The missile and the target are tracked by a ship-based radar system. The success of the mission depends on the missile navigation accuracy and the removal of ...
ar Aided Inertial Navigation System issile System Applications Renato S. Omedo and Kenneth A. Famsworth, Raytheon Systems Company Gurpartap S. Sandhoo, STANDARD Missile Company
ABSTRACT
This paper provides an overview and preliminary performance assessment of an adapted version of the Raytheon Systems Company GPS Aided Inertial Navigation System (GAINS) for missile systems. In this particular appl :ation, a missile is fired off a ship to intercept an incoming target. The missile and the target are tracked by a ship-based radar system. The success of the mission depends on the missile navigation accuracy and the removal of alignment error between the missile and radar tracking system. The missile on-board inertial navigation system implements a Kalman filter to determine in-flight corrections to the navigation and radar alignment errors. The filter processes the GPS pseudo-range and delta range measurements as well as the ship-uplinked radar data. Descriptions of the GAINS navigation and alignment processing are discussed. Performance results obtained from time domain Monte Carlo simulation analysis are presented for a representative scenario. The results of the analysis show that improved navigation and radar alignment accuracy can be achieved by using both radar and GPS measurements rather than by using radar measurements only. This translates to improved design margin and reduced performance risk. On-going laboratory, field, and flight tests are also discussed.
A version of the Raytheon Systems Company GPS Aided Inertial Navigation System (GAINS) is used for this application [l]. The existing GAINS algorithm has been modified to process uplinked radar measurements in addition to the inertial measurement unit ( M U ) and GPS measurements. A top level description of GAINS is provided below. The performance assessment process is discussed with emphasis on simulation analysis of the navigation and radar alignment algorithms in a PC-based work station. An overview of the GAINS hardware in-theloop simulation in the Raytheon GPS emulation Test Station and the GAINS van and flight test is provided.
INTRQDUCTION Figure 1 illustrates a typical mission profile of a shipbased theater-wide Tactical Ballistic Missile Defense (TBMD) system. A multi-stage missile carrying a kinetic weapon (KW) is fired off a ship to intercept an incoming target. Both the missile and target are tracked by the ship radar system. High accuracy requirements are placed on the missile guidance system because of the KW narrow field-of-view (FOV), KW divert capability, and the engagement scenario. For a successful intercept, it is necessary to eliminate the system alignment errors arising fiom ship navigation, ship radar face misalignments, and missile initialization. In addition, the missile navigation states which include three-axes position, velocity, and attitude have to be determined within the desired error levels. These errors can be eliminated during flight using an on-board missile inertial navigation system (INS) that is aided by the GPS measurements and ship uplinked radar track measurements.
Details of the flight test scheduled for late January, 1998 are also described. This test will use a ship-board mdar system to track an airbome jet aircraft as it circumnavigates the ship, thus exposing itself to the ships radar faces for tracking. The radar and GAINS data collected during the test will be post processed to obtain an estimate of radar face and initialization misalignments.
614 0-7803-4330-1/98/$10.00 01998 IEEE
Figure 1: A Typical Tactical Ballistic Missile Defense Mission. GAINS OVERVIEW
the ship fire control system decides to engage a target. A few seconds before launch, the ship provides GAINS with an initialization message which contains position, velocity, and attitude information. Once initialization takes place, GAINS uses the IMU measurement to provide navigation solution to the missile guidance and control system. Thle availability of GPS and radar measurements is not expected in the early part of the mission due to extreme missile acceleration. GAINS generates the navigation and radar alignment corrections once the ship uplinked radar measurements and GPS receiver measurements become available. The GAINS navigation solution is also used to initialize the KW navigator prior to ejection.
