paper gps kalman siptekgan 2005

8/8/2019 Paper GPS Kalman Siptekgan 2005

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EVALUATION OF LOW COST GPS APPLICATION FOR AN AUTONOMOUS

HELICOPTER IN THE PRESENCE OF KALMAN FILTER

A. Budiyono*, T. Sudiyanto and H.Y. Sutarto

Department of Aeronautics and Astronautics ITBJl. Ganesha 10 Bandung

Abstract: The design of an autonomous unmanned aerial vehicle (UAV) has been primarily driven by

system technology development. The highest added value for such a vehicle comes from the systeminstrumentation and payload and not so much from airframe technology. An important aspect of

system technology development for an autonomous UAV is the application of a low cost sensor to

overcome a prohibitive expenditure associated with high performance instrumentation. A justified approach for the implementation of a low cost sensor without compromising overall performance is

therefore desired. This paper addresses the problem of a low cost GPS application for an

autonomous helicopter. A GPS mathematical model is used in the vehicle control loop. An estimator

for GPS measurement is designed using Kalman Filtering. By using the GPS model, various GPS sensors ranging from low to high grade can be represented. The estimation signal from Kalman

Filter is then used to evaluate the performance of the GPS. The use of a low grade GPS is finally

assessed based on time domain system responses representing overall performance of the closed loop

control system. Keywords: system technology, Kalman filter, autonomous helicopter, GPS model

1 Introduction

Recent years have witnessed a rapid progress in

the enabling technologies for unmanned aerial

vehicles. Those include airframes, propulsionsystems, payloads, safety or protection systems,

launch and recovery, data processor, groundcontrol station, navigation and guidance, and

autonomous flight controllers. From all those

factors, system technology occupies the most

critical contribution to the success of UAVdevelopment and operation. Sensor technology particularly has accelerated the application of

UAV for different missions. The common

availability of Global Positioning Satellite

Navigation Systems has a profound impact to thenavigation system development for UAVs. The

satellite-based navigation provides wider coverage and more flexibility than terrestrial

navigation. The discontinuation of selective

availability of the system has further fueled

increased interest in using GPS not only for navigation but also for attitude measurement.

High perfomance and high integrity GPS,however typically places a cost barrier to most

users. The paper address the problem of using a

low cost GPS in the context of building an

autonomous helicopter. The performance of lowcost GPS will be compared to ones with the

higher grade within the framework of helicopter

feedback control system.

2 Autonomous Helicopter

A model helicopter has been chosen as the flyingtest-bed due to its potential in representing many

advanced phenomena in the study of dynamics

and control such as nonlinearity, hybrid system,

multi-input multi-output and non-minimum phase. In the mean time, those rich behavior

pose many difficulties in the design of guidance,

navigation and control for the helicopter. Toaddress the problem, a step-by-step designapproach has been taken by utilizing Hardware

In the Loop simulation facility [6]. The

autonomous helicopter hardware system isdescribed by the following figure [2]:

Fig. 2.1 Autonomous helicopter hardware system



Different data is picked-up by the sensors to

measure the vehicle attitude, positions andatmospheric data. The vehicle attitude dynamics

is measured using Inertial Measurement Unit

(IMU) which typically consists of triad

accelerometer to sense the accelerations andtriad gyros to sense the Euler angles. The vehicle

positions can be deducted from the accelerationsor obtained from GPS measurements [2]. Within

the HIL framework, all sensors are

mathematically modeled based on the available

technical specifications. The availability of thesensor model enable the evaluation of

performance of different grade or quality.

3 The GPS Model

The Global Positioning System is a satellite

navigation system that allows the user to acquire

accurate determination of position and velocity

based on noisy observation of the satellitesignals. The model has the same structure for

both position and velocity but with different parameter values. The mathematical model of

the GPS is based on that derived in the

[Prasaad]. The block diagram is presented infigure 3.1 and the values of the parameters of the

model are in table 3.1. The main characteristic of

the GPS which have been considered arelatency, update rate, accuracy and error

dynamics parameter.

The update rate represents the rate at which the

position and velocity signals are sent to thereceiving processor and is modeled as

quantization. The latency is the time delay that

occurs between the time the satellite informationis received and the time the position or velocity

output is sent to the receiver. It is modeled as a pure time delay. The accuracy is the radius of

the circle with the origin at the actual position or

velocity which contains 50% of the sensors

output values. The error of the GPS sensor package is generated as output of a first order

linear differential equation with randomGaussian input and initial condition.

Fig. 3.1 The GPS Model

Position Velocity

Update Rate 5 Hz 5 Hz

Latency 0.075 s 0.075 s

Accuracy 0.65 ft 0.1 ft/s

Error Dynamic Parameter (a) 0.5 s 2.5 s

Table 3.1 The GPS Model Parameter Values

4 The Kalman Filtering Algorithm

A discrete Kalman Filter Algorithm is

implemented to the GPS model’s outputchannels. The algorithm is illustrated in figure

4.1. The filter provides states estimation ( ˆ jx )

based on every measurement output ( jz ) by the

GPS and the previous step estimation (1

ˆ j−x ). The

process performed by the plant is considered as adynamic system which has a neutral stability

characteristic that the transition function (φ) may

be considered as an identity matrix. The

measurement’s noise covariance matrix (R ) is

provided by processing the error generated bythe GPS from time to time. Since the

experimental data which is required to computethe process’ noise covariance matrix (Q) is not

available yet, a value of about 10% of R is

considered for Q. For detailed discussion of discrete Kalman Filtering, one can refer to

[Brown].

