrees of heading error. As we assume that these

extreme cases do not occur, the position error accumulation

because of SF is insignificant. Therefore, we omit the SF error

compensation.

When the vehicle is stationary, the angular rate w is known

to be zero and thus, the gyro output consists solely of the

bias Bg and noise ng. Therefore, when the vehicle is started,

we require it to be stationary for a certain period of time during

which the gyro bias is estimated. In this initial calibration,

we compute the gyro bias simply by averaging. In real-time

implementations this can be done recursively as

Bg1 = w1

Bg

k=

k − 1

kB

g

k−1+

wk

k.

(8)

Since the gyroscope noise variance σ2g is known from the

technical specifications and laboratory tests, the initial gyro

calibration can be done by means of Kalman filtering instead

of recursive averaging. Obviously, if there is prior knowledge

available on the bias, Kalman filtering may converge faster

and be more accurate.

Whenever the vehicle stops for a longer time, the gyro bias

estimate can be refined. First of all, since we know that the bias

changes with time, the accuracy of the bias estimate degrades

as time passes; moreover, even if there is only a short time

since the initial calibration, having more data for averaging

should improve the estimate. For later updates of the gyro bias

estimate, we use a KF because it allows the estimate to adapt

to changes in the bias by gradually increasing its variance

estimate. If this was to be done using recursive averaging, the

weights in (8) should be modified to give more weight to the

current measurement.

For calibrating the gyro bias during navigation, it has to be

known whether the vehicle is stationary or not. The Doppler

radar is insensitive to speeds lower than 0.5 km/h; therefore,

additional sensors, e.g. accelerometers, are required for stop

detection. Furthermore, it may be beneficial to ensure that the

stop is sufficiently long in order to make sure there are enough

samples for averaging. If there is any uncertainty in the stop

detection, a certain number of first and last samples may be

discarded at each stop.

C. Position and heading estimation

Vehicle dead reckoning computations can be described by

the following equations

˙PN = v cos(Ψ)

PE = v sin(Ψ)

Ψ = w,

(9)

where PN and PE are the north and east components of

vehicle position, Ψ is heading, ( ˙ ) indicates the time derivative

operation, v is the ground speed (measured by GPS when

available and by Doppler radar otherwise) and w is the gyro

heading rate measurement. It should be noted that even if we

were using ideal sensors, the vehicle body heading produced

by the gyro and the ground track direction measured by GPS

may not be exactly the same during turns. In this work, we

approximate that heading measured by the gyro is same as

GPS based heading.

The EKF is used to solve this non-linear estimation problem.

The augmented state vector for the EKF is

x =[

PN PE Ψ δvD δωg]T

, (10)

where δωg and δvD are added to the EKF as additional states

in order to compensate for the residual non-white gyro and

Doppler radar errors, respectively, that remain after the sensors

are calibrated according to Sections III-A and III-B. These two

states are modeled as first order Gauss Markov process with

time constants τg and τD .

The covariance propagation in the EKF is

Pk+1|k = ΦkPk|kΦT

k +Qk, (11)

142

where Φ is the discrete equivalent of the continuous transition

matrix F and Q is the process noise matrix. In our case we

have the following transition matrix

F =

0 0 −vD sin(Ψ) cos(Ψ) 00 0 vD cos(Ψ) sin(Ψ) 00 0 0 0 10 0 0 −1/τD 00 0 0 0 −1/τg

, (12)

where heading Ψ can be calculated using previous output of

the filter and gyro.

The measurement equation is

z = Hx+ η, (13)

where

H =

1 0 0 0 00 1 0 0 00 0 1 0 0

(14)

and z =[

PDGPS

NPDGPS

EΨDGPS

]T(GPS north posi-

tion, east position and course over ground (heading) measure-

ment, respectively) and η is zero mean white noise with covari-

ance matrix R. Since GPS computes heading using arctangent

of north and east velocity components, the standard deviation

of heading is inversely proportional to the ground speed.

Therefore, accuracy of the heading measurement ΨDGPS

degrades as speed decreases [16], i.e.,

σΨDGPS =σvDGPS

v(15)

Doppler radar

GPS antenna Gyro

Fig. 2. Measurement device

0 50 100 150 200 250−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

time [s]

sp

ee

d e

rro

r [m

/s]

DGPS

speed − Doppler

speed w/o cor

DGPSspeed

− Dopplerspeed w/ cor

Fig. 3. Speed error due to lever arm

where σΨDGPS and σvDGPS are the standard deviations of

GPS heading and velocity errors. Also position error in GPS

receiver varies depending on which mode it is operating (RTK

or code DGPS). Thus this must be also taken into account

when forming covariance matrix R.

IV. EXPERIMENTAL RESULTS

As discussed in the previous sections, a similar system was

used in [11] where the test vehicle was a regular passenger

car. In this section we present the main problems we encounter

when a 13-meter-tall straddle carrier (Fig. 2) is used instead.

