WO2006090368A1

WO2006090368A1 - A calibration method and system for position measurements

Info

Publication number: WO2006090368A1
Application number: PCT/IL2006/000227
Authority: WO
Inventors: Mitchell Moshe Haspel
Original assignee: Israel Aerospace Industries Ltd.
Priority date: 2005-02-22
Filing date: 2006-02-22
Publication date: 2006-08-31
Also published as: EP1859295A1; IL185449A0

Abstract

A method and system for reducing systematic errors in an optical system that makes aerial surveillance position measurements. The flight vehicle executes a trajectory within line-of-sight of a reference target object whose actual position is known to a suitable degree of accuracy, and a set of position measurements is made. From these measurements a set of radial error values is derived, based on the known position of the target reference. From this set, coefficients are computed for insertion into functions of one or more input variables, used as compensating factors to reduce the error in the position calculations. These coefficients and compensating factors are then used in making aerial surveillance position measurements for other target objects.

Description

A CALIBRATION METHOD AND SYSTEM FOR POSITION MEASUREMENTS

FIELD OF THE INVENTION

The present invention relates to position measurements made by aerial

surveillance, and, more particularly, to a method for in-flight calibration of position

measurements.

BACKGROUND OF THE INVENTION

Aerial measurements of the global position of objects is well-known and

widely used. This is especially true in the case of UAVs (Unmanned Aerial Vehicles),

where making such position measurements during surveillance missions is a primary

task, but also applies generally to all flying vehicles which are equipped with

apparatus for measuring the angular orientation, and optionally the range, of an

observable object relative to the flying vehicle.

The objects whose absolute geographic positions are to be determined include

stationary objects on the ground, as well as moving objects in other places on the

earth's surface (such as on water), and also encompass objects above the earth's

surface, including, but not limited to: objects elevated above the earth's surface by

fixed structures such as towers; lighter-than-air objects, such as balloons, blimps, and

dirigibles; and heavier-than-air flying vehicles, such as aircraft. The terms "target

object" and "target" herein denote an object whose position is to be determined.

The position of the target object is typically measured in terms of a coordinate

system fixed to the earth's surface. Longitude-latitude-altitude systems are frequently

used, but other coordinate systems are also used, including grid systems that are

specific to the geographical locale in which the measurements are being made. Non- limiting examples of coordinate systems include: the Universal Transverse Mercator

(UTM) System; the World Geodetic System 1984 (WGS 84); and the U.S. National Grid (USNG). The term "earth coordinate system" herein denotes without limitation

any such coordinate system, both world-wide ("global") and local. The term

"position" herein denotes the position of an object in an earth coordinate system.

The aerial platforms from which the position measurements are made can

include any airborne vehicle. Typically, a heavier _fthan-air vehicle capable of true flight is used, but a lighter-than-air vehicle such as a blimp, dirigible, or balloon can

also be used. As previously noted, UAVs are frequently employed. An important

constraint is that the vehicle be capable of changing position relative to a fixed target

object. The terms "aerial platform" and "platform" herein denote any such vehicle,

and the terms "flight", "in flight", "fly", and so forth, herein denote the condition of

being airborne by any means, including, but not limited to true flight and air

buoyancy.

The position of a target object is typically measured from an aerial platform by

optical means that establishes a line-of-sight from the platform to the target. The terms

"optical" and "light" herein include, but are not limited to: the visible portion of the

electromagnetic spectrum; the infrared portion of the spectrum; and the ultraviolet

portion of the spectrum.

Optical measurements require that the target object be illuminated in some

manner, or must itself be a source of optical radiation (such as from an infrared-

emitting target), because the optical measurement depends on detecting light coming

from the target and determining the angles of incidence thereof with respect to the

detector. Illumination includes natural sources of light well as artificial sources. Light can come from the target, and. can be affected by the target, through processes including, but not limited to: reflection; refraction; scattering; absorption; occlusion;

and emission. The measuring apparatus, herein denoted by the term "optical system", typically includes at least the following: a detector capable of sensing light coming

from the target (including, but not limited to a camera or similar imaging sensor

device); and a means of determining the angles of incidence of the light from the

target relative to the detector. Typically, the angles of incidence are measured relative

to a coordinate system fixed with respect to the aerial platform. The term "on-board"

optical system herein denotes an optical system on an aerial platform.

The term "aerial surveillance system" herein denotes any system for

conducting aerial surveillance and for determining the positions of target objects,

including not only an aerial platform and on-board optical system for making direct

surveillance and position measurements, but also the support thereof. Support for an

aerial surveillance system includes, but is not limited to: personnel; communications;

data processing; and command and control systems; whether on ground, at sea, airborne, or in orbit.

Figure 1 illustrates a non-limiting prior art coordinate system with respect to

an aerial platform 101. The Cartesian coordinate system shown in this non-limiting

example has three mutually-orthogonal axes: An x-axis 103; a>>~axis 105; and az-axis

107. hi Figure I₃ x-axis 103 is shown as being along the major axis of aerial platform

101 (which is substantially in the preferred direction of forward motion of aerial

platform 101, i.e., the nominal heading thereof), and y-axis 105 is shown as being

substantially parallel to the aerodynamic lifting surfaces of aerial platform 101, and in

the direction of the port (left) side of aerial platform 101. (The coordinate system is

right-handed — z-axis 107 is shown pointing "into" the page — aerial platform 101 is

illustrated from the bottom as would be seen by an observer on the ground looking upwards, and z-axis 107 points to the zenith.) However, this particular choice of reference orientation is arbitrary and non-limiting; other conventions are also used,

such as reference frames whose z-axis points to the nadir. Also, aerial platform 101

may be a vehicle for which there is no major axis or preferred direction of forward

motion.

