US4742356A — Method and apparatus for determining remote objec…

Claim 1

Independent Claim 156 words

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having a plurality of independent components for detecting each of said transmitted electromagnetic fields; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position and orientation relative to said reference coordinate frame, said analyzing means including means for processing the components of said electromagnetic fields with quaternions.

Claim 2

Independent Claim 156 words

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having a plurality of independent components for detecting each of said transmitted electromagnetic fields; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position and orientation relative to said reference coordinate frame, said analyzing means including means for processing the components of said electromagnetic fields with quaternions.

Claim 3

Independent Claim 161 words

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having a plurality of independent components for detecting each of said transmitted electromagnetic fields; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object orientation relative to said reference coordinate frame, said analyzing means including means for processing the components of said electromagnetic fields into remote object orientation independently of remote object position.

Claim 4

Independent Claim 161 words

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having a plurality of independent components for detecting each of said transmitted electromagnetic fields; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object orientation relative to said reference coordinate frame, said analyzing means including means for processing the components of said electromagnetic fields into remote object orientation independently of remote object position.

Claim 5

Independent Claim 166 words

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having a plurality of independent components for detecting each of said transmitted electromagnetic fields; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position and orientation relative to said reference coordinate frame, said analyzing means including means for processing the components of said electromagnetic fields into at least one of remote object position and orientation with quaternions.

Claim 6

Independent Claim 166 words

An apparatus for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; a transmitter means for applying to said plurality of radiating means electrical signals which generate a plurality of radio frequency electromagnetic fields, said electromagnetic fields being distinguishable from one another; receiving means for receiving said transmitted electromagnetic fields, said receiving means being disposed on a remote object and said receiving means having a plurality of independent components for detecting each of said transmitted electromagnetic fields; and analyzing means for receiving the output of said receiving means and converting the components of said transmitted electromagnetic fields received by said receiving means into remote object position and orientation relative to said reference coordinate frame, said analyzing means including means for processing the components of said electromagnetic fields into at least one of remote object position and orientation with quaternions.

Claim 7

Dependent Claim 24 words

The apparatus of claim 3 wherein said means for processing includes means for determining both remote object position and remote object orientation with quaternions.

Claim 8

Dependent Claim 26 words

The apparatus of claim 4 wherein said means for processing includes means for simultaneously determining remote object position and remote object orientation in a parallel process.

Claim 9

Dependent Claim 68 words

The apparatus of claim 5 further including means for mounting said receiving means on the head of a user; viewing means for generating an image viewed by a user; and said means for processing further including means for generating a world image on said viewing means, the world image being associated with said reference coordinate frame and corrected according to the position and orientation of said receiving means.

Claim 10

Dependent Claim 23 words

The apparatus of claim 6 wherein said viewing means and said means for processing further comprise means for providing a binocular world image.

Claim 11

Independent Claim 113 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing said set of signals into remote object position and orientation with quaternions.

Claim 12

Independent Claim 113 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing said set of signals into remote object position and orientation with quaternions.

Claim 13

Independent Claim 114 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing said set of signals into remote object orientation independently of remote object position.

Claim 14

Independent Claim 114 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing said set of signals into remote object orientation independently of remote object position.

Claim 15

Independent Claim 117 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing said set of signals into at least one of remote object position and orientation with quaternions.

Claim 16

Independent Claim 117 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy, said radiating means having independent components defining a reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for receiving said electromagnetic fields and generating a set of signals that is representative of the received components of said electromagnetic fields; and processing said set of signals into at least one of remote object position and orientation with quaternions.

Claim 17

Dependent Claim 25 words

The method of claim 10 wherein said processing step further comprises the step of determining both remote object position and remote object orientation with quaternions.

Claim 18

Dependent Claim 25 words

The method of claim 11 wherein said processing step further comprises the step of simultaneously determining remote object position and orientation in a parallel process.

Claim 19

Dependent Claim 63 words

The method of claim 12 further comprising the steps of: mounting said receiving means on the head of a user; providing a viewing means for generating an image viewed by a user; and generating a world image on said viewing means, said world image being associated with said reference coordinate frame and corrected according to the position and orientation of said receiving means.

Claim 20

Dependent Claim 15 words

The method of claim 13 further comprising the step of providing a binocular world image.

Claim 21

Independent Claim 242 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame and for receiving said electromagnetic fields and generating a signal matrix S that is representative of the received components of said electromagnetic fields; normalizing signal matrix S=kAP.sup.t HP; where k=an attenuation factor which is a function of the separation distance between the radiating means and the receiving means; A=an orientation matrix which defines the sensor frame relative to the source frame; p=a tracking matrix; H=a relative electromagnetic field coupling matrix means to give ##EQU15## where k=[trace (S t S)/6] 1/2 determining a distance R which is the separation distance between the radiating means and the receiving means; where ##EQU16## R o=a reference separation distance k o=a corresponding reference attenuation factor determining X=(M t M-I)/3; and determining A t =M t -2M -1 where X=P t E 1 P E 1 =a zero matrix except for e 11 =1 whereby three independent algorithms are provided for the distance R, the orientation matrix A, and a position-related matrix X.