Fig. 4.1 The Kalman Filtering Algorithm

5 Performance Analysis

5.1 Open loop

The simulation results as described on figure 5.1,

figure 5.2, figure 5.3, figure 5.4, figure 5.5,figure 5.6, figure 5.7, figure 5.8, figure 5.9,

figure 5.10, figure 5.11, and figure 5.12 show

that the greater the GPS error deviation, the

better the GPS noise is supressed by the filter,yet, the greater the filter error estimation. Vice



versa, the smaller the GPS error deviation, the

supressed noise is not too significant, and yet,the smaller the filter error estimation.

Fig. 5.1 Measured Position in North Direcion

Fig. 5.2 Estimated Position in North Position

Fig. 5.3 Measured Position in East Direcion

Fig. 5.4 Estimated Velocity in North Direcion

0 100 200 300 400 500 600-1000

0

1000

2000

3000

4000

5000

6000

7000

MEASURED ALTITUDE

(second)

( m

e t e r )

σ2 = 100

Fig. 5.5 Measured Altitude

Fig. 5.6 Estimated Altitude

Fig. 5.7 Measured Velocity in North Direcion



Fig. 5.8 Estimated Velocity in North Position

Fig. 5.9 Measured Velocity in East Direcion

Fig. 5.10 Estimated Velocity in East Position

Fig. 5.11 Measured Rate of Climb

Fig. 5.12 Estimated Rate of Climb

5.2 Closed loop

To further evaluate the performance of the GPSwith various grades, three different GPS were

tested within the feedback loop of autonomoushelicopter control system. The baseline system isthe autonomous helicopter controlled using

optimal control synthesis given in Ref [3]. The

wind model with Dryden spectrum is added into

the velocity channel. The triad velocities

including the disturbance will be the input of theGPS model. The output of the GPS is taken by

the Discrete Kalman Filter algorithm prior to the

control algorithm block. Figs. 5.13 and 5.14show position tracking in the East and North

direction respectively. Whereas Figs 5.15through 5.17 give illustration of the velocity

tracking in the forward, side and verticaldirection. Finally Fig. 5.18 display the trajectory

tracking of the autonomous helicopter followinga rectangular path. The helicopter deviates from

the reference trajectory due to the added winddisturbance particularly in the vertical direction.

Nevertheless, the overall results demonstrates

that despite apparent discrepancy in performance

among the three GPS as shown by Fig. 5.10, the

tracking control performance is not affected asmuch. The result is consistent both for position

and velocity tracking. The poorest or worst GPS,

which is one represented by σ2=100, shows

comparable performance as that of better GPS.



Fig. 5.13 Comparison of East position tracking

Fig. 5.14 Comparison of North position tracking

Fig. 5.15 Comparison of forward velocity tracking

Fig. 5.16 Comparison of side velocity tracking

Fig. 5.17 Comparison of vertical velocity tracking

Fig. 5.18 Trajectory tracking

6 Concluding Remarks

The study for the low-cost GPS application for

an unmanned aerial vehicle has been presented.Within the open loop simulation, the poor GPScan be easily differentiated from a better GPS.

When placed in the feedback loop, however, the

effect of quality of the GPS is not as prominent.

The poor quality GPS shows in general acomparable performance to that of higher quality

GPS. In practical application, it should be noted

however that the quality of GPS is not solely



governed by the value of variance as studied in

this work. The update rate plays an importantrole in determining the GPS grade and therefore

its price. More elaborate study is necessary to

investigate the effect of GPS performance in the

overall performance of an autonomousunmanned aerial vehicle.

BIBLIOGRAPHY

1 Brown, R.G. and Hwang, P.Y.C.,

Introduction to Random Signals and

Applied Kalman Filtering . John Wileyand Sons, Inc., 2nd ed., 1992.

2 Budiyono, A., 27 July 2005, Design and

Development of Autonomous

Uninhabited Air Vehicles at ITB:

Challenges and Progress Status.

Aerospace Indonesia Meeting, Bandung,Indonesia

3 Budiyono, A. dan Wibowo, S., 2005,

Optimal Tracking Controller Design for

A Small Scale Helicopter , in reviewProceeding ITB

4 Nasution, S.H., Budiyono, A. and Jenie,

S.D., 2005, Design of GPS-based

Trajectory Holding System for an

Unmanned Aerial Vehicle, AerospaceScience and Technology Seminar, Jakarta

5 Perhinschi, M.G. and Prasad, J.V.R., A

simulation model of an autonomous

helicopter .

6 Sudyanto T., Budiyono A., Sutarto H.Y.,July 27, 2005, Hardware In-the-loop

Simulation for Control System Designs

of Model Helicopter , Aerospace Indonesia

Meeting, Bandung

paper gps kalman siptekgan 2005

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