Feasibility of an anticipatory noncontact precrash restraint
`actuation system
`
`Stephen W. Kerce! and William B. Dress
`
`Instrumentation and Controls Division
`Oak Ridge National Laboratory
`P.O. Box 2008
`Oak Ridge, Tennessee 37831-6318
`
`ABSTRACT
`
`The problem of providing an electronic warning of an impending crash to a precrash restraint system a fraction of
`a second before physical contact differs from more widely explored problems, such as providing several seconds of crash
`warning to a driver. One approach to precrash restraint sensing is to apply anticipatory system theory. This consists of nested
`simplified models of the system to be controlled and of the system's environment. It requires sensory information to describe
`the "current state" of the system and the environment. The models use the sensory data to make a faster-than-real-time
`prediction about the near future.
`
`Anticipation theory is well founded but rarely used. A major problem is to extract real-time current-state information
`from inexpensive sensors. Providing current-state information to the nested models is the weakest element of the system.
`Therefore, sensors and real-time processing of sensor signals command the most attention in an assessment of system
`feasibility.
`
`This paper describes problem definition, potential "showstoppers," and ways to overcome them. It includes
`experiments showing that inexpensive radar is a practical sensing element. It considers fast and inexpensive algorithms to
`extract information from sensor data.
`
`Keywords: anticipatory systems, airbag sensors, precrash restraint, advanced vehicle control systems, chirped wavelets,
`automotive radar, crashworthiness, real-time signal processing, multirate analysis
`
`1. PROBLEM STATEMENT
`
`The ultimate goal of this project is the development of a sensory system that predicts with great accuracy, based on
`its knowledge to the present moment, whether or not it is about to become the victim of a crash. The prediction includes an
`estimate of the energy and direction of the crash. The vehicle will have a suite of restraint devices, driver and passenger
`airbags, side stiffeners in the right and left doors, and possibly other devices, each of which allows for a range of degrees
`of deployment. It is not desirable to fully deploy all restraint devices for every crash, and a context-sensitive decision must
`be made as to which devices to deploy and to what degree.
`
`An anticipatory sensor can do this; an accelerometer-based sensor cannot. The accelerometer indicates two things:
`whether or not a crash is already in progress and, if so, the severity of the crash. This is a purely reactive system. It knows
`nothing until the crash actually starts. The information it provides to the restraint system requires that the restraint system deal
`with a situation that is already occurring. For many types of crashes, there is not sufficient time to determine that a crash is
`already in progress, decide what to deploy, and complete the deployment before the crash energy is transmitted to the
`occupants of the vehicle. To obtain the necessary extra milliseconds, what is needed is an anticipatory system.
`
`This paper covers only the feasibility study phase of an anticipatory sensory system. The objective of any feasibility
`study is to answer the question, "Can the thing being studied really be done?" A reasonable way to answer the question for
`this case is to determine whether or not there are "showstoppers" that might preclude the implementation of an anticipatory
`sensory system for the proper deployment of precrash restraints.
`
`For practical deployment in a vehicle, the anticipatory system must meet several constraints. Since the predictions
`pertain to the state of affairs -100 ms in the future, the process of converting sensor data into a prediction has to happen in
`much less than 100 ms. The error rate (false positive and false negative) must be extremely low. Finally, the whole system
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`72 I SPIE Vol. 2592
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`0-8194-1956-7/95/$6.00
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`Mercedes-Benz USA, LLC, Petitioner- Ex. 1010
`Mercedes-Benz USA, LLC v. American Vehicular Sciences LLC
`IPR2014-00644
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`must have a reasonable potential to be producible for a few tens of dollars per copy when produced in quantities of several
`million.
`
`It is tempting to consider the arming function to the exclusion of the firing function. Arming requires information
`about target dynamics, which can be obtained from radar returns. It does not require target class or mass. 1 The consequences
`of error may be tolerable. A false positive means that the system arms but no crash occurs. If a crash does not occur within
`some prescribed amount of time after arming, the system can disarm, probably with no harm done. A false negative means
`that a crash occurs, but the system does not arm until forced to do so by the crash detection accelerometers; in that instance,
`the advantages of the anticipation are lost. Swihart and Lawrence have produced experimental data that show at least a 10%
`reduction in firing time for accelerometers supplemented by radar-based crash prediction for arming?
