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h n d EEE Conferenceon Control Applications, September

13 - 16, 1993 Vancouver,

B.C.

Flight Test Development and Evaluation

of

a

Kalman Filter State Estimator for Low-Altitude Flight

Richard E. Zelenka,NASA Ames Research Center, M ofett Field, CA

94035

Andre Zirkler, Vitronics Inc., E atontown,

NJ

07724

Zee Yee, U.S. rmy Comm andlControl and Systems Integration, Ft . Monmouth,

N J

07703

Abstract Flight operations dependent on digitized ter-

rain elevation data for navigational reference

or

trajecto-

ry generation are constrained in minimum flight altitude,

due to airborne navigation errors and inaccuracies of the

reference terrain elevation data. This limitation

is

not

re-

strictive in traditional medium-altitude implementations

o f such databases, such as in unmanned aerial vehicles,

missiles,

or

high-performance, high-speed aircraft.

I n

low-altitude, lower speed terra in hugging helicopter mis-

sions, however, such constraints on minimum flight alti-

tudes greatly reduce the effectiveness of their missions

and diminish the benefits of employing terrain elevation

maps.

A

Kalman filter state estimator has been devel-

oped which blends airborne navigation, stored terrain

el-

evation data, and a radar altimeter in estimating above-

ground-level

AGL)

altitude. This

AGL

state estimator

was integrated in a near-terrain guidance system aboard

a research helicopter and flight tested in moderately rug-

ged terra in over a variety of flight and system conditions.

The minimum operating altitude of the terrain database

referenced guidance system was reduced from

300

ft to

150

ft with the addition of this Kalman filter state estima-

tor.

Terrain elevation databases of actual geographic regions

have found extensive use

in

aircraft systems development

and operations. Development applications range from com-

puter generated imagery for flight simulation

to

terrain mod-

els for evaluation of radar and other sensors. Operational

applications include mission planning, enroute navigation,

and terrain following/terrain avoidance

[

11. Perhaps the most

successful application of terrain elevation databases has been

for terrain-referenced navigation, where radar altimeter re-

turns are used to achieve a positional f ix within a given ter-

rain database. The SITAN (Sandia Inertial Terrain-Aided

Navigation) system can achieve navigational accuracies

comparable with contemporary strap-down inertial units

subject

to

spectral properties

of

the particular topography

123.

Avionic systems that depend on digitized terrain elevation

data are constrained in minimum flight altitude due to navi-

gation and terrain database inaccuracies. As lower altitudes

are approached and more aggressive maneuvering attempt-

ed,

the

ability of the aircraft to reliably and accurately posi-

tion itself relative to the ground becomes vital. Unrecorded

features and map horizontal shifts have been observed in

flight tests [3]. Persistent above-ground-level AGL) bias er-

rors

due to navigation and terrain map errors,

in

addition to

higher frequency terrain features unrepresentedin the stored

terrain database, must be identified and accounted.

I. Introduction

A

low-altitude, terrain-referenced maneuvering terrain fol-

lowing/terrain avoidance (TF/TA) guidance system for heli-

copters has been under development at NASA Ames

Research Center [4]. The guidance algorithm uses mission

requirements, aircraft performance capabilities, navigation

data, and digitized terrain elevation data to generate a low-

altitude, valley-seeking trajectory. It seekstominimize

mean

sea

level (MSL) altitude, heading change from a straight line

nominal path between waypoints, and lateral offset from the

nominal path. This trajectory is generated in real-time and

presented to the pilot on a helmet-mounted display. The sys-

tems performance is principally limited in

its

ability

to

posi-

tion itself within the terrain, and

its

inability to detect and

avoid unmapped obstacles, such

as

trees and wires. After

evaluation in several full-motion, piloted simulations, the

system has reached sufficient maturity for flight evaluation.

A

joint NASNAnny program

to

flight test the system on the

IJ.S.

Anny

NUH-60

STAR (Systems Testbed for Avionics

Research) helicopter is currently being conducted.

An

appraisal of the digital terrain map accuracy was

per-

formed prior

to

flight evaluation to establish a minimum

clearance altitude

to

be used during flight tests

[ 5 ] .

This was

accomplished by comparing predicted terrain elevation data-

base values based on measured horizontal position

with

ele-

vation obtained by taking the difference between measured

navigational vertical position and radar altitude. Precision

navigation data (from a differentially corrected Global Posi-

tioning System (GPS) receiver) and r a waltimeter data were

recorded as a test aircraft flew low-altitude missions over

rugged and plain

areas.

The combined precision navigation

and terrain database errors in terrain elevation were found to

be as great as 220 ft, establishing a minimum clearance alti-

tude for flight test of 220 ft AGL. Recent flight experience

witnessed even greater unrecorded terrain features that limit-

ed flight

to

above 300

ft.