GAINS unit serves as the navigator for the last stage of the missile prior to the KW ejection. A more detailed design overview of GAINS is provided in Reference 1. The GAINS consists of the Receiver Processor Unit (RPU) and inertial measurement unit ( I N ) as shown in Figure 2. The RPU consists of a navigation processor board, GPS receiver board, and interface board. The IMU is a production Advanced Medium Range Air-to-Air Missile (AMRAAM) form factor IMU. The navigation processor board contains ADA software that performs the navigation function. The modification to this function in order to accommodate the radar measurements in addition to the IMU and GPS measurements is discussed later in the paper. Other modifications were made to the existing GAINS reported in Reference 1 in order to meet new requirements on interface and rapid GPS signal acquisition after launch. To achieve rapid acquisition, GAINS implements initial time uncertainty reduction via “hot start.” This solution involves the initialization of the GAINS GPS receiver using ephemeris data ftom the ship own GPS navigation system.
I
a d
I
Figure 2: Raytheon GAINS RPU and IMU
The GAINS operation sequence commences by performing a GPS time and ephemeris data initialization using the ship provided data. This operational step takes place after
The missile navigation and radar alignment algorithms are performed in the GAINS navigation processor. The
615
estimates the radar misalignment by comparing the radar derived position measurement with the blended INS, GPS and radar position solution. The details are provided below. A top level GAINS fhctional block diagram is shown in Figure 3.
navigation function integrates the inertial measurements fiom the strapdown IMU to determine the instantaneous missile position, velocity, and attitude. Errors in the navigation solution due to initialization and IMU errors are corrected by using a Kalman filter that processes both the radar and GPS measurements. The Kalman filter also
Figure 3: GAINS Functional Block Diagram
NAVIGATION AND RADAR ALIGNMENT PROCESSING
GAINS corrects the navigation error by using direct Kalman filtering. With this approach, the Kalman filter directly uses the GPS pseudo-range and delta-range measurements instead of the GPS receiver-derived position and velocity measurements. This design allows the INS to aid the receiver tracking loops as mentioned earlier. As shown in Figure 4, the predicted values of the pseudorange and delta-range derived li-om the INS solution are compared to the receiver measured values to form measurement error vector or measurement residual. The GPS measurement residual can be attributed primarily to the INS state and GPS measurement errors. The filter determines the corrections to these error sources by using a model of the INS error dynamics and GPS measurement error characteristics. With GPS update, the GAINS filter provides corrections to the missile position, velocity, attitude, accelerometer bias, gyroscope bias, GPS clock bias, and GPS clock drift rate. The GAINS navigation and Kalman filter equations are not provided for brevity. However, background information on GPS and INS topics are provided in References 2 to 5.
The GAINS navigation and radar alignment algorithms are performed in the GAINS navigation processor as illustrated in Figure 4. It consists of the navigation fimction and a Kalman filter to blend the IMU, GPS, and radar measurements and to estimate the radar misalignment. In return, the navigation function provides the GPS receiver with navigational state information to aid the receiver code and carrier tracking loops. This approach improves satellite tracking during periods of high vehicle dynamics especially during launch, unfavorable satellite geometry, and jamming. The IMU consists of a set of accelerometers and gyroscopes which measure specific force and body rates respectively. The IMU provides this information to the navigation function (or navigator) in the form af incremental velocity and incremental angle measurements. The navigator then uses these measurements to solve the inertial navigation equations. The solution is provided at a relatively high rate. It consists of instantaneous position, velocity, and attitude states of the missile. Errors in the navigation states are expected to grow with time due to navigator initialization error, navigation algorithm implementation error, and IMU errors.
GAINS also uses the uplinked radar measurements to correct the INS errors. As in the GPS measurement processing, the radar measured missile position is compared with the INS derived position to form a radar
616
attitude, accelerometer bias, and gyroscope bias. In addition, it also corrects the radar measurement error due to radar misalignment between a ship reference W e and the radar coordinate m e . Background information on radar measurement aided INS is provided in References 6 and 7.
measurement residual in a common coordinate h e . The radar measurement residual can be attributed to the INS position error and to the radar measurement error. The filter determines the corrections to these error sources by using a model of the radar measurement error characteristics and the same model of the INS error dynamics. With radar update, the GAINS filter also provides corrections to the missile position, velocity, ~
~~~~
Missile Position, Velocity, Attitude, and IMU Bias Corrections
IMU Inertial MeasurementUnit Specific Force. & Body Rates
I
4 -
I
I I
-
Missile Navigation Solution
‘ 1I
1
Error Correction Calculation
I
-U I
GPS Clock E r r o k Corrections
GPS Tents
lVlCMUlCl1
Missile States
-+
I
I
I
I Ship Radar
GPS Measurement
MResidual e2zment
1 J^.._.._^
Uplinked
RadarMeasurement Residual
7 .
