zelenka et al 1993
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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.
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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.
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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
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the actual time increment
to be
used.
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