To

improve above-ground-levelaircraft positioning, a

Kal-

man filter was developed which blends radar altimeter mea-

surements, navigation system vertical position

measurements, and stored digital terrain data. The result is a

more accurate estimate of AGL altitude for the

TF/TA

guid-

ance system. The estimate is also more robust, stable, and

accurate than what would

be

provided by a simple noise-fil-

tered radar altimeter. The

linear,

sequential measurement

processing Kalman filter was implemented in a test helicop-

ter and flight tested in moderately rugged terrain. The Kal-

man filter was found to substantially reduce the AGL

positioning limitation of the afore-mentioned guidance sys-

tem, leaving the flight envelope constraint imposed by obsta-

cle detection and avoidance.

CH3243-3/93/0000-0783 1.00 993 IEEE

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The paper begins with the problem formulation and Kalman

filter augmented guidance system description. State models

are

then developed and the Kalman filter defined. The air-

craft implementation is then described and its in-flight, real-

time performance is appraised. Concluding remarks and fu-

ture directionsare then discussed.

11. Problem Description

Figure1 describes key variables and definitions involved in

the low-altitude, digital terrain map referenced flight envi-

ronment.

Navjgation

System

Altitude

A l t i t ub

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

------------

L

hiwed hrod

True Terrain

rue Terrain

MSL

erraLData

Fig. 1. Problem Description.

The aircraft is depicted on a nominal flight path with AGL

altitude denoted as h . Navigational mean sea level altitude is

denoted as h,,,, and sampled terrain elevation data as h,,

The difference in these two values is the predicted AGL

altitude (hprCd= hm,l- hh). the current method of deter-

mining height above ground. The accuracy of hprrds deter-

mined by the accuracy of the navigation system and the

terrain database. The radar altimeter measurement for AGL

altitude is represented as

brad.

This measurement, along with

the

predicted measurement of AGL altitude, is

to

be blended

to

yield an improved estimate

of

h .

The satellite-based Global Positioning System would pro-

vide the most accurate and reliable positioning solution. The

coarse acquisition,or civil code of GPS gives position accu-

racy of

66-131

ft (20-40 m), degrading to

328

ft

(100

m)

when Selective Availability (intentional degradation of the

GPS by the Department of Defense) is activated. The preci-

sion, or military code yields 33-66 ft (10-20 m) accuracy.

Differential GPS can yield 7-10 f t (2-3 m) positioning accu-

The accessed value for terrain elevation, hdm, is an imper-

fect approximation of the terrain, and is referenced using the

imperfect latitude-longitudeoutput from the navigation sys-

tem.

A

Level 1 Defense Mapping Agency (DMA) Digital

Terrain Elevation Data (DTED) database consists of a uni-

form matrix of MSL terrain elevation values. These database

values have

an

accuracy objective of

98

ft (30 m) at 90%

linear error for absolute vertical elevation, and 427 ft (130

m) at 90% circular error

for

absolute horizontal position.

Each 1 deg by 1 deg latitude-longitude cell carries its own

accuracy specifications, however, which depend on the data

collection method used for that area, and can

be

grealer than

the general database accuracy objectives. Because the terrain

elevation stored in the DMA database is accessed via the lat-

itude-longitude value

of

the navigation system, horizontal

positioning errors

will

reference offset terrain data. The sum

of these hdm. errors, combined with those of the navigation

system, can lcad to large crrors in the predicted absolute

racy

[61.

AGL altitude, although relative, lower frequency AGL alti-

tude movement will be fairly accurate and reliable.

The

radar altimeter is a direct measurement of the above-

ground-level altitude. Typical radar altimeters are limited in

operational altitude and degrade in accuracy with altitude.

Most are fan-type, i.e., a conical

beam

is transmitted, and

height above ground or nearest obstacle is returned. The

measurement is thus relatively insensitive to aircraft roll and

pitch attitude, and returns distance to the nearest terrain fea-

ture. The spreading of the radar

beam

footprint can yield

radar altimeter returns registered from nearby higher terrain,

rather than that directly below the aircraft. Flight over a

dense forest may yield height above the treetops (canopy

height), while flight over bare (winter) trees may give height

above the ground [7,81.

111.

Kalman

Filter Implementation

A block diagram of the Kalman filter augmented terrain-ref-

erenced guidance system, termed the Computer Aiding for

Low-Altitude Helicopter Flight (CALAHF) system, is

shown in Fig. 2.

Fig. 2. Kalman Filter-augmented System.

