Integrated Strapdown Avionics for Precision Guided Weapons Jack Richman David Haessig Jr
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Integrated Strapdown Avionics for Precision Guided Weapons Jack Richman David Haessig Jr

and Bernard Friedland ABSTRACT Conventional avionic config urations for precision guided weapons are often unnecessarily costly and inefficient be cause of builtin but unused redundancy in instrumentation attributed to the present day independent sy

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Integrated Strapdown Avionics for Precision Guided Weapons Jack Richman David Haessig Jr

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Integrated Strapdown Avionics for Precision Guided Weapons Jack Richman, David Haessig, Jr., and Bernard Friedland ABSTRACT: Conventional avionic config- urations for precision guided weapons are often unnecessarily costly and inefficient be- cause of built-in (but unused) redundancy in instrumentation attributed to the present day independent systems design approach. De- scribed in this paper is an integrated design approach using strapdown avionic compc- nents that has the potential for lowering cost, increasing reliability, and improving overall performance as a result of

using fewer and less costly instruments in an efficient manner. Introduction The avionics associated with present day guided weapons have conventionally been configured by design engineers as being comprised of three separate and independent systems; namely, navigation, guidance (midcourse and/or terminal), and autopilot. The navigation system, whose purpose it is to provide position, velocity, and attitude of the vehicle with respect to some reference coordinate frame, is conventionally config- ured as an inertial system equipped with high-accuracy components (gyros and accel- erometers) in

either a gimbaled or strapdown mode. The guidance system, whose purpose it is to generate midcourse and/or terminal steer- ing commands, is, in many applications, configured as a system having an inertially stabilized seeker that directly measures the angular rates between the weapon and its tar- get in some fixed-coordinate frame. The autopilot, whose purpose it is €0 match the commanded acceleration of the guidance system by issuing its own com- mands to appropriate aerodynamic and/or thrust controls of the weapon, is usually configured as a system equipped with low- accuracy inertial

components (gyros and accelerometers). Clearly, the above conventional avionic configuration of a precision guided weapon lends itself to duplication and redundancy of components (gyros, accelerometers, and Presented at the 1985 American Control Con- ference, Boston, MA, June 19-21, 1985. Jack Richman, David A. Haessig, Jr., and Bernard Friedland are with the Singer Company, Kearfott Division, 1150 McBride Avenue, Little Falls, NJ 07424. June 1986 gimbals). Yet, in spite of this obvious redun- dancy, no attempt has been made in con- ventional designs to combine the multiplicity of output data

from these individual systems in some efficient manner; furthermore, no provision has been made to channel the re- dundant data from one system to another in case of component failure. This obvious in- efficiency in the conventional avionic design process has its roots in the fact that design of the navigation. guidance, and autopilot sys- tems has historically been performed by three separate design groups, each having different disciplines and each meeting the required specifications of their own system with a self-contained design. With the avionics portion of precision guided weapons

representing as much as 80 percent of the cost, an obvious approach to cost reduction is through the use of inte- grated avionics-a common set of compo- nents shared by all systems. In addition to having lower cost and higher reliability, in many cases superior perfokmance can be achieved with this integrated strapdown de- sign approach. Described in this paper is an approach for designing such an integrated system using strapdown instruments. For simplicity, the description of the system’s operation is limited to the case for which the guided weapon is directed toward a nonmaneuvering (i.e.,

nonaccelerating) target. Although the integrated strapdown concept is also applicable to a maneuvering INERTIAL SENSORS r ----- target, the problem becomes more complex and requires an algorithm for estimating the target’s acceleration [ 11, [2]. The Integrated Strapdown Design In our integrated avionics design approach for a precision guided weapon, the following basic components are considered: 0 A single set of strapdown gyros and ac- celerometers to be shared in all functions of navigation, guidance, and control. 0 A strapdown midcourse and/or terminal 0 A computer that includes Kalman

mixer/ filter computations for combining the avionics data in an optimum manner and the steering and autopilot computations. The general structure of such an integrated strapdown avionics system (for guiding to- ward a nonmaneuvering target) is shown in Fig. 1. In describing the operation of the overall system, it is convenient to fist trace the path of the inertial subsystem through the navigation, guidance, and autopilot func- tions as if the inertial subsystem operated independently, and then to show the mutual aiding that exists between the seeker and in- ertial subsystems. The navigation