In Figure 1, an optical system 121 observes a target object 123 via a beam of

light 125. Optical system 121 is capable of being oriented at different angles with

respect to aerial platform 101, and the parameters of the orientation are typically

measured in terms of angle systems such as Euler angles, direction cosines, or

equivalent systems. An angle α 131 is the azimuthal angle of optical system 121 with

respect to the plane defined by x-axis 103 and z-axis 107. The azimuthal angle is also

referred to in the literature as the "direction" or "bearing" — but this is not in the

same sense as the term "bearing" is used herein (as defined below). An angle β 133 is

the elevation angle of optical system 121 with respect to the plane defined by x-axis

103 and y-axis 105. The elevation angle is also referred to in the literature as the

"altitude" angle, or the "declination". The term "bearing" is used herein to denote the

vector direction of the target object relative to the on-board optical system. The term

"bearing" as used herein refers to the complete angular orientation and thereby

includes both azimuth angle and elevation angle.

For a given angle oc 131 and a given angle β 133, the parameters of beam 125

in the coordinate system of aerial platform 101 are determined by well-known

methods. Angle 131 and angle 133 establish the bearing of target object 123 relative

to the coordinate system of aerial platform 101. A range 135 is the radius vector in the

spherical coordinate system of aerial platform 101, and determines the distance from the aerial platform to the target object. Range 135 is sometimes referred to as the -

"slant range", which is the direct line-of-sight distance to the target object, as distinct

from "ground range", which includes only the horizontal component of the slant range. It is also recalled that two angles are not sufficient to describe the orientation of

the aerial platform, which is illustrated in Figure 2.

It is noted that target object 123 is treated herein as substantially a point object

for purposes of illustration and discussion. Optical location and ranging involves the

position of the surface of most target objects rather than the center of the target

objects. The errors inherent in position measurement by aerial surveillance, however,

are of the order of several meters to several tens of meters, and many target objects of

interest have overall physical dimensions which are comparable or small relative to

this distance. Thus, the point-object approximation is reasonable for purposes of illustration herein.

If the position of aerial platform 101 is known in earth coordinates, and the

orientation of aerial platform 101 is also known relative to earth coordinates; and if

the orientation of the optical system 121 relative to aerial platform 101 is known; and

if range 135 is known; then it is possible to compute the position of target object 123

in earth coordinates. It is also possible to compute the position without measuring the

slant range directly, by using a digital terrain map (DTM), where the vector is drawn

and the first point to strike the earth's surface is found. This is less accurate, however,

than measuring the slant range directly.

As noted above, the parameters of beam 125 are in terms of the coordinate

system of Figure 1, which is relative to the aerial platform. In order to obtain a bearing

reference (the angular orientation) for beam 125 in terms of earth coordinates: 1. it is necessary to know the angular orientation of the aerial platform

relative to the local orientation of the earth coordinate system (relative to

a plane tangent to the earth's sphere); and

2. it is necessary to apply a 3-dimensional rotation to the angular parameters

of beam 125 in order to express the angular parameters of beam 125 in terms of the earth coordinate system.

Then, with the angular orientation of beam 125, given the spatial position of

the aerial platform in terms of earth coordinates, it is possible to obtain the locus of

points for beam 125 in the earth coordinate system.

A position-determining system obtains the spatial position of the aerial

platform's coordinate system with respect to the earth coordinate system. This is

typically done using Global Positioning System (GPS) methods. An angular- orientation-determining system obtains the angular orientation of the aerial platform's

coordinate system with respect to the earth coordinate system. This is typically done

by gyroscopic means or by Inertial Navigational system (INS) methods. The position

of the on-board optical system is considered herein to be the same as that of the aerial

platform. Similarly, the angular orientation of the optical system's coordinate reference frame is considered herein to be the same as that of the aerial platform's

coordinate reference frame. Thus, the position of the on-board optical system's

coordinate reference frame is obtained by the same position-determining system, and

the angular orientation of the on-board optical system's coordinate reference frame is

likewise obtained by the same angular-orientation-determining system.

It is well-known that there are 6 degrees of freedom for the aerial platform

(three global positional and three angular orientation). Global positional degrees of

freedom are equivalent to the degrees of freedom represented by longitude, latitude, and altitude. Angular orientation degrees of freedom are equivalent to the degrees of

freedom represented by "roll", "pitch", and "yaw" of the aerial platform in flight. There are 2 degrees of angular freedom for the optical system within the aerial

platform, equivalent to the degrees of freedom represented by azimuthal angle and

elevation angle.

There are various well-known mathematical methods for applying a 3-

dimensional rotation to the angular parameters of beam 125 according to the angular

orientation of the aerial platform relative to the local orientation of the earth

coordinate system. Figure 2 illustrates a rotation using Euler angles as determined via

step 2. above. The coordinate system relative to aerial platform 101, as previously

described, is illustrated in Figure 2 rotated with respect to earth coordinates, which

include a north-south axis 201, an east-west axis 203, and a zenith axis 205, which is

normal to the north-south-east- west plane. An axis 207 is the intersection of the north-

south-east- west plane and the plane specified by x-axis 103 and >>-axis 105.