The gyro was located at the top of the vehicle and the

Doppler radar was mounted between the right wheels. Thus,

as discussed in Section III-A, a lever arm error will occur. The

speed difference due to the lever arm is shown in Fig. 3.

Although the Doppler radar is insensitive to wheel slippage

and to other wheel based errors, new disturbances were

encountered during straddle carrier tests. As the radar was

mounted between the tires, water and mud may splash to the

radar beam, causing errors in the velocity measurement. This

error can be reduced only by changing the location of the

radar. An example of a test made on a wet road is shown in

Fig. 4. It can be seen that the largest errors occur during high

speeds.

Another difference in the behavior of large vehicles com-

pared to passenger cars is the vehicle swing as illustrated

in Fig. 5. Usually, this can be observed as an oscillation

in the GPS heading measurement, as in Fig. 6. In order to

compensate for this error we need to increase the variance

of GPS heading measurement error in the EKF or model the

oscillations directly in the navigation algorithm. However, as

the swinging does not occur all the time, it is easier to just

increase the heading error variance in Kalman filter.

In a real harbor environment there are obstacles which

obstruct the view to GPS satellites. Occasionally, an in-

sufficient number of visible satellites prevents the receiver

from computing a fixed RTK solution, forcing it to operate

in an inferior mode. However this can be compensated by

143

0 50 100 1500

2

4

6

8

time [s]

sp

ee

d [

m/s

]

DGPSspeed

Dopplerspeed

0 50 100 150−1

0

1

2

3

time [s]

sp

ee

d e

rro

r [m

/s]

DGPSspeed

− Dopplerspeed

Fig. 4. Splashing water causes errors in the Doppler radar speed measurement

using different covariances in navigation filter for the different

modes.

Our test vehicle was driven along several trajectories in a

harbor area while data delivered by the gyroscope and the

Doppler radar was recorded. A sample route is presented in

Fig. 7. The red curve presents GPS trajectory and the black

dashed line is the DR trajectory when GPS data was not used.

Several 15-second GPS outages were generated in order to

evaluate the horizontal position accuracy of the DR solution.

Fig. 8 presents the distribution of horizontal position errors

of the trajectory shown in Fig. 7 with multiple artificial 15-

second outages made into the GPS data. The figure shows

that during this test, in approximately 80 % of the outages, the

maximum position error did not exceed 2 meters. Mean square

error in this case is approximately 1.9 meters. In general,

compared to the passenger car results [11], the navigation

accuracy during DGPS outages degraded slightly. Most likely,

Fig. 5. Vehicle swing

128 130 132 134 136 138 140 142

0

10

20

30

40

50

60

Time (s)

He

ad

ing

(d

eg

)

DGPS

Gyro

Fig. 6. GPS heading error due to the vehicle swing

the largest errors in the data were caused by the splashing

water which induced significant non-Gaussian errors to the

Doppler radar measurements. Fortunately, large errors were

fairly rare and in the most of cases after 15 second GPS

outage the position error was less than 2 meters. By using

other types of sensors e.g. wheel encoders would arguably

improve the results, as it is shown in [17]. However, the use

of wheel encoders has other drawbacks which were discussed

in the section I.

V. CONCLUSION

In this paper we showed that a Doppler radar and a MEMS

gyro can be used as an accurate DR system to aid differential

GPS during signal outages for straddle carriers and other

harbor vehicles. If the vehicle does not have a standard speed

Outage ends

Outage starts

20 m

Fig. 7. Example route with 15 second GPS outage

144

0 20 40 60 80 1000

1

2

3

4

5

Horizonta

l positio

n e

rror

[m]

%

Fig. 8. Distribution of maximum horizontal position errors during multiple15 second GPS outages

sensor or if the wheels are expected to slip considerably, a

Doppler radar is advantageous compared to wheel encoders.

This paper shows that there are many aspects that are needed

to take into account when designing this kind of navigation

system for large vehicles. The mounting place of Doppler radar

is crucial because a significant part of large position errors

can be related to increased speed measurement errors on wet

surfaces. For example, water splashing from the tires can cause

more than 1 m/s of speed error. In addition, during turns, the

dynamics of an all-wheel-steered straddle carrier is in general

very different from that of front-wheel-steered passenger cars.

Our test vehicle, a straddle carrier, was driven along various

trajectories in a harbor area while the heading rate and

speed measured by the gyroscope and the Doppler radar were

recorded. Separate Kalman filters were used to estimate the

scale factor error of the Doppler radar, the gyroscope bias,

and the vehicle position and heading. The test results also

showed that during short 15 second outage, an accuracy better

than 2 meters is usually attained. Currently, the performance

goals are not fully achieved, but improvements are to be

made in the future. The current implementation is for post-

processing real-world data, but the algorithm can be adapted

for implementation as a real-time system.

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