..
I
nesiauai
q -
igure 4: GAINS Navigation and Radar Alignment Algorithm Block Diagram there is no guarantee that they are synchronized. GAINS implements an algoritlhm to time-align the radar and GPS data in order to simplify the software mechanization. The Kalman filter update is executed only once per expected GPS and radar measurement cycle. Furthermore, it is possible that either the radar or GPS data may not be available. Thus, the: filter has been designed to handle radar only, GPS only, and combined GPSIradar processing. However, it should be noted that the Kalman filter cannot estimate the radar misalignment without radar measurements.
The GAINS Kalman filter corrections are implemented as a feedback process. Both the GPS and mdar measurements are used together to obtain a blended INS, GPS, and radar solution of the missile INS states. The error sources corrected by the GAINS Kalman filter represent the filter states. They are summarized in Table 1. The first seventeen states are the original GAINS filter states. They consist of the INS and GPS error corrections. The last three states represent the radar measurement error due to radar misalignment. The incorporation of radar error states involves minimal modification of the existing GAINS software to preserve its integrity and heritage [l].
Another issue of interest is the process of tuning the filter. In general, the GPS pseudo range and delta range measurements are corrupted by low level noise. However, the pseudo range measurement contains inherent bias that can be attributed to user range error [2]. The mdar measurements, on thie other hand, have relatively small bias error but corrupted by noise that grows with range. For this application, the radar measurements become available sooner after launch than GPS measurements. This means that the INS solution is corrected by the noisy radar measurement early in the flight. The Kalman filter is designed and tuned to minimize the effect of filter transient in the navigation solution when the GPS measurements become available for update.
Table 1: GAINS Kalman Filter States Error State Number of States Missile Velocity 3 Missile Position 3 Missile Attitude 3 IMU Accelerometer Bias 3 3 IMU Gyro Bias GPS Receiver Clock Bias and Drift 2 Radar Misalignment 3 The challenge in updating the INS with both GPS atld radar measurements derives fi-omthe synchronization of the measurements. For this application, the GPS and radar measurements are provided at the same rate. However,
617
PERFORMANCE ASSESSMENT PROCESS The assessment of the GAINS performance is a multi-step process as depicted in Figure 5. The existing navigation algorithm is modified to handle the radar measurements and to estimate the radar alignment error. The process starts with simple calculations to show proof of principles of the navigation and alignment algorithms. An error covariance simulation technique [SI is then used to assess preliminary sensitivity of the algorithm to various system error sources. The result of the error covariance study determines which radar alignment error sources are included in the GAINS Kalman filter. The resulting GAINS navigation and radar alignment algorithm software is then linked with a PC-based simulation driver. The driver provides the GAINS algorithm with simulated IMU, GPS, and radar data. A series of time domain Monte Carlo simulation runs is conducted. The GAINS calculated missile position, velocity, and attitude as well as radar alignment angles are compared with the corresponding known reference values or “truth” values. The resulting error provides a preliminary assessment of GAINS performance. This is discussed in details below. A brief overview is also provided of the GAINS hardware in-the-loop simulation in the Raytheon GPS emulation Test Station and the GAINS van and flight.
Figure 6: GAINS Computer Simulation Diagram GAINS Computer Simulation Analysis
I
Simple
Ship Parameters
Speed Heading (ramp) Pitch Amplitude (sinusoidal) Pitch Period
Field / Flight Testing
Figure 5: GAINS Performance Assessment Process The GAINS computer simulation block diagram is shown in Figure 6 . A simulation driver program contains a kinematic model of the missile, GPS, and ship radar based upon a specified missile and ship trajectory. It generates IMU, GPS, and ship uplinked radar measurement data files for the GAINS algorithm. The simulation driver also generates a “truth” data file. The error between the truth data and the GAINS generated data is used to assess the performance of the GAINS algorithm. The statistics of the error is obtained fi-om a series of Monte Carlo simulation runs.