There are several different conventions for labeling and using Euler angles, a

common one of which is the "x-convention", wherein a rotation through an Euler

angle φ 209 is first performed around zenith axis 205. This rotation brings north-south

axis 201 into coincidence with axis 207 and thereby into the x-y plane. Then a rotation

through an Euler angle # 211 is performed around axis 207, which brings zenith axis

205 into coincidence with z-axis 107. Finally, a rotation through an Euler angle ^ 213

is performed around the now-coinciding zenith axis 205 / z-axis 107, which brings

north-south axis 201 into coincidence with x-axis 103. Because north-south axis 201

now coincides with x-axis 103, and because zenith axis 205 now coincides with z-axis

107, it follows that east-west axis 203 must coincide with .y-axis 105. These same Euler angle rotations can be applied to an arbitrary vector expressed in the aerial

platform coordinate system so that the components of that vector become the components of the vector expressed in the earth coordinate system.

In addition to Euler angles, there are other angle systems for describing an

arbitrary angular orientation. Roll, pitch, and yaw, for example, are commonly used as

pilot references for deviation from straight-ahead level flight. Making arbitrary

angular re-orientations of certain vehicles (such as spacecraft) is often accomplished

in practice by performing a single rotation around an eigen axis. These different angle

systems are equivalent in that they can all describe angular orientation, but in different

applications, a particular system may possess certain advantages. The Euler angle

system is a relatively intuitive way to describe arbitrary angular orientations and

rotations, and is used here as a non-limiting aid to illustrating the principles of the

present invention.

As noted, there are variations on the identification and employment of Euler

angles, so the previous description is a non-limiting example only. Furthermore, there

are other well-known mathematical methods for performing equivalent rotations.

Regardless of how the rotation is performed, however, the net result is that the angular

parameters of beam 125 are now expressed in terms of earth coordinates, and thereby

express an earth-coordinate bearing of target object 123 relative to the origin of the

coordinate system of aerial platform 101.

Measurement of range 135 may be directly made by an active optical system

— that is, an optical system that emits radiation and can detect reflections of the

emitted radiation from the target object. LADAR (LAser Detection And Ranging —

also known as LIDAR, for Light Detection And Ranging) rangefinders, for example,

are available, which can measure range 135 by measuring the elapsed time for the reflected emitted radiation to return. Here, the laser is used only for range

measurement, not for illuminating the target object for other purposes. Traditional

RADAR systems can also be employed in ranging.

Typically, however, the measurements of the target position are passive. For

passive measurements, illumination of the target object does not depend on the optical

system, but rather is supplied by other sources, including, but not limited to: reflected

or scattered ambient light; and contrasts in self-emitted radiation, such as by visible

light emitters on the target object, or by thermal emission of infrared, for a target

object at a different temperature from the background.

In the case of passive measurements, wherein the target object is not

illuminated by the optical system, a measurement of range 135 is not directly

available. Instead, it is possible to calculate range 135 for a target object at ground (or

sea) level, if the altitude h of aerial platform 101 is known. If the angle of beam 125

relative to the vertical is γ, then for small ranges the curvature of the earth's surface

can be ignored and the range 135 is approximated by r = h/cos γ. In general, if the

altitude of the aerial platform above the target object is known, an iterative procedure

may be employed to solve for the target's position, taking into account the earth's

curvature.

If the range is not available, however, it is possible to calculate the position of

a stationary or slow-moving target object by triangulation using several sightings of

the target object from different positions that yield different instances of beam 125.

■ Errors in Measurement

Figure 3 illustrates an error in the position measurement of a target object. In

Figure 3, optical system 121 on aerial platform 101 is accurately trained on target

object 123, via beam 125, as previously illustrated and described. Target object 123 has a position vector r 301. Position vector 301 is the true position of target object

123. However, due to a measurement error, the measured position is position vector

r 303 rather than true position vector 301. The radial error vector Δr 305 is the

displacement of measured position 303 of the target object from true position 301 of

the target object, so that from the measurement the target object has an apparent

position 307. The error can be in the apparent position on the earth's surface as well as

in altitude above the earth's surface. Errors in repeated measurements generally result

in a distribution of apparent positions throughout a region 309. Additional erroneous

measurements can result in apparent positions outside this region.

Errors in measuring the position of a target object are classified as either:

1. stochastic errors (also known as "random errors"); or

2. systematic errors (such as due to faulty instrumentation or poor

calibration).

Stochastic errors are probabilistic and are generally not predictable. Stochastic

errors are typically considered as unavoidable, but may be analyzed and treated

statistically, and in many cases tend to average toward zero, because for any given

random error there is often a similar probability that there will occur an opposite error.

That is, for many types of measurement the expected value of a stochastic error is

zero. For stochastic errors of this sort, region 309 (Figure 3) tends to be symmetrically

distributed around the actual position of target object 123.

Systematic errors, on the other hand, arise from inaccuracies in measurement

apparatus or other imperfections in the observation and measurement process. Unlike

stochastic errors, systematic errors do not average toward zero. That is, the expected

value of a systematic error is non-zero. For systematic errors, region 309 (Figure 3) often tends to be asymmetrically distributed with respect to "the actual position of

target object 123.

Certain aerial platforms used for aerial surveillance may be especially

susceptible to systematic errors arising from changes to the payload, particularly

changes to the optical system thereof. In a non-limiting example, for certain UAVs

the optical system is removed and reinstalled, possibly with modification, over the

operational cycle of the aircraft, such as for specific missions. The removal and

reinstallation of the optical system in an aerial platform necessarily introduces a

source of new systematic errors, which require calibration and compensation.

It is possible and desirable to reduce systematic errors, and there are in general

various techniques for doing so. The term "calibration" herein denotes any technique

or procedure for reducing systematic errors in measurement, including, but not limited

to: marking, or placing graduations on measuring apparatus; making corrections in the

graduations of measuring apparatus; making adjustments to measuring apparatus;

compensating for errors in the readings of measurements; and modifying the readings

of measurements obtained from measuring apparatus.