computa- tion starts with an initial estimate of the inertial position and velocity of the missile with respect to its target, and knowledge of the inertial attitude of the missile. The in- seeker. NAVIGATION SEEKER MIXER/ SEEKER +!GET ACCELERATION Fig. 1. Integrated strapdown navigation, guidance, and control system. 0272-1708/86/06M)~9 $01.00 0 1986 IEEE 9
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ertial sensors (strapdown gyros and acceler- ometers) perform the continuous updating of the position, velocity, and attitude of the mis- sile. This state of the missile with respect to the target can readily be

transformed into appropriate guidance states to be used as input to the guidance (or steering) law. For example, if the guidance.state is the inertial line-of-sight rate vector A between the rnis- sile and its target [as would be the case for simple proportional-navigation (ProNav) guidance]. the transformation between the navigation state and guidance state is A = (R x V)/lRI (1) The output of the guidance law is usually a commanded acceleration a, which the auto- pilot attempts to achieve by issuing com- mands to its appropriate controllers, which in the case of an aerodynamically controlled

missile are commanded aerodynamic surface deflections 6,. (Note that the autopilot also uses the same inertial sensors as those used for navigation.) From the above description of the guid- ance system. it is clear that if the navigation computation started withperfecr estimates of the initial state of the weapon with respect to its target and if the inertial sensors were error-free, the weapon would not require a seeker. The seeker is needed only because the inertial system has errors associated with it. The primary function of the seeker in this integrated configuration is to provide cor-

rections to the inertial navigationlguidance system. (For the case in which the guided weapon is directed toward a maneuvering target, the role of the seeker, in addition to aiding the inertial navigation system. would be to provide estimates of target acceleration to be incorporated into the navigation com- putation block shown in Fig. 1 .) The lower portion of the block diagram of Fig. 1 shows the role of the seeker and its interaction with the inertial system. The seeker system is shown as consisting of a strapdown seeker “head plus data processing. The head pro- vides the basic strapdown

measurements of a target with respect to the vehicle’s (body) coordinate frame. The data processing block combines the strapdown measurements of the head with the vehicle attitude to produce seeker measurements with respect to an in- ertial reference frame. For example, if the seeker head measured discrete line-of-sight angles with respect to the vehicle’s coordi- nate frame, the output of the seeker and the data processor would be line-of-sight angles with respect to an inertial coordinate frame. In particular. if the strapdown seeker mea- surements in the vertical and horizontal planes of

the vehicle (body line-of-sight angles) are Am and AHB, respectively, and the transformation from the inertial coordi- nate frame to the body coordinate frame (as obtained from processing the strapdown gyro data) is denoted by the transformation matrix TBI = E,I :; i] the inertial line-of-sight angles are computed in accordance with I2 Avl = tan- l3 f m3 tan AHB + n3 tan Am + ml tan AHB + nl tan hvB 1 tan- lz + m2 tan AHB + nz tan AVB lI + m, tan AHB nl tan Am An independent estimate of the seeker out- put can always be obtained from the inertial navigation system. For example, if the

seeker-system measurements consist of the vertical and horizontal (i.e.. elevation and azimuth) angles of the target with respect to an inertial coordinate frame, the estimates of these measurements obtained from the in- ertial navigation system are given by where PI, fl I and il are the estimated coordi- nates of the weapon with respect to the target as supplied by the navigation system. The difference, or residual, between the actual seeker measurements and the independent estimates is the input to the Kalman mixer/ filter, the outputs of which are corrections to the navigation state as well

as corrections to seeker systematic errors that may have been modeled and included in the Kalman filter. The most significant feature associated with the operation of the integrated strap- down system is that the inertial navigator and seeker work together in providing the input to the guidance law. This mutual aiding of the systems can be described from two differ- ent points of view. One interpretation is that the inertial navigator is the primary system that provides the input to the guidance law and the function of the strapdown seeker is to provide corrections to the inertial system.