`
`The firing function is costlier and riskier but leads to a greater potential payoff than the arming function. In addition
`to target dynamics, the firing function requires information about target class and mass. It has not been proven that class and
`mass data are obtainable by a device that must meet the constraints of an automotive precrash restraint sensory system, nor
`was it an objective of this study to explore the question. The consequences of error are quite severe for an anticipatory firing
`system. A false positive is very likely to cause a crash where none would have occurred otherwise. A false negative might
`cause the restraint to fail to actuate during a crash, causing more severe injury (or loss of life) than would have otherwise
`occurred. The payoff for an anticipatory firing system is that it would deploy the restraint device several tens of milliseconds
`faster than a contact-based firing system.
`
`Before practical development of such a sensor goes forward, the choice must be made between these two
`functionalities. If the sensory system's predictions are to be used only to arm the restraint system, then the risk is relatively
`low, but the payoff is marginal. If the sensory system's predictions are to be used to actually deploy the restraint system, then
`the prospect of payoff is relatively high, but the consequences of error are severe.
`
`2. BACKGROUND
`
`Research sponsored by the National Highway Traffic Safety Administration (NHTSA) in predictive crash sensing
`goes back to the work in the early 1970s by Holstrom and associates.3 These researchers defined active restraints as devices
`requiring some action on the part of the vehicle occupant, such as seatbelts, and defined passive restraints as devices not
`requiring action by the vehicle occupants, such as airbags. Their report uses "anticipatory" to mean "precrash"; it does not
`describe a formal anticipatory system.
`
`They recommended a hybrid system. They asserted that accelerometer-type actuators are adequate below 30 mph
`but that precrash warning is needed at higher speeds and suggested a system with both accelerometers and microwave radar.
`Below 30 mph, only the accelerometers would be used, in conventional fashion, and the radar would not operate. Above
`30 mph, the radar would provide advance warning, and the accelerometers operating at a low threshold would provide
`confirmation. In the 30- to 60-mph range, they did not recommend making a decision to deploy based solely on radar data.
`
`Holstrom and associates3 did not prescribe an acceptable false alarm rate but speculated that it should fall in the range
`from one occurrence in 4 years (probability of accident involvement) to one occurrence in 2500 years (probability of fatal
`injury). Their rates of occurrence were based on statistics for the early 1970s. Statistics for 1990 result in averages of one
`police-reported crash involvement per 14.8 years of driving and one fatal crash involvement in 2910 years of driving.4
`
`More recent literature changes the adjective from "anticipatory" to "predictive," but the emphasis is still on the
`sensing hardware element and not the processing. It does not discuss formal anticipatory systems. Swihart and Lawrence2 are
`concerned with the same result as the early NHTSA work: precontact warning of an impending crash. Their application is
`more demanding, requiring information for context-sensitive deployment. Their system would use radar-based prediction to
`perform the arming function and not the firing function. Their experimental data show at least a 10% reduction in firing time
`for accelerometers supplemented by radar-based crash prediction for arming. They assert that a system that fires an airbag
`solely on the basis of a noncontact prediction requires not only much better target dynamics than their system provides but
`also the class (type and/or mass) of vehicle.
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`Many different sensor technologies have been explored for crash-avoidance sensing. A systematic comparative survey
`of these technologies was performed by Najm.5 His emphasis was on the sensor technology rather than on the signal
`processing details. He notes that filtering or gating of radar returns is used to provide an estimate of target dynamics. Useful
`dynamical information does appear to be present in practical radars; and good, fast, cheap signal processing should do a better
`job of extracting it than is being done by present commercial devices.
`
`While the recent literature on crash warning provides insights into the capabilities and limitations of radar, it does
`not provide (nor was it intended to provide) much guidance of the processing side of the precrash restraint problem.6 For
`example, a vehicle control system investigated by Ozguner et al.7 uses a good radar-reflecting target as an integral element
`of the overall system. Helpful exceptions include the work of Fujita, Akuzawa, and Sato8 and Najm, Mironer, and Fraser; 1
`both of these studies provide insight into the extraction of target dynamics from sensor data.
`
`An unresolved engineering problem in having the vehicle sense its own dynamical state is the determination of the
`minimal set of precrash information actually required by the system model and the signal processing task of extracting it from
`the output of existing on-vehicle sensors. This problem appears to be straightforward, and its solution does not seem to require
`any new conceptual breakthroughs.
`
`The element that the precrash restraint actuation sensor has in common with the other crash-predicting technologies
`is the element used to sense the environment. Almost all propose using microwave radar. Infrared proximity detection works
`for robot guidance but only in low-speed indoor situations.9 The same has been demonstrated for ultrasonic sonar. 10
`
`3. ANTICIPATION
`
`A formal anticipatory system is based on mathematically formalized principles of anticipation. The term generalizes
`the notion that the system can take present action based on an expectation of a future state. It refers to a system in which
`decisions are made by an algorithm that emulates the anticipation process found at a primitive level of biological intelligence.