The dashed blocks describe the baseline CALAHF guidance

system. CALAHF computes in real-time a valley-seeking

TFn

trajectory based on a stored terrain elevation data-

base, navigational aircraft state, and a nominal flight plan

[4].

Tke Kalman filter output for the predicted AGL altitude

error, h,,,, is used in altering the nominal guidance trajectory

before presentation to the pilot on the helmet mounted dis-

play (HMD). That is, the solely airborne navigation and

stored

terrain elevation database referenced trajectory of the

baseline CALAYF system ( [P,,,~] ) is modified with respect

to the value of

he,,

to produce

[P,,,~]

The principal flight envelope constraint of any terrain data-

base referenced system derives from its ability to position

the aircraft with respect to the terrain (Fig. 1). This limita-

tion, thought

to

confine operations

to

above

220 f t [51,

was

found through flight testing to be even more restrictive in

sections of the flight test course, setting a minimum AGL

al-

titude ceiling of 300

ft.

Such flight altitudes greatly compro-

mised the benefit and effectiveness of the CALAHF system,

particularly

to

the military helicopter community. where op-

erations restricted to such mid-level altitudes would not

jus-

tify

its

cost and complexity.

The solid blocks of Fig. 2detail the extension to the baseline

CALAHF system resulting from the Kalman filter augmenta-

tion. The predicted AGL altitude from the navigation system

and the stored map hm,, hdmo).ogether with the radar al-

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timeter measurement, are blended in a Kalman filter to yield

an improved estimate of AGL altitude, andan estimate for

the difference error fro? the predicted AGL altitude. This

difference error value,

he,,

is then used to alter the terrain

elevation database referenced guidance trajectory at the

AGL-error blending block of Fig.

2.

The discrete-time Kalman filter is a recursive optimal control

filter most appropriate for estimating a noisy signal given

noisy measurements. The Kalman optimal criteria is the

minimization

of

mean-square error. The gains which satisfy

this

criterion are computed after each measurement sample.

These gains take into account prior pexformance of measure-

ments and states, in addition

to

a priori statistical knowledge

of the random processes present. The Kalman filter recursive

equations

are

describcd in the Appendix, using the notation

of Brown

[9].

The author's earlier work details the design

and non real-time assessment of the Kalman filter [lo], and

will only

be

briefly described here.

The state models are defined as:

X , = h (1)

x 2

=

h e n =

h p r r d -

( 2 )

The first state is the AGL altitude, and the second is the error

between

the first state and the predicted (navigation/terrain

database) AGL altitude. The explicit separation of the by-

product state he,, in the state equations allows for greater

flexibility in flight test implementation of the filter.

The first state ( h ) s modcled as a random walk:

x1 = w1 3)

where

w 1

s Gaussian zero-mean white noise with power

spectral density

of

set to

202 t2.

Physically, this describes a

system driven by white noise. This rather simplistic model

was taken due

to

this state's strong dependence on flight pro-

file. The AGL altitude signal would

be

quite different for an

aircraft flying a low-level (constant MSL) mission over hilly

terrain versus a contour (constant AGL) flight over the same

area. Terrain characteristics (flat versus mountainous) would

also generate different AGL altitude traces. More sophisti-

cated, perhaps mission dependent,AGL altitude state models

could

be

considered in future work.

The second state

h e r , )

is modeled as a first-order Gauss-

Markov process described by:

x =

- p x 2 + 5

w 2 (4)

where p- is the process time constant and

w 2

s Gaussian

zero-mean white noise

with

power spectral density a:.

A

Gauss-Markov process is a stationary Gaussian process (all

probability density functions are normal) with an

x

nen-

tial autocorrelation of E [ x2 I ) x2 I T) = cr:e-R'POThis

presents a slowly varying model for the coupled navigational

and terrain database errors. Spectral analysis of earlier flight

data established p- at

10

sec and o at

452

t2. Note that a

p- of 10

sec

corresponds to

an

along-track distance of

-114

mile for an aircraft

flying

at

90

kts.

The measurement models are definedas:

'1 = hnd

d n a

5 )

= X I x 2 V I

2 2

= h r o d 6)

=

x , v 2

where the measurement noise

v ,

and

v

are Gaussian zero

mean white noise processeswith power spectral densities of

IO2 t2 and 202 t2,respectively.

11.

should

be

noted that the state equations model above-

ground-level altitude given two measurement sources with

distinctly different characteristics. The first measurement,

A h , ,

gives good relative height-above-ground infor-

mation. This measurement is expected to

be

quite smooth

and reliable, although it will carry a bias due to

both

the nav-

igation vertical position solution and the stored terrain data-

base (DMA map). The radar altimeter complements the

navigatiodterrain database measurement in registering high-

er frequency absolute height-above-ground movements. This

measurement, however, will be somewhat noisy and of high-

er variance than the first. The Kalman filter serves

to

blend

these two measurements in producing a more stable, respon-

sive, and accurate estimate of AGL altitude.