Another interpretation (from the point of view- of the seeker designer) is that the seeker is the primary instrument that provides the input to the guidance system and the function of the inertial system is to smoorh the data between the discrete seeker measurements. Regardless of the interpretation. the two sys- tems operate in an optimum, integrated manner. Early investigators who looked at the pos- sibility of using strapdown seekers for mis- sile guidance came to the conclusion that strapdown seekers cannot be used in guided weapon systems. Indeed, these early in- vestigators were correct,

in the sense that attempting to obtain useful guidance data from an unaided strapdown seeker will al- most always be doomed to failure. The seeker random errors plus small systematic errors combined with high vehicle rotational rates have a tendency to produce large errors in the derived guidance data that must be ex- tracted from the measured strapdown seeker. It is the integration with the strapdown in- ertial sensors that permits the strapdown seeker to have a useful role in the overall guidance system. Another significant advantage of the inte- grated strapdown approach over the indepen-

dent systems approach occurs when the seeker is no longer capable of supplying use- ful data as a result of either loosing track of the target or due to poor vehicle-to-target geometry (e.g., when the seeker becomes “blind as a result of the target image filling the field of view of the seeker). In the con- ventional configuration (which would proba- bly use an inertially stabilized seeker) all guidance commands would remain constant, based on the last seeker measurement (1.e., zero-order hold). On the other hand, with an integrated system the guidance commands are based on the inertial

navigation system which continues to operate even after the seeker stops providing data (and can also in- terpolate between missing data points en- route). In fact, at the point when the seeker usually stops providing useful data. the in- ertial system often has been quite accurately “calibrated by the earlier seeker data so that it is capable of providing accurate guidance signals to the very end of flight. This feature is illustrated in the strapdown configuration described below. Illustrative Example An analytical investigation was conducted to evaluate the performance that could be

achleved for a number of existing guided weapons if equipped with variously config- ured strapdown systems in the integrated mode previously described. The weapons considered for this study varied from slug- gish skid-to-turn glide bombs to high-per- formance bank-to-turn missiles. In all in- stances. we were able to demonstrate via six- degree-of-freedom simulation that relatively low-cost strapdown systems. when properly TO I Control Systems Magazine
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integrated, are capable of accurately guiding the weapon to its target [3]. One of the most unconventional strapdown

configurations analyzed, which clearly illustrates the benefit derived from efficiently integrating the in- ertial and seeker components, is an inertial strapdown system aided by a synthetic aper- ture radar (SAR) seeker for use in an air- to-surface weapon. A SAR is a strapdown imaging radar seeker that is capable of pro- viding discrete measurements of the cone angle y between the vehicle velocity vector and target (see Fig. 2) when the cone angle is above a threshold of approximately 15 de- grees. The system is also capable of quite accurately measuring the distance r to the target and very

crudely measuring the base angle p. Within the framework of combining the SAR measurements with inertial navigation data, the three SAR measurements are related to the six inertial states (x, !. 2. V,, Vv. V.) used in the Kalman filter by p = cos-’(kl * k?) where kl = R X V/IR X VI k2 1 [-V,’(Vf + V-;)-”’, V,(Vl + v;)-1’2, 01 A FYoNav guidance law was assumed in which the steering commands are propor- tional to the inertial line-of-sight rate. The line-of-sight rates are obtained from the esti- mated inertial states using Eq. (1); the re- sulting commanded vehicle accelerations are computed as

a, = -klVlA A skid-to-turn autopilot was used to achieve MISSILE Fig. 2. Sensor geomety. these accelerations through a control com- mand having the following structure: 6, = cla, + c2A + cgO where A and 6 represent accelerometer and rate gyro output, respectively. The major problem associated with a SAR-type seeker is that shortly after the weapon starts to steer toward the target, the cone angle falls below its imaging threshold angle and ceases to provide useful data. Be- cause of this nonlinearity associated with the observation process, one cannot apply the separation principle to the

design of the guid- ance system. That is? one cannot assume that a separately designed optimum estimator can be linked in tandem to a separately designed optimum steering law to yield an optimum guidance system. Most steering laws would, in a very short time, tend to direct the weapon toward the target and thereby cause the SAR system to become ineffective. The errors associated with the inertial naviga- tion system at this early stage are too large for the inertial system to provide guidance commands without the aid of the seeker. We have learned, however, that by shaping the trajectory in a

manner such that the weapon does not completely steer toward the target for approximately one-half of its flight (al- lowing the cone angle to remain above its 15-degree threshold), the SAR data during this portion of flight can be processed to “calibrate” the inertial system well enough for it to accurately guide the weapon toward the target in a pure inertial mode for the re- mainder of the flight. Clearly, this efficient use of the above strapdown sensors can be used only in an integrated mode with a mixer/filter to combine the data in an opti- mum manner. A typical simulated trajectory is