`The principles of anticipatory systems were rigorously derived by Robert Rosen, a mathematical biologist. 11
`
`The most important use of the anticipation mechanism in nature is to preserve the safety of the creature doing the
`anticipating. Based on an extremely sparse set of percepts describing the present state, a creature performs the remarkable
`feat of recognizing, with sufficient time to take corrective action, whether or not the future state constitutes a danger. Since
`eons of natural selection have caused the anticipation mechanism to abound in nature, not only must it be effective, but also
`it must have superior survival value compared to other paradigms for identifying threats.
`
`The anticipation process is conceptually well founded. Anticipation is one of the most primitive functions of
`biological intelligence. Unlike higher cognitive functions, it is deterministic. It does not require that the creature doing the
`anticipating make a volitional choice to do so. Being deterministic, the rigorous development of a theoretical foundation for
`a mathematical description of anticipation is straightforward, albeit tedious.
`
`If we learned how to perform the seemingly impossible task of heavier-than-air flight by observing how it was done
`in nature, does it not make sense to try the same thing in the development of robust safety systems? This was precisely the
`approach taken by Tsoukalas in the development of anticipatory controls for large systems such as nuclear power plants. 12
`
`The implementation of a formal anticipatory system in a small instrument has never been reported in the literature.
`The most likely reason for this is that, before the recent development of high-performance processors and algorithms, it was
`probably impractical. However, as this feasibility study indicates, at the present level of technology, the development of an
`anticipation engine in a small system is the next logical step in the progression. It is reasonable to expect that the development
`of an anticipatory system applied to vehicular safety should lead to a high payoff in reduction of accidental death and injury.
`
`An anticipatory system is a formal mathematical scheme based on interacting predictive models, as shown in Fig. 1.
`One model takes information about the past and present state of the vehicle and makes a prediction of its dynamical state in
`the near future. Another model takes information about the past and present state of the environment (i.e., likely targets) and
`predicts the dynamical state of the targets in the near future. Based on these sets of predictions, the system develops its
`prediction about the impending crash.
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`74 I SPIE Vol. 2592
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`ploy?
`De
`.
`Ye sorNo
`
`System
`
`Model r '~
`
`Decision
`J~
`\.
`Environment
`Model
`
`- -
`
`Syst
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`lnfor mation
`
`Afe wnos.
`
`Envir onment
`Inform ation
`
`A few nos.
`
`For a model to
`operate, it needs real(cid:173)
`time data streams
`to
`the "present(cid:173)
`provide
`information on
`state"
`the vehicle and
`the
`targets. This requires a
`suite of
`sensing
`transducers
`that
`provides
`"data" and
`real-time
`signal
`processing that extracts
`"information" from the
`data. Thus
`the
`anticipatory system is
`not a sensor with some
`incidental built-in intelligence. Rather, it is an integrated intelligent system that incidentally uses an array of sensing elements,
`signal processors, and an anticipation engine.
`
`Fig. 1. Anticipatory system.
`
`The major unsolved problem is the algorithm, not the hardware. Specific questions are as follows: Can a formal
`anticipatory system consisting of interacting nested models reliably predict the onset and severity of a crash? What are the
`computationally cheapest models that provide an adequate prediction? What input information does the system model need,
`and how sparse can the information be without significantly diminishing the performance of the system model? What input
`information does the environment model require? Do the output data of available sensor elements contain the information
`needed by the models? What are the computationally cheapest signal processing methods for extracting the information needed
`by the models from the data produced by the sensors?
`
`The dynamical models for crash prediction are based on deterministic classical physics. The development of the
`specific models themselves would be tedious but straightforward. The models should be implementable in no more than a
`few thousand machine language instructions. Given present-day microprocessor clock rates, it should be possible to transform
`the initial dynamical conditions into a prediction in less than a millisecond.
`
`Rosen 11 identifies five necessary attributes that distinguish an anticipatory system. The first is that an anticipatory
`system, S2, must contain a model, M, of another system, S1• Second, the anticipatory system, S2, contains a set of observable
`quantities that can be linked mathematically to S1 and an orthogonal set of observables that cannot. Third, the predictions of
`the model, M, can cause an observable change in the state of S2• Fourth, there must be some observable difference in the
`interaction between S 1 and S2 when the model is present and when the model is not. Finally, M must be a predictive model;
`based on the present conditions, M must change state faster than S1 (operate faster than real time) such that M's changed state
`constitutes a prediction about S1•
`
`Since the vehicle and its environment (the set of objects into which the vehicle might crash) are everyday-sized
`objects moving at ordinary speeds, the equations of classical dynamics should provide an adequate model.