These linear state models

are

now written in discrete-time,

state-space form as:

and for the measurements

The Kalman filter is implemented to process the measure-

ments sequentially, an established procedure [11,121 which

allows a measurement rejection test to be applied. The struc-

ture of the filter matrix equations remains unchanged (A6)

-

(AlO), but the measurement matrix H, becomes a row vec-

tor

and the measurement covariance matrix R, becomes a

scalar corresponding to the scalar measurement2 being pm-

c'essed.

'Ibe rejection test compares each measurement with that pre-

dicted from the measurement model

(9)

whereby a measurement deemed statistically unreasonable is

thrown out and not used to update the state and error covari-

ance matrices. The measurement residual

(10)

k =

2 -

2,

is compared with the expected standard deviation of that

measurement

in determining acceptanceof a measurement.

In this work, a two standard deviation

2a1)

riterion was

established for

p 1

(residual from navigation/terrain database

predicted AGL altitude measurement) and a

4a2

riterion

for p2

(radar altimeter measurement residual). Thus, if

p1

exceeded

2a1,

r

if

p 2 was greater than

4a2,

hat measure-

ment was discarded. These thresholds were set based on the

behavior of the instruments used in acquiring the flight test

data considered

in

this report, and reflect a greater confi-

dence in the radar altimeter measurement than the naviga-

tion/terrain

database measurement. Such rejection limits

would have

to

be adjusted for different measurement sources

than

those considered here, and possibly for flight conditions

o.g.,

poor GPS satellite navigation data due to satellite ge-

ometry

or

intermittent reception).

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For numerical stability, the symmetric error covariance ma-

trix P , was forced to remain symmetric after every mea-

surement update by averaging the off-diagonal elements.

Divergence of a Kalman filter without such a constraint is

well documented [9, 111 although this is not sufficient to

guarantee a positive semi-definiteerror covariance matrix.

A more detailed understanding of the presentation of the

guidance trajectory

to

the pilot is necessary in order

to

com-

plete the description of the Kalman filter augmentation. A

simplified pictorial

of

the pilot presentation symbology on

the

head.tracked helmet mounted display is shown as Fig. 3.

The pathway troughs and phantom aircraft are drawn in iner-

tial space along the desired trajectory. The troughs are 100 ft

at the base, 50 ft in height, and

200

ft at top, and are drawn in

1 sec increments

of

the trajectory out to 8 sec ased on the

aircrafts auspeed. The

top

center of each pathway

is

the de-

sired, computed trajectory. The phantom aircraft dutifully

flies at the top center of the forth trough (the desired trajecto-

ry 4 sec in the future). The aircrafts flight path vector is also

drawn on the helmet mounted display, as predicted 4 ec

ahead. Hence, by tracking the phantom aircraft with the

flight path vector, the pilot is able to fly the desired TF/TA

guidance trajectory. Additional aircraft status information is

also displayed but not shown here, e.g. airspeed and heading

[41.

Component

Aircraft

Flight

Compu

en

Pilot Display

Navigation

Radar Altimet er

Terrain

Database

Other

I I

Manufacturer/Model

U.S. Army NUH -60A Blackhawk Helicopter

Motorola 68030.68020 VME

Silicon Graphics 4D/120

lBM

P S n

Honeywell IHADSS

Litton LN-39 INU

Rockwell-Collins RCVR-OH

GPS Receiver

Honeywell APN-209

DMA Level I Digital Terrain Elevation Data

D)

FLIR

Systems 2000 Infrared Camera

Fig. 3. Pilot Display.

The inertial symbology of Fig. 3 in the baseline CALAHF

system is drawn based entirely on the aircrafts airborne nav-

igation and its stored terrain elevation database, and is the

crux

of

the main referencing problem. The Kalman filters

estimate of

h,,

is used to correct for navigation and terrain

database error by repositioning his trajectory. In order

to

en-

sure a smooth symbology presentation of the-guidance tra-

jectory to

the

pilot, the change in the value of h,,, is actually

ramped in linearly over the 8 troughs presented. That is, (af-

ter initialization) the eighth troughjs always altered

in

verti-

cal position by

the

full chang9 in h,,,, but the first trough is

only moved by 1/8 of this Ah,,,. Although such ramping

will slightly retard the information transfer to the trajectory

symbology (and henGe the pilot), the scheme is bounded by

the current value of

h,,,.

This lag must

be

considered when

establishing the Kalman filter augmented guidance system

flight envelope.