shown in Fig. 3. The weapon has an initial altitude of 1250 ft and an initial velocity of 750 ft/sec. The target is 8000 ft down range and 4000 ft cross track. In the figure, the dots appear at 0.2-sec intervals and the missile profiles appear at 2.0-sec intervals (the total time of flight shown is 15.7 sec). The trajectory shaping was a two-step process - for a por- tion of the flight the vehicle was directed to steer to a phantom target located at the same altitude of the vehicle and 20 degrees astride the instantaneous direction of the target. (A 20-degree reference was used to guarantee

the 15-degree SAR cone angle threshold.) At some appropriate point along the trajectory, the phantom target location is changed to a position directly above the actual target but at the vehicle altitude. This point is denoted in the figure by the arrow R1. A short time later (denoted in the figure by the arrow R2) the Fig. 3. Trajectory of missile to target. phantom target switches to a position that is coincident with the actual target, which causes the weapon to dive down onto the target. The ability of the Kalman filter to improve the estimates of the navigation states used in the guidance

law is illustrated in Fig. 4. Shown in the figure is the decrease in altitude error (actual and standard deviation) from an initial uncertainty of 200 ft to less than 20 ft by the midpoint of the flight. The other navi- gation states showed similar improvement during the flight. Terminal miss distance accuracy was evalu- ated by performing Monte Carlo simulations to several stationary target locations. The circular error probability (CEP) was less than 2 m. Although this method of trajectory shaping achieved quite acceptable accuracy, it is ad- mittedly ad hoc. A more systematic method of

shaping the trajectory to minimize termi- nal miss distance in critical scenarios merits further study. Before concluding the discussion on the benefits of using integrated strapdown avi- onics, it is worth considering some aspects of implementation. Although all of our simu- lation studies have shown that comparable or superior performance to a conventional sys- tem could be achieved with a less expensive integrated strapdown configuration, in some cases it was necessary to augment originally programmed algorithms in order to compen- sate for certain unexpected effects that were discovered to

be unique to strapdown sys- tems. When one replaces more elaborate in- ertially stabilized instruments with their strapdown equivalents, the computer is re- 10 5 m TAME SKI Fig. 4. Error in estimated altitude. June 1986 11
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quired to perform the function of the hard- ware being removed (this, in fact, is one of the cost-saving features associated with the integrated strapdown approach). One must be careful, however, to make sure that the algorithm accounts for all factors (not always obvious), which under certain conditions can be sensitive to an instrument in a strapdown mode

and yet insensitive to one stabilized inertially. For example, small strapdown seeker boresight errors (offset misalignments between the body-fixed coordinate frames of the strapdown seeker and the strapdoujn in- ertial platform) when coupled with high un- controlled vehicle roll rates can seriously degrade performance. (On the other hand, seeker misalignment error in an inertially sta- bilized seeker does not interact with roll rate.) However, if one includes the boresight error as an additional state to be estimated by the Kalman filter, the problem is com- pletely eliminated. Similarly,

strapdown seeker and gyro scale-factor errors, if large enough and not included in the filter, can cause the closed-loop guidance and control system to become unstable. The level of scale-factor error causing the instability is a function of the characteristics of the closed- loop system (guidance law, autopilot, and airframe characteristics) [4]. While all of the weapon configurations in our investigation could adequately accommodate the instru- ment scale-factor errors. a more advanced guidance law!autopilothehicle configuration could present stability problems if the scale- factor errors

are not properly compensated for in the algorithm. Conclusions An extremely effective way of reducing the avionics cost of precision guided weap- ons is to integrate the design of the various subsystems of navigation, guidance, and control with a common set of strapdown components and a Kalman mixerlfilter. In addition to reducing the cost and improving the reliability of the overall system, proper mixing of the strapdown data can. in many cases, result in performance which is supe- rior to that obtained with more expensive avionic components used in the conventional independent navigation,

guidance! and con- trol configuration. References [I] D. A. Haessig and B. Friedland, “Maximum Likelihood Estimation of Target Accelera- tion, IEEE Conf. on Decision and Control, Las Vegas, NV, Dec. 12-15, 1984. [2] T. E. Bullock and S. Sangsuk-Iam, “Ma- neuver Detection and Tracking with a Non- linear Target Model, Proc. of 23rd Conf. on Decision and Control, Las Vegas, NV. Dec. 1984. [3] D.E. Williams. J. Richman, and B. Fried- land. “Design of an Integrated Strapdown Guidance and Control System for a Tactical Missile, Proc. AIM Guidance and Con- fro/ Conf., Gatlinburg. TN, pp. 57-66. .4ug.