Claim 22

Independent Claim 242 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame and for receiving said electromagnetic fields and generating a signal matrix S that is representative of the received components of said electromagnetic fields; normalizing signal matrix S=kAP.sup.t HP; where k=an attenuation factor which is a function of the separation distance between the radiating means and the receiving means; A=an orientation matrix which defines the sensor frame relative to the source frame; p=a tracking matrix; H=a relative electromagnetic field coupling matrix means to give ##EQU15## where k=[trace (S t S)/6] 1/2 determining a distance R which is the separation distance between the radiating means and the receiving means; where ##EQU16## R o=a reference separation distance k o=a corresponding reference attenuation factor determining X=(M t M-I)/3; and determining A t =M t -2M -1 where X=P t E 1 P E 1 =a zero matrix except for e 11 =1 whereby three independent algorithms are provided for the distance R, the orientation matrix A, and a position-related matrix X.

Claim 23

Dependent Claim 29 words

The method of claim 15 further including the steps of: determining ##EQU17## where (X,Y,Z) are the position coordinates of the receiving means in the radiating means reference coordinate frame.

Claim 24

Dependent Claim 67 words

The method of claim 15 further including the steps of: determining A=transpose of (A t ) which is equal to the direction cosine matrix; determining sin E=-a 13 tan iH=a 12 /a 11 tan R=a 23 /a 33 where H, E, R are the Euler angles for heading, elevation and roll, respectively, of the receiving means reference coordinate frame relative to the radiating means reference coordinate frame.

Claim 27

Dependent Claim 73 words

The method of claim 15 further including the steps of: determining A t M=M t M-2I=Y determining a -1 Ya=uMu -1 where a=au -1 =an estimate of a quaternion a u=an error quaternion in a, determining uMu -1 =(I-2U)M where U=is a matrix of the components of the error quaternion u determining a next estimate of a new =a old u; and repeating the process to determine an error free orientation quaternion a.

Claim 28

Dependent Claim 94 words

The method of claim 15 further including the steps of: ##EQU18## determining X1=p -1 (X)p=c(E 1 P)c -1 =(I-2C)E 1 P where actual tracking quaternion p=pc, and p=the estimated tracking quaternion c=the error quaternion in the estimate C=an error matrix whose elements are in the error quaternion c ##EQU19## where the term -4CE 1 C is assumed negligible thus defining the tracking error quaternion C=(1, 0, C.sub.2, C.sub.3) then determining the new estimate for the tracking quaternion p as: p.sub.new =p.sub.old c and repeating the process until C o =1 and C approaches zero.

Claim 29

Dependent Claim 105 words

The method of claim 15 further including the steps of: determining ##EQU20## where (x,y,z) are the position coordinates of the recieving means in the radiating means reference coordinate frame; determining A=transpose of (A t ) which is equal to the direction cosine matrix; determining sin E=-a 13 tan H=a 12 /a 11 tan R=a 23 /a 33 where H, E, R are the Euler angles for heading, elevation and roll, respectively, of the receiving means reference coordinate frame relative to the radiating means reference coordinate frame; providing first and second parallel processors; and simultaneously determining orientation and position in said first and second processors, respectively.

Claim 30

Dependent Claim 86 words

The method of claim 15 further including the steps of: determining ##EQU21## where (x,y,z) are the position coordinates of the receiving means in the radiating means reference coordinate frame; determining A=transpose of (A t ) which is equal to the direction cosine matrix; determining sin E=-a 13 tan H=a 12 /a 11 tan R=a 23 /a 33 where H, E, R are the Euler angles for heading, elevation and roll, respectively, of the receiving means reference coordinate frame relative to the radiating means reference coordinate frame.

Claim 31

Dependent Claim 131 words

The method of claim 15 further including the steps of: determining M=AP t HP=QHP when Q=AP t determining M=q -1 [H(p -1 Ip)]q where q=the quaternion representative of Q p=the quaternion representation of P q=ap -1 and a=the quaternion representation of A determining estimates for quaternions p and q denoted p and q, respectively where p=pc -1 and q=e -1 q where c=error in quaternion p and e=error in quaternion q determining M4=p[H -1 (qMq -1 )] t p -1 ; determining error quaternions c k 's and e k 's from M4 determining new letter estimates for p and q, namely p new =p old c and q new =e q old and repeating the process with these new estimates until the vector part of the error quaternions approach zero.