It is desirable to minimize systematic errors. Non-limiting measures of

systematic error include: the expected value of radial error; the median of radial error;

or other meaningful statistical measure. Unfortunately, there is currently no generally-

available means of directly calibrating an optical system in the environment of an

aerial platform, for minimizing the effects of systematic errors. There is thus a need

for, and it would be highly advantageous to have, a method of field-calibrating an

optical system on board an aerial platform. This goal is met by the present invention. SUMMARY OF THE INVENTION

The present invention is of a method for calibrating an optical system on-board

an aerial platform, for increasing the accuracy of position measurements of target objects by reducing the effects of systematic error.

The present invention performs a calibration of the optical system for an aerial

platform, reducing the effect of systematic errors, independent of the particular

individual systematic errors that may be present, and independent of the particular

combination of systematic errors that may be present.

The present invention also performs a calibration of the optical system for any

aerial platform, independent of the specific design of the optical system, and

independent of the particular mounting, orientation, and control apparatus of the

optical system.

Furthermore, the present invention performs a calibration of the optical system

independent of the coordinate system employed.

Further still, the present invention performs a calibration of the optical system

in an automated fashion, requiring minimal human intervention.

In addition, the present invention performs a calibration of the optical system

in a rapid and efficient manner, requiring little time and with a minimal disruption of

scheduling of the use of the aerial platform and optical system.

Embodiments of the present invention are able to perform an in-flight

calibration of an optical system on board an aerial platform, using a fixed reference

target object, whose actual geographical position is known to a suitable degree of

accuracy. In an embodiment of the present invention, the reference target object is

located near a take-off or launching area, so that the calibration can be performed conveniently, right after the aerial platform is airborne. By making a series of compensated angle measurements of the reference target object by the optical system

while the aerial platform is in flight, correcting factors for compensating angle

measurements can be estimated, and the systematic error can be thereby reduced.

In the most general embodiments of the present invention, the systematic error

is reduced by providing a compensating factor for the "raw" (i.e., unprocessed) sensor

values (such as angles). This results in a measured position of the reference target

object whose value is a corrected position which more accurately approximates the

true position thereof. In this manner, systematic error is reduced and greater accuracy

is realized than by using the "raw" sensor data to obtain the position. Such a

compensating factor can be embodied in a compensating algorithm using raw

measured sensor data as input and having an adjusted position as output. In

embodiments of the present invention, such a compensating factor is applied to the

raw measurements made by the optical system in order to correct for systematic error.

In embodiments of the present invention, this procedure is formalized and has a

specific mathematical form, wherein the compensating factor is a function

characterized by a set of coefficients, such as the coefficients of a polynomial

expansion.

Regarding correcting of systematic error, it is noted that the accuracy of the

entire system is limited by the accuracy of the input data and by the magnitude of

random error. For example, if the accuracy of earth coordinate system measurement

by ordinary GPS techniques is 6 meters (a typically-quoted distance), then this

distance establishes a practical limit on the ability to compensate for systematic error.

(It is noted that GPS errors are random, but may possibly vary slowly enough to give a

short-term appearance of being systematic.) Therefore, according to the present invention there is provided a method for

calibrating an optical system mounted on-board an aerial platform to reduce a

systematic error of a selected variable in making position measurements of target

objects made during a certain cycle of operation, the method including: (a) having the

aerial platform execute a calibration trajectory substantially within line-of-sight of a reference target object of known position, for collecting calibration measurements

including a plurality of raw measurements of the position of the reference target object

while on the calibration trajectory; (b) computing an error of the calibration

measurements with respect to the known position; (c) based on the error, determining,

for the selected variable, a compensating factor; and (d) applying the compensating

factor to raw measurements or derivatives thereof made by the optical system during

the cycle of operation.

In addition, according to the present invention there is provided a

measurement system for measuring the position of a target object by aerial

surveillance, including: (a) an optical system having two degrees of angular freedom,

wherein each degree of angular freedom has an angular transducer with an output; (b)

a position-determining system for obtaining the earth coordinate position of the

optical system, wherein the positioning system has an output; (c) an angular-

orientation-determining system for obtaining the angular orientation of the optical

system, wherein the angular-orientation-determining system has an output; (d) an

angular compensator for an angular output of at least one of the angular transducers,

wherein the compensator is operative to apply a compensating factor for reducing a

systematic error in the angular transducer, and wherein the compensator has an output;

and (e) a target object bearing and range calculator operative to calculate the position

of the target object from outputs which include the output of the angular compensator. Furthermore, according to the present invention there is provided a calibration

system for reducing systematic error of a selected variable in determining a position of an object during a cycle of operation of an aerial surveillance system, the aerial

surveillance system having an aerial platform and an optical system mounted thereon;

the aerial surveillance system including a position sensing system for providing

position data indicative of the position of the aerial platform with respect to the earth

and an orientation sensing system for providing orientation data indicative of the

orientation of the optical system with respect to the aerial platform, the position data

and orientation data allowing the determination of the position of the monitored

object; the calibration system including a processor and a memory coupled to the

processor, the processor is configured for storing a plurality of calibration

measurements including a plurality of raw measurements of the position of a

predefined reference target object of known position, collected per cycle of operation

while the aerial surveillance system executes a predetermined calibration trajectory

substantially within line-of-sight of the reference target object.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is herein described, by way of example only, with reference to

the accompanying drawings, wherein:

Figure 1 illustrates a non-limiting prior art coordinate system for an aerial

platform with an on-board optical system for determining bearing and range of a target object;