IV. Aircraft Integration

The

Kalman

filter augmented terrain-referenced guidance

system (CALAHF) was implemented and flight tested

aboard a highly-modified Sikorsky NUH-60A Blackhawk

helicopter (Fig. 4). The Systems Testbed for Avionics Re-

search (STAR) aircraft is operated by the U S Army, Ft.

Monmouth,

NJ.

The components of the NUH-60A STAR are

cataloged in Table 1.

786

The NUH-60A STAR hosts the Army Digital Avionics Sys-

tem (ADAS). This system allows fully integrated control and

display capabilities for the pilot and co-pilot through two

identical pairs of multi-function displays. These displays,

with their adjacent line mounted keys, provide digital moni-

toring of aircrafl state and instrumentation and associated

control. A flight engineers station at the rear of the aircraft

includes an additional ADAS display for flight test direction

and control.

All

components of this network

are

connected

through a 1553B interface.

The principal flight computer for the CALAHF research

guidance system is a Motorola 68030 and 68020 multipro-

cessor VME computer. The 68030 processor provides VME

bus arbitration and rear engineers station interface, while

three 68020 processors host the research application soft-

ware in a real-time, multiprocessor environment. The TFnA

guidance algorithm is dedicated

to

one

of

the processors,

with input/output distributed across the others.

The VME computer acts as the central processor for the re-

search work conducted on the aircraft, and is interfaced to

several other computers and devices. A 1553B interface con-

nects the VME

to

the INU (32 Hz), GPS

1

Hz), IHADSS

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(32 Hz),

radar

altimeter (8 Hz), and IBM PS/2 (8 Hz). the

later used as a route planner. The fiber optic Scramnet net-

work is used to connect the VME with the Silicon Graphics

4D/120 computer (20 Hz), which generates the display sym-

The Kalman filter resides on the VME computer, with each

of its distinct measurement processing loops triggered by the

incoming measurements. When a navigational solution is

provided (at 32 Hz), the DMA terrain elevation prediction is

found and the state and covariances matrices are updated

(i.e. the measurement

z1

is processed). Similarly, when a ra-

dar

altimeter measurement is returned

(z2),

the state and co-

variance matrices are pla te d. The filters estimate for AGL

positioning error (i.e.

h,,,)

is sampled at 20 Hz and passed

to

the Silicon Graphics computer for use in altering the guid-

ance trajectory, by the ramping technique discussed. This

yields the modified guidance trajectory.

Navigation is provided by

an

integrated 2-channel Precision-

code GPS receiver and platform stabilized I N . The 1 Hz

GPS navigation solution is

ramped

into the 32 Hz GPS out-

put

for

driving the IHADSS display at a 20 Hz rate. Accura-

cy is typically 33 ft (10 m) CEP horizontal and 53 ft (16 m

vertical. The fan-type 4.3 GHz radar altimeter returned

height above ground

or

closest terrain obstacle

to

altitudesof

1500

ft, and through pitch and roll angles of

45.

Radar al-

timeter accuracy is specified

to

be

3

ftf3%

of

actual altitude

L7.81.

The terrain elevation database was Level I DMA DTED

in

the 1 by 1 cell from 77 to 78OW longitude and from 40 to

41N latitude. This database carried accuracy specifications

of 260

m

(853 ft) in absolute horizontal position and 50

m

(164 ft) in absolute vertical elevation, both at 90% confi-

dence level. The database prediction of terrain elevation is

found by forming a triangular plane

of

the nearest three

posts

of DMA data. The interpolated value of this plane

below the aircraft is taken as the database elevation predic-

tion.

Flight data were recordcd at-5

Hz

on the VME and included

the Kalman filter output of

h,,,

and sampled values of radar

altimeter and navigational state information. Infrared video

was also recorded.

bology.

V. Flight Test Results

The flight test evaluation of the Kalman filter-augmented

system and the baseline system was conducted in moderately

rough terrain just south of Harrisburg, PA. The

area

includes

diverse features, such as flat plain sections and South Moun-

tain,

running diagonally northcast-southwest hrough the test

area.

The more rugged sections of the region contain rather

densely populated deciduous trees. Flight data discussed and

presented in this report was collected during winter

of

1992

/

1993 and spring 1993.

The evaluation of the CALAHF terrain-referenced guidance

system included assorted combinations of

speed,

set clear-

ance altitude, trajectory algorithm aggressiveness,and pi-

lot

display options over a

test

course of several waypoints. A

partial flight test ground track is shown in Fig.

5.

The refer-

ence origin of the test area corresponds

to

400345

N

lati-

tude, 771845 W longitude. The

TFDA

guidance

algorithm, which is not required to pass directly over any

given waypoint, is computing a valley-seeking low-altitude

path in the test region.