`
`dx.
`- ' = f(xt, ... ,x ),
`'
`dt
`n
`
`l, ... ,n
`
`dy.
`-' = g .(y!, ... ,y ),
`dt
`
`m
`
`1
`
`j
`
`l, ... ,m
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`SPIE Vol. 2592 I 75
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`Here the vector xi characterizes the state of the vehicle at an instant, and the vector dx/dt characterizes the time rate
`of change of the state of the vehicle at an instant, where the state has i degrees of freedom, and}; is a mapping function that
`is not necessarily linear and not necessarily conservative. The vector yi characterizes the state of the environment at an instant,
`and the vector dyjdt characterizes the time rate of change of the state of the environment at an instant, where the state has
`j degrees of freedom, and gi is a mapping function that is not necessarily linear and not necessarily conservative.
`
`Since they must operate faster than real time, neither model is an exact characterization of the system it describes.
`A major task of a subsequent phase of the development of a practical air bag actuation sensor is to determine the minimal
`set of vectors xi and yi that account for the necessary observables and the functions .t; and gi that adequately characterize the
`system for this particular application.
`
`How these models and the interaction between them are to be implemented in the sensory system hardware is a
`computational detail. One promising method would be to implement the two dynamical models as two different cellular
`automata, each on its own set of simple dedicated massively parallel very large scale integrated circuit hardware. (Note: A
`cellular automaton is a replacement rule that forces the next state of a cell to be a function of its current state and neighbors.)
`The interaction between them could be modeled as fuzzy set membership; there already exists a dedicated fuzzy logic chip
`that is probably suitable to the task. (Note: Fuzzy set membership is a mathematical measure of the degree to which an object
`is a member of a set.) However, this example illustrates only one possible method. Others might tum out to be faster, better,
`or less expensive.
`
`Sensing the state of the vehicle and extracting the information from the sensor data should not be a showstopper.
`On-vehicle sensors for velocity, acceleration, strain, etc., represent a mature technology; and processing can be done in real
`time with cheap, dedicated digital signal processing (DSP) chips. In fact, it is the abundance of inexpensive sensor data
`describing the state of the vehicle that defines the engineering problem for this part of the system. How sparse can the data
`set be made to still provide an adequate description?
`
`If there is a showstopper, it is in developing the information about the state of the environment. Optical techniques
`are not practical; they are too easily disrupted by environmental effects. Radio-frequency (RF) radar offers the proper range
`and resolution but historically has been extremely expensive and has required absurdly fast processing times. If RF radar is
`used in an impending crash detector, are there ways of implementing it within the cost constraints of consumer electronics?
`Does RF radar generate the information that the environment model needs? Can target dynamics be extracted from the data
`fast enough for it to be practical? Can target class be extracted at all?
`
`To show that the anticipatory airbag sensing system is feasible, the experimental and analytical research effort in this
`project has concentrated on extracting information on target dynamics from the output data of cheap sensors. This project does
`not confuse the system with its transducers; the global objective remains the development of an anticipatory system. Rather,
`the feasibility study focused its primary effort on analysis of environment transducer outputs because uncertainty about the
`availability of environment information constitutes the most likely barrier to practical development.
`
`4. EXPERIMENT
`
`Because of budget limitations, the only experimentation of any consequence was done with a surplus burglar alarm
`radar unit purchased from an amateur radio supplier for $20. This was a Doppler radar that puts out 10 mW at 10 GHz. It
`uses a Gunn diode both as the transmitter oscillator and as the receiving local oscillator and a hot carrier diode as a mixer.
`A hom antenna is used with the radar; its beam width is 23° in azimuth and 21 o in elevation, and it has a gain of 16.6 dB.
`
`Doppler radar experiments were performed with three vehicles, a Ford Econoline van; a small cart with a flat,
`adjustable reflecting screen; and a passenger sedan. The experimental geometries are shown in Fig. 2.
`
`The experiments were conducted with the radar antenna 3 ft above the ground. In the head-on experiments, the
`vehicle was run directly toward the antenna. The vehicle was 50 ft away at the start of the run and 5 ft away at the end of
`the run. In the side-swipe and pass-by geometries, the radar was positioned back from the edge of the roadway, and the
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`Fig. 2. Experimental geometries.