Figure 2 illustrates a prior art coordinate system rotation using Euler angles;

Figure 3 illustrates an error in the measurement of the position of a target object;

Figure 4 is a block diagram of a general aerial surveillance target object

position measurement system with systematic error compensation according to-

embodiments of the present invention;

Figure 5 illustrates angular compensating parameters according to

embodiments of the present invention;

Figure 6 conceptually illustrates the making of calibration readings during a

calibration trajectory according to embodiments of the present invention;

Figure 7 is a flowchart illustrating a method for determining calibration

coefficients according to an embodiment of the present invention;

Figure 8 illustrates an example of systematic errors in raw measurement data,

compared with the improvement after applying the method of the present invention; and

Figure 9 is a conceptual block diagram of a calibration system according to an

embodiment of the present invention. DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The principles and operation of a calibration method according to the present invention may be understood with reference to the drawings and the accompanying

description. Correcting Systemic Errors by Compensating Factors

It is well-known that imperfections in the behavior of one part of a system may

sometimes be corrected, to varying degrees, in another part of the system (or in

another system altogether). In particular, an erroneous measurement may sometimes

be compensated by a corrective factor applied after the erroneous measurement is

made. For example, it is well-known that atmospheric pressure readings using a

mercury barometer are temperature-sensitive, and there exist tables for correcting

erroneous readings according to the temperature of the barometer, in order to obtain

the actual barometric pressure free of systematic errors introduced by changes in

temperature.

In general, the correction of systematic errors in measurements can be modeled

in terms of a compensating factor which is a mathematical function. If m_r denotes a

raw measurement (an uncompensated measurement subject to a systematic error), and

f_c denotes a function serving as a compensating factor for the systematic error, then

m_c -fc (m_r) is the compensated measurement with the systematic error reduced, or

substantially removed. (As noted previously, the term "calibration" herein denotes

processes which include, but are not limited to, the use of compensation.)

As is well-known, it is possible to express an analytic function as a power

series. Typically, functions used as compensating factors are analytic, so f_c can be

written

fc (mr) = Fo + Fι*mr + F₂W + F₃W + ... (1) Aerial Surveillance Target Object Position Measurement Systems

The term "measurement system" herein denotes any system which handles

measurement data, including, but not limited to: performing, supervising, and

scheduling measurements; recording, storing, and retrieving measurement data; transmitting and receiving measurement data; analyzing, reporting, and otherwise

processing measurement data; and utilizing measurement data.

Figure 4 is a block diagram of a general aerial surveillance target object

position measurement system 400 with systematic error compensation according to

embodiments of the present invention. A target object bearing α angle transducer 401

outputs a signal corresponding to azimuthal angle 131 (Figure 1), and the signal is

translated into an angular measurement (e.g., in degrees, radians, grads, or other

suitable angular units) by an α angle translator 403. An α angle compensator 404

corrects for systematic errors in α angle measurement according to embodiments of

the present invention. The resulting corrected angular measurement is input to a target

object bearing and range calculator 409. Likewise, a target object bearing β angle

transducer 407 outputs a signal corresponding to elevation angle 133 (Figure 1), and

the signal is translated into , an angular measurement by a β angle translator 407,

corrected by a β angle compensator 408 according to embodiments of the present

invention, and the corrected β angle output is also input to target object bearing and

range calculator 409.

It is understood that the system illustrated in Figure 4 is non-limiting in the

compensating for α and β only. In other embodiments of the present invention,

additional angles are also compensated. In another embodiment of the present invention, α angle compensator 404

applies a correction for systematic error in α angle reading prior to translation by α

angle translator 403. In yet another embodiment of the present invention, α angle

compensator 404 is incorporated into α angle translator 403 and is a part thereof.

Likewise, in still another embodiment of the present invention, β angle

compensator 408 applies a correction for systematic error in β angle reading prior to

translation by β angle translator 407. In yet another embodiment of the present

invention, β angle compensator 408 is incorporated into β angle translator 407 and is

a part thereof.

An aerial platform global position detector 411 determines the earth coordinate

system positions of aerial platform 101, and an aerial platform angular orientation

detector 413 determines the angular orientation of aerial platform 101 (for example, in

terms of Euler angle φ 209, Euler angle 0211, and Euler angle ^ 213 as shown in

Figure T). The earth coordinate system positions and angular orientation are input to

target object bearing and range calculator 409.

ha embodiments of the present invention, compensation is applied to other

measured variables in order to reduce systematic error. Thus, a global position

compensator 412 adjusts for systematic errors in the measurement of the earth

coordinate system position of aerial platform 101; and an angular orientation

compensator 414 likewise adjusts for systematic errors in the measurement of angular

orientation.

With input from α angle translator 403, β angle transducer 405, aerial platform

global position detector 411, and aerial platform angular orientation detector 413,

target object bearing and range calculator 409 is able to calculate an accurate bearing of the target object (it is noted that the range is not necessary to compute the target

object bearing). Furthermore, if the target object is at ground level (or sea level), target

object bearing and range calculator 409 can estimate the target object's range based on an intersection of the calculated bearing with the earth's surface. Having calculated

the bearing and range of the target object, and knowing the earth coordinate system

position of the aerial platform, target object bearing and range calculator 409 outputs

the target object earth coordinate system position in a report 415.