A

flight test mission for a particular

c 2t

2

I O N

/

12 bas indicatecoune waypoinu

150

A. 80 kts.

TF/IA mission

1

I

?:

2 .i

1

2 3 4

Position East,

l o 4

ft

Fig.

5.

Flight Test Course.

flight mission configuration begins at waypoint 2 in the

northeast, follows a meandering trajectory to the southwest,

loops around waypoints 9 through 12. and then retraces the

course from

8

through 2.

A

typical 80kts flight covers the

20

n.mi. course in about 20

min.

Note that because the guidance

algorithm computes a trajectory solution in real-time, based

on the aircraft state, stored terrain data, mission flight plan,

and aircraft state history (Fig.

2),

no two test missions will be

identical. Slight differences

n

pilot tracking of the guidance

trajectory result

in

different guidance solutions by the guid-

ance algorithm.

Ihe vertical flight profiles of a representative portion of two

separate

80

kts terrain following

(TF)

missions are presented

as

Fig.

6.

Terrain following flight,

or

contour flight, is flown

at constant heading between waypoints with only vertical

maneuvering, The ground track of such flight results in

straight lines between waypoints. These two flights, flown

between waypoints 8 and

10,

produced nearly identical

ground tracks, and hence were over the same terrain. The

dashed upper line traces the aircraft MSL altitude while con-

figured with the baseline terrain-referenced guidance system

at 300 ft set clearance altitude. (Set clearance altitude is that

PIGL altitude selected by the pilot to which

the

guidance al-

gorithm will nominally produce). The solid line near it tracks

the aircraft MSL altitude while flying with the

Kalman

filter

enhanced system at 150

ft

set clearance. The stored DMA

digital map prediction of terrain elevation is shown as the

lower dashed line of Fig.

5,

and the aircrafts MSL altitude

niinus radar altimeter measurement (during the 150 ft AGL

flight) is given as a truth measurement of

the

terrain eleva-

tion.

In

this region, vertical navigation error and horizontal

navigation error were both

30

ft. Combined vertical naviga-

tion error and radar altimeter error sets this

truth

estimate of

the terrain elevation to within 40

ft

error. During the baseline

CALAHF flight, vertical navigation error was 43

ft

and hori-

zlontal navigation error was 23 ft.

The vertical accuracy limitation of the digitized terrain ele-

vation data is markedly apparent from Fig. 6. During the first

20 s of the flight, the DMA prediction is nearly identical to

that

of

the truth terrain. The following hills, however, from

20 to 55 s, and then from

55 s to

100

s,

are drastically under-

estimated and smoothed by over 150

ft

in sections. Other

flight test missions and regions revealed DMA underestima-

tion of terrain by

as

much as 300

ft.

Note that overestimation

of the actual terrain

in

the stored terrain elevation database

would result in a baseline terrain-referenced rajectory high-

er than desired in actual above ground level altitude. In the

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C

2400

Baseline

System

l

;L Altitude

. 1000

c

KF-augmented System AircraftMS

Aircraft MSL

Altitude

4 nM

t

I 5 0 ft AGL Set Clearance

2

200

80

ku.

TerninFdowing

Miuimr

----

1800

I

4

-I

MA Te Gi n Elevation

True Terrain Elevation

1

military

application higher altitudes translate to greater ex-

posure and risk to ground based threats. An underestimation

of terrain elevation by the database would uanslate to lower

th ndesired

trajectories above the terrain. This could lead to

a ground collision.

In the first 20

s

of flight,

the

DMA accurately places the ter-

rain at

about 1350

ft

MSL. The baseline CALAHF system

results in an aircraft altitude of 1650ft to 1700 ft, or 300-350

ft above

the

terrain, in general agreement with the 300

ft

set

clearance selected. Similarly, the KF-augmented system re-

sults in a flight path around 1500 ft MSL, approximately 150

ft above the terrain and approximately the set clearance alti-

tude selected for that flight. The benefit of the Kalman filter

integration is first realized when the

hill

from

20

to 55

s

is

traversed. As the terrain rises to a peak of 1750 ft, the KF-

augmented system maintains an AGL clearance between 140

and 230 ft, while the baseline system, triggering solely on

the DMA predicted terrain brings the aircraft from 170

to

360

ft above the ground. The closest separation

to

the ground

(170 ft)

occurs

at the hilltop of 45

s.

Similar terrain tracking

differences are evident in the second

hill

from

60

100 s,

where the DMA representation

of

the terrain is again

too

low. The

K F

improved system generally maintains a separa-

tion above the ground of 140

- 220 ft,

very near the 150

ft

AGL altitude desired.The Kalman filter is allowing the au-

craft

to

fly a trajectory more reflective of the true topography

at a lower AGL set clearance altitude than that provided by

the baseline system.