Claim 32

Independent Claim 181 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame and for receiving said electromagnetic fields and generating a signal matrix S that is representative of the received components of said electromagnetic fields; normalizing said signal matrix S=kAP t HP; where k=an attenuation factor which is a function of the separation distance between the radiating means and the receiving means; A=an orientation matrix which defines the sensor frame relative to the source frame; P=a tracking matrix; H=a relative electromagnetic field coupling matrix means to give M=AP t HP=1/kS; determining A t =M t -2M -1 whereby the orientation matrix A is determined independently of position parameters.

Claim 33

Independent Claim 181 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame and for receiving said electromagnetic fields and generating a signal matrix S that is representative of the received components of said electromagnetic fields; normalizing said signal matrix S=kAP t HP; where k=an attenuation factor which is a function of the separation distance between the radiating means and the receiving means; A=an orientation matrix which defines the sensor frame relative to the source frame; P=a tracking matrix; H=a relative electromagnetic field coupling matrix means to give M=AP t HP=1/kS; determining A t =M t -2M -1 whereby the orientation matrix A is determined independently of position parameters.

Claim 34

Dependent Claim 67 words

The method of claim 23 further including the steps of: determining A=transpose of (A t ) which is equal to the direction cosine matrix; determining sin E=-a 13 tan H=a 12 /a 11 tan R=a 23 /a 33 where H, E, R are the Euler angles for heading, elevation and roll, respectively, of the receiving means reference coordinate frame relative to the radiating means reference coordinate frame.

Claim 35

Dependent Claim 73 words

The method of claim 23 further including the steps of: determining A t M=M t M=2I=Y determining a -1 Ya=uMu -1 where a=au -1 =an estimate of a quaternion a u=an error quaternion in a determining uMu -1 =(I-2U)M where U=is a matrix of the components of the error quaternion u determining a next estimate of a new =a old u; and repeating the process to determine an error free orientation quaternion a.

Claim 36

Independent Claim 194 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame and for receiving said electromagnetic fields and generating a signal matrix S that is representative of the received components of said electromagnetic fields; normalizing said signal matrix S=kAP t HP; where k=an attenuation factor which is a function of the separation distance between the radiating means and the receiving means; A=an orientation matrix which defines the sensor frame relative to the source frame; P=a tracking matrix; H=a relative electromagnetic field coupling matrix means; to give M=AP t HP=1/kS; determining X=(M t M-I)/3; where X=P t E 1 P E 1 =a zero matrix except for e 11 =1 whereby a position-related matrix X is determined independently of orientation parameters.

Claim 37

Independent Claim 194 words

A method for determining the position and orientation of a remote object relative to a reference coordinate frame comprising: providing a source of electromagnetic radiation including a plurality of radiating means for radiating electromagnetic energy said radiating means having independent components defining a source reference coordinate frame; applying multiplexed electrical signals to said radiating means and thus transmitting a set of distinguishable electromagnetic fields; providing a sensor including a plurality of receiving means disposed on a remote object for defining a sensor reference coordinate frame and for receiving said electromagnetic fields and generating a signal matrix S that is representative of the received components of said electromagnetic fields; normalizing said signal matrix S=kAP t HP; where k=an attenuation factor which is a function of the separation distance between the radiating means and the receiving means; A=an orientation matrix which defines the sensor frame relative to the source frame; P=a tracking matrix; H=a relative electromagnetic field coupling matrix means; to give M=AP t HP=1/kS; determining X=(M t M-I)/3; where X=P t E 1 P E 1 =a zero matrix except for e 11 =1 whereby a position-related matrix X is determined independently of orientation parameters.

Claim 38

Dependent Claim 59 words

The method of claim 26 further including the steps of: determining a distance R which is the separation distance between the radiating means and the receiving means; where ##EQU22## R o=a reference separation distance k o=a corresponding reference attenuation factor determining ##EQU23## whee (X,Y,Z) are the position coordinates of the receiving means in the radiating means reference coordinate frame.

Claim 39

Dependent Claim 119 words

The method of claim 26 further including the steps of: determining X=P t E 1 P=p(E 1 P)p -1 determining X1-p -1 (X)p=c(E 1 P)c -1 =(I-2C)E 1 P where actual tracking quaternion p=pc, and p=the estimated tracking quaternion c=the error quaternion in the estimate c=an error matrix whose elements are in the error quaternion c ##EQU24##3 2E 1 C - 2CE 1 - ACE 1 C12c 3-2 c 22 c 300-2 c 200? where the term -4CE 1 C is assumed negligible thus defining the tracking error quaternion c=(1, 0, c.sub.2, c.sub.3) then determining the new estimate for the tracking quaternion p as: p.sub.new =p.sub.old c and repeating the process until c o =1 and c approaches zero.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1991-05-03	1991-11-02	1992-05-03	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1995-05-03	1995-11-02	1996-05-03	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	1999-05-03	1999-11-02	2000-05-03	$7700.00	Window Closed / Lapsed

Method and apparatus for determining remote object orientation and position

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