As previously noted, the use of a Digital Terrain Map (DTM) is a well-known

technique for correlating ground height with position. Because the ground height is a

function of position, an iterative method is needed to use DTM dataJn a further

embodiment of the present invention, α angle compensator 404 is incorporated into

target object bearing and range calculator 409 and is a part thereof. In a still further

embodiment of the present invention, β angle compensator 408 is incorporated into

target object bearing and range calculator 409 and is a part thereof. In general, the

systematic error compensations of the present invention can be performed in various

parts and locations of aerial surveillance target object position measurement system

400, and therefore the examples and illustrations given herein are understood to be

non-limiting.

A general aerial surveillance target object position measurement system 400

optionally includes means for more accurately and more generally computing target

object range 135 (Figure 1). An optional direct range measurement unit 416 contains

an active range-finder 417 for measuring target object range 135 directly. A range

compensator 418 adjusts for systematic errors in range measurement. Furthermore, an optional range triangulation calculator 419 computes target

object range 135 using a trigonometric unit 421 which receives triangulation data from

target object bearing data storage 423. For triangulating target object range, it is

sufficient to have two intersecting bearings from two different known earth coordinate

system positions. The distance between the two earth coordinate system positions is

easily calculated, and forms the base of a triangle whose length is thus known. The

two angles on either side of the base are obtained from the bearing data, and thus the

angle opposite the base is known. Using the law of sines, the triangle is easily solved,

and thereby the range is obtained. In addition, the solution of the triangle provides the

position of the target object directly, not just the range. Because of errors that can

normally be expected, however, it is expected that the two legs of the triangle (formed

by the respective bearings, as in the direction of beam 125 in Figure 1) are not likely

to intersect. The nominal intersection point, however, can be reckoned as the point

where the two legs come closest together. In practice, however, the measurements of

interest are the angles subtended by the base of the triangle and the respective bearing

lines to the target object, and these can always be computed, even if the bearing lines

do not precisely intersect to form a triangle.

It is noted that α angle translator 403, α angle compensator 404, β angle

translator 407, β angle compensator 408, target object bearing and range calculator

409, global position compensator 412, angular orientation compensator 414, range

compensator 418, and triangulation calculator 419 may generally be implemented in

software.

It is noted that functions used as compensating factors are functions of selected

variables which govern measured values either directly or indirectly. In the non-

limiting examples above, direct variables are those of the optical system itself, including azimuthal angle α 131 and elevation angle β 133 (Figure 1). Indirect

variables are those of the aerial platform, including the global position coordinate

variables (e.g., longitude, latitude, altitude) and the angular orientation variables (e.g.,

φ, θ, and ψ) of the aerial platform (Figure T). All of these variables are needed in

order to compute the bearing of the target object relative to the earth coordinates of the aerial platform, and all are subject to systematic error, hi addition, the range of the

target object from the aerial platform is an additional variable subject to systematic

error. Compensating Measurement Systems

In a measurement system it is typically possible to include a means of

compensating measurement data for systematic errors, as described above. Modern

measurement systems commonly include general-purpose data processing capabilities,

in which case the means of compensating measurement data for systematic errors can

often be embedded in software at little cost.

Continuing with Equation (1) above, it is possible to characterize a function

for a compensating factor according to the set of coefficients F₀, F₁, F₂, F₃, ..., etc.

Moreover, because a compensating factor typically makes only relatively small

corrections to a measurement, the higher-order terms of Equation (1) are generally

ignored, and therefore the set is typically limited to only the first several coefficients.

Furthermore, it is assumed that a function used as a compensating factor is a function

only of the variable being compensated (in general, such a function might be a

function of other variables as well, but this is not considered herein).

It is noted that there are other mathematical means of approximating functions

besides power series expansions. Thus, the elements {Po, P₁, P₂, P₃, ...} herein denote generalized coefficients for computing a function used as a compensating factor, which are not limited to the coefficients of a power series expansion.

Figure 5 illustrates a compensation coefficient P_ao 501, a compensation

coefficient P_αl 503, a compensation coefficient P_an 505, a compensation coefficient

P_βo 507, a compensation coefficient Pp₁ 509, and a compensation coefficient Pp_n 511

for α angle compensator 404 and β angle compensator 408. In embodiments of the

present invention, these compensation coefficients may be individually or collectively

set as part of a calibration procedure, and may be repeatedly set during subsequent

calibration procedures. It is also understood that Figure 5 is non-limiting, in that in

other embodiments of the present invention, other compensators for reducing

systematic error also have compensation coefficients which may be set as part of a

calibration procedure.

As previously noted, the most significant coefficients very often correspond to

the low-order coefficients in Equation (1). If coefficients are restricted to those

corresponding to Fo and Fi, then the compensation is linear (a first-order

compensation). If only a single coefficient is used, corresponding to Fo, the

compensation is limited to a constant offset (a zero-order compensation), and the

compensating factor is thereby characterized by the constant offset. In an embodiment

of the present invention, linear functions are used as compensating factors; in another

embodiment of the present invention, only constant offsets are used as compensating

factors.

Calibrating Systematic Error Compensation

In order to perform systematic error compensation according to embodiments

of the present invention, it is necessary to determine the coefficients of a function used as a compensating factor, as described above and as illustrated in Figure 5. According

to embodiments of the present invention, this determination is done during an in-flight calibration operation.

Figure 6 conceptually illustrates the making of calibration measurements

during a calibration trajectory 601 according to embodiments of the present invention.