The aircraft trajectories flown differ slightly from those com-

puted and presented

to

the pilot

for

tracking on the helmet

mounted display. Pilot tracking inconsistencies are apparent

during the Kalman filter augmented system flight of Fig. 6

when the system appears not to react to the valley at55

s

and

to balloon over the terrain from 80 - 90

s.

Although the Kal-

man filter estimator did provide a correction that brought the

trajectory

into the valley and without the later

hill

overshoot,

this trajectory was not followed very rigorously during these

two periods. Although the trajectory commanded is con-

stmined to be within the aircrafts performance capabilities,

the pilot can never track the symbology perfectly, and at

times will override the recommended pathway. Circumven-

tion of the commanded trajectory occurs most often when an

obstacle, such as a tree

or

wire, is encountered. Such obsta-

cle avoidance is the pilots responsibility, and is a fundamen-

tal limitation of

both

the baseline terrain-referenced

guidance system and the augmented system. The Kalmanfil-

ter enhancement, although able to substantially improve

AGL positioning of the aircraft and hence reduce the mini-

mum

operational altitudes of the system, has no look-ahead

capability for obstacles, and limited predictive abilities of

the terrain (ground) itself.

Figure 7 traces a five minute section of a TFnA flight of the

Kalman filter augmented terrain-referencedguidance system

at 110 kts and 150 set clearance altitude. The region de-

scribed is between waypoints 2 and

8

(Fig.

5 ) .

The lower

dashed line tracks the DMA prediction of terrain elevation,

while the lower solid line describes the true elevation, as cal-

culated by subtracting the aircrafts radar altimeter return

from its navigational MSL altitude. During this flight, verti-

cal navigation error was 4 1

f t

and horizontal error

28 ft.

This

places the calculated truth terrain elevationto within

50

ft.

The upper dashed and solid lines of Fig. 7are the desired,or

commanded, trajectory MSL altitude and the actual air-

craft MSL altitude, respectively. The commanded trajectory

is that computed by the trajectory algorithm (and subse-

quently modified in altitude using the Kalman filter output)

and presented to the pilot using the display symbology. As

mentioned, due to the human (pilot) element, however, this

commanded trajectory altitude is never followed exactly.

During the majority of the flight, the commanded and actual

MSL altitude of the aircraft are in general agreement. The

several unmodeled hills are recognized by the KF-augment-

ed system and flight at approximately 150

ft

AGL is main-

tained. There are periods where the pilot had difficulty

tracking the symbology, at times over-controlling and then

having to catch the trajectory. During the flight document-

ed in Fig.

7,

pilot tracking of the desired commanded trajec-

tory

was of 2.5 f t mean error laterally, (T = 17.8 ft, and 0.7 ft

mean error vertically,

(T

=

18.9 ft. Such pilot tracking perfor-

mance was typical throughout the flight evaluation. The gen-

eral relationship between the aircrafts actual vertical flight

path and that commanded by the enhanced system is that of a

slight lag and slightly higher and smoother flight paths.

788

8/11/2019 Zelenka Et Al 1993

7/8

Time,

sec

Fig.

7.

KF-augmented System during a

TF F A

Mission.

Flight

Config.

The several unmodeled hills (e.g. those centered at 140

s,

230 s,

and 320

s),

at times over 140

ft

higher than that pre-

dicted by the stored DMA database of terrain elevations,

are

clearly recognized by the radar altimeter and hence the Kal-

man

filter. Flight over these regions is maintained nominally

at

150ft,

the desired set clearance altitude.It must be empha-

sized

that

flight at this set clearance without the Kalman

f i l -

ter, i.e. by the baseline, solely DMA dependent system,

could not have been attempted,

as

the terrain database errors

surely would have resulted in a ground collision.

Kalman

ilter

augmented system

150 ft AGL set clearance)

Baseline system

300

ft

AGL set clearance)

Table

2.

KF-augmented and Baseline System Comparison

I 1

I

T F n A I

h

= 197.5 ft, oi = 58.6 ft I h = 296.2 ft,

GI;

= 72.1 f t

T F

I

h

= 182.3 ft,

oi

= 50.8

f t

I

h

=

348.3

ft,

ai =

82.5

f t

where h = mean AGL altitude.