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`perpendicular distance from the antenna to the side of the vehicle was 12 ft at nearest approach. Some of the tests were
`conducted in light rain and snow. Doppler radar returns were not affected by weather effects.
`
`The objective of these experiments was proof of principle. Can we establish that the radar returns really contain the
`information needed to feed the environment model? The experiments were not conducted with the exhaustiveness or the
`precision needed to establish engineering specifications.
`
`The only independent check of target dynamics was provided by a set of two wheel-actuated switches. These provide
`an accurate measure of average target velocity in the time interval during which the front wheel of the target passes between
`the two switches. Data describing the profile of velocity as a function of time were not collected. In a course of experiments
`to establish engineering specifications for a practical sensor (as opposed to proof of principle, as was done here), the velocity
`profile should be collected.
`
`The duration of each signature was 2 to 4 s. A sampling rate of 1000 samples per second was used for digitizing.
`A typical Doppler signature has 2000 to 4000 samples.
`
`What the Doppler experiments yielded were sets of time series data whose modulation corresponds to the
`instantaneous velocity of real-world targets, collected under real-world conditions with cheap hardware. The major result of
`these experiments is that a good estimate of real-time acceleration can be obtained. The implication is that with a system (such
`as pulsed radar) that also provides displacement, it should be possible to obtain good estimates of acceleration, displacement,
`and velocity. Our experiments did not yield information on angle of approach.
`
`5. ANALYSIS
`
`After the experiment, analysis was performed to determine whether or not the observed signatures contain useful
`information. One way to examine a signal for its information content is the Karhunen-Loeve Transform (KLT) (Ref. 13,
`pp. 25-30). The KLT is the optimal transform for detecting information buried in a signal; however, it is impractical to
`implement in real time.
`
`The KLT is impractical as an information extractor in an anticipation engine. What it can do is to establish principle.
`If the information is there, the KL T will find it. For example, if KL T analysis demonstrates that both velocity and acceleration
`information is extractable from a Doppler signature, then the engineering task of developing an information extractor
`degenerates to the job of finding a computationally cheap transform that approximates KL T performance in extracting these
`two features but discards everything else.
`
`The KLT amounts to using the principal eigenvectors of the covariance matrix as a basis to represent the process.
`There are (physically) three dimensions to the state space of a Doppler chirp. (Note: The Doppler chirp is the frequency
`modulated pattern returned by a Doppler radar.) Application of the KLT can be appreciated by comparing Figs. 3, 4, and 5.
`
`Figure 3 is the time domain plot of the last 750 ms of the slowing-down event for the van. There are three separate
`regions identifiable as to amplitude. A likely reason for the amplitude variation is that different portions of the van, having
`different reflectivities, are being viewed by the receiver as the van approaches. These regions are quite evident in the plot.
`
`If we now form a time-delay matrix consisting of
`
`A = ai, Gz, ... , am
`a2, a3, ... , am+l
`
`we create a square, positive definite matrix of dimensions m by m from A multiplying it by its transpose. The eigenvalues
`are found, and the first three are used to reconstruct the signal in phase space. The optimum value for m is determined by
`taking the ratio of the first two eigenvalues; when they are approximately equal, we have spread out the signal to a maximum
`extent (we assume that the dominate process is a simple sine oscillation).
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`3
`
`2
`
`1
`
`0
`
`-1
`
`-2
`
`-3
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`
`0
`
`50
`
`100
`
`150
`Time (ms)
`
`200
`
`250
`
`300
`
`350
`
`Fig 3. Doppler signature with possible multiple reflections.
`
`The result of analyzing the above signal
`in this fashion is shown in Fig. 4. First, we show
`the eigenvalues form= 9. This value of m spreads
`out the fundamental oscillation equally along the
`first two directions.
`
`If we use the first three eigenvectors as a
`basis for the phase space, we obtain the plot in
`Fig. 4 using all 350 data points. Note that there are
`three disks, each tilted with respect to each other.
`The
`three almost-planar
`trajectories
`roughly
`correspond to the three regions in the data set.
`
`We can now look more closely at the
`event in the same phase space by considering only
`50 events at a time, resulting in six regions over
`the 350-point data set. These plots are shown in
`Fig. 5, where the first 50-point region is shown in
`the upper left and the last, in the lower right.