In the vicinity of calibration trajectory 601 is placed a reference target object 603 so

that an aerial platform 605 having an optical system 607 and executing calibration

trajectory 601 will be in line-of-sight with reference target object 603 throughout

calibration trajectory 601. The actual earth coordinate system position of reference

target object 603 is known to suitable precision. Aerial platform 605 is shown

conceptually in Figure 6 as being in a position 605A₃ a position 605B, a position

605C, a position 605D, a position 605E, and a position 605F. Substantially over

calibration trajectory 601, optical system 607 maintains a bearing on reference target

object 603. During the flight over calibration trajectory 601, measurements are made

of the position of reference target object 603. These measurements are collected into a

data set which is processed to obtain optimal values of the compensation coefficients,

discussed above.

hi an embodiment of the present invention, calibration trajectory 601 includes

maneuvers selected from a predetermined set of flight maneuvers, including, but not

limited to: banks; turns; and climbs, dives, and other changes in altitude; rolls, . In

another embodiment of the present invention, calibration trajectory 601 has a

substantially predetermined flight path.

Method for Determining Compensation Coefficients

Figure 7 is a flowchart of a method for determining systematic error

compensation coefficients for variables according to an embodiment of the present invention. In a step 701, the actual position of a reference target object (such as

reference target object 603 in Figure 6) is determined to suitable accuracy.

Next, in a step 705, an aerial platform (such as aerial platform 605 in Figure 6)

executes a calibration trajectory (such as calibration trajectory 601 in Figure 6) within

a line-of-sight of the reference target object, while making a series of position

measurements of the reference target object, which are collected into a data set 707.

In a non-limiting embodiment of the present invention, a coefficient set 713 is

used, where predetermined coefficients P₀, P₁, P₂, ••• etc., are defined for

compensating each variable as previously described. For each variable, the zero-order

coefficient Po is a constant additive offset (or subtractive offset, depending on the

sign) to the variable, to compensates for systematic error. The zero-order coefficient is

typically the most significant, and in many measuring systems is the only meaningful

compensating coefficient. In a step 711, compensation coefficient set 713 is

initialized. The initialization is typically to zero (i.e., P₀ = Pi = P₂ = ... = 0), but non¬

zero offsets may also be used as initial values.

Then at a step 715, a statistical measure of the error over data set 707 is

computed, hi an embodiment of the present invention, vector error is used. A

statistical measure of error (herein denoted as "error") expresses the overall

discrepancy in the measurements with respect to the known position of the reference

target object. For each element of data set 707, the individual error is the difference

between the measured position of the reference target object and the known position

of the reference target object. Commonly-used statistical measures of error include,

but are not limited to: mean (average); median; and RMS of the error over data set

707. For mean and median computation, the magnitude or absolute value of each error

reading is typically used. For RMS computations, squaring the individual errors removes the effect of sign differences therein. Step 723 is a decision-point to

determine if the measure of error indicates that a minimum error point has been

reached. If so, then compensation coefficient 713 represents the optimum

compensation, and at step 731, the procedure terminates. Otherwise, if a minimum

error has not been reached, a step 725 modifies compensation coefficients 713, and step 715 is repeated.

According to an embodiment of the present invention, the modification of

compensation coefficient set 713 in step 725 is performed by considering all

coefficients at the same time. For example, this could be done by iterating in nested

loops, in which the modification of any one of the coefficients of coefficient set 713 is

done in the context of modification of all the other coefficients, hi this fashion, it is

possible to locate a global minimum error at decision point 723.

Determining the quantitative modification to take place in step 725 can be

done through various techniques. As a non-limiting example, the derivative of the

error with respect to a compensation coefficient in coefficient set 713 is computed by

numerical means, and when this derivative approaches zero, this represents a

minimum error. Care must be taken, however, not to be restricted to a local minimum,

so it is necessary to test over a sufficiently large region of the coefficient space in

order to find the proper global minimum.

An Example

To illustrate the effects of a calibration according to the present invention, a

test in-flight calibration was conducted, during which approximately 1,500 position

measurements of a reference target object were made and collected into a data set.

This portion of the flight along the calibration trajectory lasted approximately two

minutes. Figure 8 is a plot of position calculations based on the received data samples, and along an axis 801 which plots the calculations in the order in which the data

measurement readings were taken. The magnitude of the radial error of the readings in

meters is plotted along an axis 803 (such as the magnitude of radial error vector Δr

305 as illustrated in Figure 3). A plot 805 illustrates the radial error of the calculations based on the raw position measurements. After computing the compensating offsets

for the azimuthal angle and the elevation angle, however, the compensated readings

result in a significantly reduced radial error, as shown in a corresponding plot 807.

Statistics for the raw and compensated data radial error appear in Table 1

below.

Table 1. Statistics of Raw and Compensated Position Error

The reduction of systematic error in the above example is significant. The

maximum error has been reduced to 56% of the raw data value, and the minimum

error has been reduced to a negligible value. The mean and median have been reduced

to 26% and 21%, respectively, of the raw values. It is noted that to achieve such

results in this test, the compensating offsets for the azimuthal angle and the elevation

angle were of the order of 0.25 degrees and 0.37 degrees, respectively. Typical ranges

can vary from 3 to 5 kilometers or more, so that compensation of this order can result

in significant improvement in accuracy. Calibration System

An embodiment of the present invention provides for a separate calibration system, for correcting systematic errors. Figure 9 is a conceptual block diagram of a

calibration system 907 within the environment of an aerial surveillance system 90I₅

which may include ground support equipment and systems, and an aerial platform

903. On board aerial platform 903 is an optical system 905 and calibration system

907, which includes a processor 909, a memory unit 911, a compensation module 913,

and an application module 915. A position sensing system 917 and an orientation

sensing system 919 provide input to calibration system 907 as previously detailed.

Compensation module 913 computes the error in the calibration measurements with

respect to the known position of the reference target and derives appropriate

compensating factors. Application module 915 in turn applies the compensating

factors to raw measurements or processed data therefrom, which are made by optical

system 905.