G =

standard dev. o f

The Kalmanfilter enhanced terrain-referenced guidance sys-

tem was flown and assessed over the entire flight test enve-

lope

of

the baseline system. Table

2

gives a comparison of

the baseline and enhanced systems for

T F n A

and

TF

mis-

sions. The enhanced system allows for lower flight altitudes,

and for closer adherence (shown by the lower

o

values)

to

the desired clearance altitude above the terrain. Test varia-

tions for the Kalman filter enhanced system included aircraft

performance (speeds of

80

and 110

kts),

maximum bank

an-

gle

20

and

30),

trajectory algorithm settings (TF, TFRA

flight), and assorted display symbology options. Throughout

these conditions, the test pilots felt that the enhanced Kal-

man filter system created a reliable and more accurate low-

altitude guidance trajectory than the baseline system. The

modified trajectories were deemed more representative of

the contours and topography of the region. The ramping

in

of the Kalman filter estimate of the

AGL

referencing error of

the baseline system was found

to be

very smooth.

In

fact, a

common pilot comment about the enhancement was their

lack of knowledge of when and

to

what degree the KF-based

modification

to

the trajectory was occumng.

Based on the assessment of flight test data gathered, pilot

recommendations, Kalman filter tracking ability, and lag

as-

sociated with the pilot display integration, the enhanced

Kal-

nian

filter terrain-referenced guidance allows flight to an

Altitude of

150 f t AGL,

subject

to

pilot avoidance of obsta-

clles. This is considerably lower than the

300

f t

AGL

limita-

tion of the baseline terrain-referenced guidance system.

Flight at lower altitudes will require a forward-looking sen-

sor

for obstacle detection and avoidance.

VI. Concluding

Remarks

1

.)A

Kalman

filter

state estimator

was

developed

to

improve

the above ground level positioning of

a

terrain-referenced

guidance system,

as

warranted by vertical navigation error

and stored terrain database error. The filter incorporates a ra-

dar

altimeter measurement of height above ground

to

esti-

mate the error present in the vertical positioning of

trajectories generated by a baseline terrain-referenced guid-

ance system. The Kalman filter modified trajectory is pre-

sented

to

the pilot on a helmet-mounted display.

2.)

The filter was implemented for real-time operation

almard a U.S.

rmy

Blackhawk helicopter. The resulting

augmented system was flight tested in moderately rugged

terrain under the same wide range of test conditions as the

baseline system.

3.)

The Kalman filter enhancement was found

to be

robust

and accurate

in

modifying the vertical position of the base-

liine terrain-referenced guidance system trajectories. The en-

hancement produced trajectories more reflective of the

topography and allowed for lower altitude operation. The

minimum flight altitude was reduced from 300

f t

above

ground to

150 ft.

789

8/11/2019 Zelenka Et Al 1993

8/8

Terrain-referenced guidance system Right restrictions are

now govemed by pilot obstacle detection and avoidance,

which could be assisted by

a

forward-looking sensor. Vari-

ous combinations

of

active and passive sensors for this role

are being considered.

The authors would like to acknowledge the assistance of test

pilots

Gordon Hardy and Munro Dearing (NASA), and Tom

Davis

nd

Gary Amatrudo

U . S .

Army) in developing and

flying the Kalman filter augmented system discussed. Project

managers of the joint

U.S.

Army/NASA flight test program,

of which this work

is

a

part

are Paul Cannan

U . S .

Army)

and

Harry

Swenson (NASA).

Acknowledgments

Appendix: Kalman Filter Equations

State and measurement equationsare written as:

xk+l

=

@ k x k + w k

(AI)

2 )

=

H k+vk

a)

where

Ok

s the state transition matrix,

Hk

is the observation

matrix, and

wkand vk are

uncorrelated white noise.

The updating of the state equations for given measurements

is accomplished by constantly computing the error covari-

ance matrix

where

ei = x k- ti

is the estimation error, and

4,

is the esti-

mated value of

x based

on all measurements up

to

but not

including, those at step time

tk.

Statistical

properties of the white noise sequences

wk

and

vk

are defined by the covariance matrices

Qk =

E [WkWrl

(A4)

Rk =

E

[ v k v l ]

(A5)

The state and measurement white noise disturbances are

un-

correlated, i.e.

E [

w , v ~ ]

= 0

for all

k

and

i .

Aftex initial values i o o for the states and error covariance

are established, the recursive Kalman filter equations are:

(A61

(A71

Kk = PiH: [HkPiHk 4 Rk1-I

= i i

k Kk [ ?k H ;]

where

K

s the Kalman gain matrix,

i k

is the updated state

estimate given measurements through

zk ,

and

Pk

is the up-

dated error covariance matrix. The initial state values,

x , ,

were set with respect to the

first

measurements received,

equivalent

to

setting the elements of

Po

at infinity.

The state and error covariance matrices are projected ahead

to he

next time step as:

i i + l

=

@ k

(A91

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In actual operation where time steps are asynchronous, these

projections occur upon receipt of the measurements, to allow

the actual time increment

to be

used.

790