`
`Note that all but the first are nearly two(cid:173)
`dimensional trajectories. The first one clearly
`shows the presence of acceleration during the
`entire 50 time steps by the helical structure. The
`last
`trajectory
`is as decidedly different an
`orientation than the previous four.
`
`Fig. 4. Projection onto first three eigenvectors.
`
`The KLT analysis shows that the information is there but is too costly to use as a practical system. There are cheaper
`analysis methods that approach the information-extracting power of the KLT. In this application, chirped wavelet analysis
`appears to be the most promising method.
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`Fig. 5. Resolution of projection into distinct surfaces.
`
`Chirplet analysis uses a number of chirp wavelets, each with a different deceleration (linear frequency behavior). 14
`The Fourier transform (Ff) of such a set convolved with the FT of data segments picks out the appropriate components,
`identifying regions as to both acceleration and velocity.
`
`Each data section, each perhaps 100 ms in duration, will require a fast FT (of the data) and a convolution with each
`of several chirplets (of various linear frequency variations) at each of several scales (corresponding to basic frequency or
`velocity). The wavelet with the largest correlation is presumed to be the best description of the data. An alternative is to
`convolve segmented portions of the Doppler signal with a set of filters, each representing a particular velocity and
`acceleration. If this set is arranged in a hierarchical manner, processing time can be greatly reduced.
`
`The concept of chirp let analysis is that of a bank of matched wavelet-packet filters chosen to span the Doppler signals
`anticipated. To illustrate the concept, we constructed a set of chirp functions in the frequency range corresponding to five
`velocities between 5 and 25 mph and five accelerations for each velocity ranging from -10 mphls to +10 mphls. Only one
`generic set is shown in Fig. 6.
`
`I \ A A
`I
`\
`\
`\!f
`
`(\
`I
`
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`
`I
`I
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`v v
`
`80 I SPIE Vol. 2592
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`(\ A (\
`
`(\
`
`A (\
`I
`
`v ~
`
`II
`v
`Fig. 6. One row of the chirplets set.
`
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`
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`

`

`6. BEAMFORMING
`
`Beamforming is a multireceiver variation of the time-domain pulse method that builds up a picture in distance-angle(cid:173)
`velocity space. This method has several advantages over the simple Doppler and time-of-flight methods. Conventional methods
`cannot provide an indication of bearing-the angle of the target with respect to the base vehicle. Thus, we are able to get
`velocity and acceleration from the Doppler radar, and if we time the pulses, we also get the critical distance parameter.
`However, with a single transceiver, there is no sure way to identify the bearing of the target.
`
`In addition to being a crucial input datum to the environment model, the advantage of knowing the bearings of a
`collection of targets is that we may safely ignore any target whose angle changes from one pulse to the next: The only
`possible collision candidates are those targets whose bearing remains constant over several measurements. This ability to
`prefilter the space of all possible targets will greatly aid the next processing stages and reduce the computational burden at
`all later stages. Note that if we are moving, all stationary objects are removed from consideration by the constant-bearing
`criterion. Considering only the constant-bearing targets, we next ask which of those are moving toward our vehicle at a speed
`greater than a predetermined (damage-capable) amount. These are the only targets that the anticipatory subsystem need
`consider in its predictive model.
`
`7. CONCLUSIONS
`
`An anticipatory precrash restraint sensor for the arming function appears to be feasible but is not yet developed. A
`system based on formal anticipatory principles should produce significantly fewer errors than do conventional technologies.
`The information needed to determine the dynamical state of the vehicle should be available from the suite of on-board sensors
`already installed for other functions. The information needed to determine the dynamical state of the target includes
`displacement, velocity, and acceleration, all of which are extractable from the returns of inexpensive radar. For the arming
`function, the missing piece in the target dynamics is inexpensive determination of the bearing of the target.
`
`This study found that inexpensive radar in a "real-world" setting does return useful data on target acceleration. The
`principle has been proven with a $20 Doppler radar. The velocity and acceleration of the target can easily be extracted from
`the Doppler radar signal by any of several methods that are implementable in real time.
`
`While Doppler radar proves the principle that dynamical information is buried in the returns of cheap radar, it does
`not provide displacement information. Displacement information is necessary to feed the environment model of an anticipation
`engine. Frequency modulated continuous wave or pulsed broadband radar both appear to be workable alternatives. Each is
`able to provide displacement, velocity, and acceleration data for multiple targets. The makers of both claim that their
`technology can be mass-produced for a few tens of dollars per copy.
`
`The data produced by a radar system can be converted to target dynamical information by good, fast, and inexpensive
`sig