In one embodiment of the present invention, the calibration procedure is done

in real-time during the calibration flight itself. In another embodiment of the present

invention, the calibration procedure is done off-line using data collected during the calibration flight.

While the invention has been described with respect to a limited number of

embodiments, it will be appreciated that many variations, modifications and other

applications of the invention may be made.

Claims

CLAIMS:

1. A method for calibrating an optical system mounted on-board an aerial platform to reduce a systematic error of a selected variable in making position

measurements of target objects made during a certain cycle of operation, the method comprising:

• having the aerial platform execute a calibration trajectory

substantially within line-of-sight of a reference target object of known

position, for collecting calibration measurements including a plurality of raw measurements of the position of said reference target object

while on said calibration trajectory;

• computing an error of said calibration measurements with respect to

said known position;

• based on said error, determining, for the selected variable, a

compensating factor; and

• applying said compensating factor to raw measurements or derivatives

thereof made by the optical system during said cycle of operation.

2. The method of claim 1, wherein said compensating factor is defined by a

function that minimizes said error.

3. The method of claim 1 , wherein said compensating factor is determined by a compensating algorithm having the raw measurement as an input and a corrected

measurement as an output.

4. The method of claim 1, wherein said compensating factor is characterized by a set of coefficients.

5. The method of claim 4, wherein said compensating factor is determined by

a linear function.

6. The method of claim 5, wherein said compensating factor is characterized

by a constant offset.

7. The method of claim 1, wherein said calibration trajectory includes

maneuvers selected from a predetermined set of flight maneuvers.

8. The method of claim 1, wherein said calibration trajectory has a

substantially predetermined flight path.

9. The method of claim 1, wherein the selected variable is a variable of the

on-board optical system.

10. The method of claim 9, wherein the selected variable is selected from the

group consisting of azimuthal angle and elevation angle.

11. The method of claim 1 , wherein the selected variable is the range from the

on-board optical system to the target object.

12. The method of claim 1, wherein the selected variable is a variable of the

aerial platform.

13. The method of claim 12, wherein the selected variable is a global position

coordinate of the aerial platform.

14. The method of claim 12, wherein the selected variable is an angular

orientation of the aerial platform.

15. The method of claim 1, wherein said reference target object is an object at

the vicinity of a location from which the aerial platform takes off for said cycle of

operation.

16. The method according to claim 1 wherein said compensating factor relates

to the orientation of the optical system with respect to the aerial platform.

17. A measurement system for measuring the position of a target object by

aerial surveillance, comprising:

• an optical system having two degrees of angular freedom, wherein

each degree of angular freedom has an angular transducer with an output;

• a position-determining system for obtaining the earth coordinate

position of said optical system, wherein said positioning system has

an output;

• an angular-orientation-detenmning system for obtaining the angular

orientation of said optical system, wherein said angular-orientation-

determining system has an output;

• an angular compensator for an angular output of at least one of said

angular transducers, wherein said compensator is operative to apply a

compensating factor for reducing a systematic error in said angular

transducer, and wherein said compensator has an output; and

• a target object bearing and range calculator operative to calculate the

position of the target object from outputs which include the output of

said angular compensator.

18. The measurement system of claim 17 furthermore comprising a

compensator selected from the group consisting of:

• a global position compensator for an output from said position-

determining system; and

• an angular orientation compensator for an output from said angular-

orientation-determining system;

wherein said compensator is operative to apply a compensating factor for

reducing systematic error, and wherein said compensator has an output to said target

object bearing and range calculator.

19. The measurement system of claim 17 furthermore comprising:

• a direct range measurement unit for measuring the range to the target

object, said direct range measurement unit having an output; and

• a range compensator, wherein said range compensator has an output

to said target object bearing and range calculator.

20. The measurement system of claim 17 wherein said angular compensator is

operative to receive a compensation coefficient set by a calibration procedure.

21. The measurement system of claim 18, wherein said compensator is

operative to receive a compensation coefficient set by a calibration procedure.

22. The measurement system of claim 19, wherein said range compensator is

operative to receive a compensation coefficient set by a calibration procedure.

23. A calibration system for reducing systematic error of a selected variable in

determining a position of an object during a cycle of operation of an aerial surveillance system, the aerial surveillance system having an aerial platform and an

optical system mounted thereon; the aerial surveillance system comprising a position

sensing system for providing position data indicative of the position of the aerial platform with respect to the earth and an orientation sensing system for providing

orientation data indicative of the orientation of the optical system with respect to the

aerial platform, said position data and orientation data allowing the determination of

the position of the monitored object; said calibration system comprising a processor

and a memory coupled to the processor, said processor is configured for storing a

plurality of calibration measurements including a plurality of raw measurements of the

position of a predefined reference target object of known position, collected per cycle

of operation while the aerial surveillance system executes a predetermined calibration

trajectory substantially within line-of-sight of the reference target object.

24. A calibration system according to claim 23, wherein said processor

includes a compensation module and an application module, said compensation module is configured for computing an error of said calibration measurements with

respect to said known position and based on said error determining, for the selected

variable, a compensating factor; and said application module is configured for

applying said compensating factor to raw measurements or derivatives thereof made

by the optical system during said cycle of operation.

25. A calibration system according to claim 23 or claim 24, wherein said

calibration system is mounted onboard said aerial surveillance system.

26. A calibration system according to claim 23 or claim 24, wherein said aerial surveillance system is controlled by a control station and said calibration system

is integrated with said control station.

27. A calibration system according to claim 23, wherein said calibration trajectory is predetermined.