I DataLatency
15 knots 451140 dedsec 5 den amplitude 1 1 seconds
I
None
I
The position error grows with time when the filter only processes the radar measurements. The error growth can be attributed to the range-dependent radar measurement error which is primarily due to the radar misalignment and radar angle measurement noise. The velocity error is corrupted by the noisy radar measurement. When the GPS measurements become available, the position and velocity errors are reduced. This can be attributed to the relatively low noise and error characteristics of the GPS measurements. The position error drops to a level that is
618
proportional to the pseudo range bias. The missile attitude and radar alignment errors also improve with GPS for the representative missile trajectory used in the simulation. Table 3: Simulated System Errors Error Source GAINS Initial Navigation Errors Position (each axis) Velocity (each axis) Attitude (local level to body each axis) GAINS IMU & GPS Receiver Errors Accelerometer Bias Gyro Bias Accelerometer Scale Factor Gyro Scale Factor Accelerometer Misalimment Gyro Misalignment Accelerometer Random Walk (PSD) Gyro Random Walk (PSD) GPS Pseudo Range Bias GPS Clock Bias GPS Clock Drift Pseudo Range Noise Delta Range Noise Shin and Radar Related Errors Ship Position (each axis) Ship Navigation Attitude (each axis) Radar Face to Ship Nav Frame Misalignment
I
I
1-Sigma Value
I
10 m 0.1 mls 10 mrad
lo.*
1 milli-g 1 de& 300 ppm 150 ppm 0.5 mrad 0.5 mrad 85 micro-g/Hz’’2 0.125 de&’” 5.1 m 300 m 3 m/s 1.5 m 0.1 m
I
10 m 1 mrad 17 mrad
1
GPS Acqluired 0 30 sec 40
20
0
100
80
60 TIME (WC)
Figure 8: Missile Velocity Error with Updates from Radar/GPS and Radar Only 40
- - - - - RADAR ONLY 6.30
P P5 Y
’-
K
1
20
W
E
e
h*-, 10
I
QPS Acquired 8 30 sec C
20
40
60 TIME (Sec)
80
100
Figure 9: Missile Attitude Error with Updates from Radar/GPS and Radar Only lo3
-
-
.\
.-0-*
/-‘
: “lf,
102
GPS Acquired (iD 30 sec
GPS Acquired 0 30 sec
t
0
20
‘
40
60
80
L.
100
TIME (sec)
OO
20
40
60
80
1W
TIME (sec)
Figure 7: Missile Position Error with Updates from Radar/GPS and Radar Only
Figure 10: Radar Alignment Error with Updates from Radar/GPS and Radar Only
619
In summary, the results indicate the system errors can be effectively reduced to lower levels. With radar and GPS available, GAINS provides a better system perflormance than with radar only available. This translates to greater design margin and improved probability of mission success. Furthermore, by reducing alignment errors early in the flight trajectory, the sensitivity of accuracy to potential jamming later in flight is also reduced.
manner that can be associated directly with the radar to ship body coordinates, and ship body to absolute earth coordinates. Furthermore, under post test processing, the GAINS in-flight algorithm estimate of the &I& navigation states and radar alignment will be compared to those obtained or derived fiom the GPS-based differential scoring system and EGI unit. Three separate scenarios are planned for this captive carry test that would allow the GAINS in-flight alignment algorithm to estimate these misalignments. The geometry of each of the three consecutive runs enables specific determination of the misalignment components. The first run requires the ship to be on a constant course and speed to enable determination of the radar misalignment. The aircraft executes a fly-around of while the ship proceeds on a constant course (Figure 11). The second run requires the ship to execute eight successive 90 degree port turns at a tum rate of approximately 2'Isecond while the aircrai? also executes a continuous 360' fly-around of ship. After each 90' turn, the ship will steady up on a course f a approximately 2 minutes in preparation for the next turn. This will enable determination of the ship body fixed misalignment angles between the radar faces and the ship fmed deck coordinate frame. The third run requires the ship to steady up on any safe course and slow speed while the aircraft executes a descending inbound radial run. This run will provide data representative of a missile flyout with the most difficult geometry for alignment determination.