15-17, 1983. [4] R. K. Mehra and R. D. Ehrich. “Strapdown Seeker Advanced Guidance,” Workshop on Bank-to-Turn Controlled Terminal Homing Missiles, Laurel, MD, Sept. 19-20. 1984. Jack Richman received his bachelor’s degree in civil engineering from the City College of New York in 1954. the M.S. degree in physics in 1964, and the M.S. degree in mathe- matics in 1974. the latter two from New York Uni- versity. From 1954 to 1964. Mr. Richman wras with the Republic Avia- tion Corporation, starting as a stress analyst in their Engineering Division and later becoming a Principal Mathematician in

their Research Center. While at Republic he worked in a number of diverse areas, including stress analysis, aircraft flutter and vibration analy- sis, orbital and celestial mechanics, and estimation and control theory. In 1964, Mr. Richman joined the Kearfott Division of The Singer Company as a Unit Head in their Systems Analysis section and later as a Pnncipal Scientist in their Research Cen- ter where he is presently engaged in the devel- opment of new concepts in missile and aircraft navigation, guidance. and control. He has pub- lished several papers in this field and holds one patent.

During 1969-70, Mr. Richman worked for Compudat Scientific Systems, Inc., a small con- sulting firm which he helped found. As Director of Engineering he was responsible for engineering and scientific analysis and programming services. He also provided consulting services to two aero- space companies and directed the development of large-scale digital simulation programs used in evaluating the flight performance and navigation systems of two high-performance military aircraft. Mr. Richman is an Adjunct Faculty Member in the Graduate Electrical Engineering Department of the Polytechnic Institute

of New York. David A. Haessig, Jr., was born in Boonton, New Jersey, in 1957. He received the B.S.M.E. and M.S.M.E. degrees in 1979 and 1981, respec- tively, from Lehigh University, Bethlehem, Pennsylvania. From 1979 to 1981, he was a Re- search Assistant with the Department of Mechani- cal Engineering, Lehigh University. There he investigated the effectiveness of modem control theory for improving the “fire-on-the-move” capabilities of ta&s. From 1981 to 1983, he was employed by General Dy- namics, the Electric Boat Division, in Groton, Connecticut, where he was involved in the dy- namic

modeling and design of controllers for submarine systems. Since 1983, he has been with The Singer Company. Kearfott Division, where he is engaged in the application of modern control theory and signal processing techniques to aero- space systems and inertial components. Bernard Friedland was born and educated in New York City. He received his A.B. (1952), B.S. (19531, M.S. (1953). and Ph.D. (1957) degrees from Columbia Univer- sity where he served on the faculty of the Depart- ment of Electrical Engi- neering from 1954 to 1961. Since 1962 he has been with the Kearfott Division of The Singer

Company where he is Manager of Systems Research. He has also served as an Ad- junct Professor at several schools in New York City: currently. he is at the Polytechnic Institute of New York. He is the author of the new textbook Control System Design: An Introduction to State Space Methods, and the cc-author of two other textbooks, Linear Svstems and Principles of Linear Nehvorks, and over sixty technical papers, mostly on applications of modem control theory to guidance, navigation. and avionics. He holds nine patents in these fields. In 1982 he was awarded the ASME Oldenburger Medal for

contributions to guidance and navigation systems. Dr. Friedland is a Fellow of the IEEE and a Member of the Board of Governors of the Control Systems Society. He was an Associate Editor of the IEEE Transactions on Automatic Cormol from 1974 through 1976, and from 1978 through 1980, and is now an Asso- ciate Editor of the WAC Journal, Automica. He is a Fellow of the ASME. an Associate Fellow of the AM, and a Registered Professional En,%eer in the state of California. He served as General Chairman of the 1980 Joint Automatic Conbol Conference. 12 IEEE Control Systems Magazine