GAINS Laboratory and Field Testing
As discussed earlier, GAINS undergoes more extensive testing in the laboratory and field environment. Figure 11 illustrates the GAINS laboratory ad field testing process. Raytheon Systems Company has a GPS emulation test facility that allows end-to-end testing of the GAINS hardware and s o h a r e in the laboratory environment. Ongoing and future field testing of GAINS involves the installation of a GAINS unit in a van, aircraft, and test missile to simulate low and high dynamic operational scenario. In Figure 11, the radar portion of the algorithm is not evaluated during the van and flight test phases. To quanti@ the radar misalignment and to ver@ the proposed missile in-flight alignment algorithm, a captive carry test is scheduled to be conducted. The ship radar will track an aircraft circumnavigating the ship. Simultaneously, the on board aircraft instrumentation will record the IMU and GPS data from GAINS, the data h m a GPS-based differential scoring system, and the airmfl attitude &om a high accuracy Embedded GPS INS @GI) unit. Post test analysis will determine the radar misalignment by comparing the radar track position with that obtaincd fi-om the scoring system. The presence of misalignments causes the position vectors to m e r in a
Figure 11: GAINS Laboratory and Field Testing
620
cenario
Figure 12: Flight Test Scenarios [4] R. Britting. b r t i a l Navigation Svstem Analvsis, Wiley-Interscience, New York, NY, 1971. A [5] M. Siouris, Aerospace Avionics Svstems. Modern Svnthesis, Academic Press, Inc., San Diego, CA, 1993. [6] .Ohlmeyer and T. Pepitone, “ In-flight Removal of TBMD System Alignment Errors Using GPS and Radar Measurements”, Proceedings of AIAA/BMDO Technology Readiness Conference”, San Diego, CA, August 18-22, 1997. [7] R.S. Omedo, “Performance Evaluation of the Radar Misalignment Filter”, Hughes Aircrafi Co. meeting notes, August 29, 1996. [SI A. Gelb, Ed.,, M.I.T. Press, Cambridge, MA, 1974.
SUMMARY
This paper provides an overview and preliminary performance assessment of an adapted version of the Raytheon Systems Company GPS Aided Inertial Navigation System (GAINS) for Theater Ballistic Missile Defense system application. The INS design incorporates the use of IMU, GPS, and radar measurements to obtain a blended INS/GPS/radar navigation solution. It also estimates radar measurement misalignment. The accurate estimation of the navigation and radar alignment errors is crucial to mission success. The simulation results indicate that these errors can be reduced to lower levels. Furthermore, the results of the analysis show that improved navigation and radar alignment accuracy can be achieved by using both radar and GPS measurements rather than by using radar measurements only. This translates to improved design margin and reduced performance risk. The GAINS design is currently undergoing a series of laboratory and field testing. The results of the test will be published in the near future. ACKNOWLEDGMENT
The authors wish to acknowledge our colleagues at Raytheon GPS Navigation Technology Center in El Segundo and the members of the SM-3 Navigation Working Group for the insightful discussions into the subject of this paper. REFERENCES
[I] T.A. Moore et. al., “Use of the GPS Aided Inertial Navigation System in the Navy Standard Missile fa the BMDO/Navy LEAP Technology Demonstration Program”, Proceedings of ION GPS-95, Palm Springs, CA, September 12-15, 1995. [2] B. Parkinson et. al. , Ed., Global Positioning z s , Vols. I and 11, American Institute of Aeronautics and Astronautics, Inc., Washington DC, 1996. [3] R.G. Brown and P.Y.C. Hwang, WQ Random Signals and Amlied Kalman Filtering, 2nd Edition, Wiley, New York, NY 1992.
621
