Patent Publication Number: US-11656316-B2

Title: Position and orientation tracking system, apparatus and method

Description:
FIELD 
     This disclosure generally relates to the detection and tracking of an electronic device in an augmented and/or virtual reality environment. The disclosure more particularly relates to determining a position and angular orientation of an electronic device relative to an environment and/or a coordinate frame, and thereby sending signals to a graphic display based on determining the position and angular orientation of the electronic device. 
     BACKGROUND 
     An augmented reality (AR) and/or a virtual reality (VR) system may generate a visual three-dimensional (3D) immersive environment. A user may experience this virtual environment through interaction with various electronic devices, such as, for example, a helmet or other head mounted device including a display, glasses or goggles that a user looks through when viewing a display device, gloves fitted with sensors, external handheld devices that include sensors, and other such electronic devices. Once immersed in the AR/VR environment, user interaction with the AR/VR environment may take various forms, such as, for example, physical movement and/or manipulation of the handheld electronic device and/or the head mounted device to interact with, personalize and control the virtual environment. 
     A user immersed in an AR/VR reality environment wearing, for example, a head mounted display (HMD) device may explore the 3D virtual environment and interact with the 3D virtual environment through, for example, physical interaction (such as, for example, hand/arm gestures, head movement, walking and the like) and/or manipulation of the HMD and/or a separate electronic device to experience the virtual environment. For example, in some implementations, the HMD may be paired with a handheld electronic device, such as, for example, a controller, a gyro mouse, or other such handheld electronic device. User manipulation of the handheld electronic device paired with the HMD may allow the user to interact with the features in the virtual environment generated by the HMD. 
     However, tracking objects for AR/VR within the virtual environment is a challenging problem since tracking must be fast and accurate enough to track real-time motion for an AR/VR operator to use a variety of motions without motion sickness or a sense of “clunkiness.” Typical problems that exist with six degrees of freedom tracking in AR/VR environments may include: the lack of smooth and accurate tracking of a controller&#39;s position and attitude relative to another sensor system, e.g., the HMD, and/or relative to the world and real objects in the immediate environment; large latency issued leading to non-real-time tracking; a lack of robustness of tracking performance when line-of-sight between the HMD and a controller is obscured or blocked; and high system and component cost and complexity not suitable for commercial applications. 
     SUMMARY 
     The illustrative embodiments of method, systems and devices presented herein provide high resolution position and orientation determination of RF devices based on carrier signals being transmitted between two corresponding RF devices. Once the carrier signals are received by corresponding antennae on each of the RF devices, the carrier signals are processed to determine a number of distance and velocity products that may be coupled with RF device inertial data to very accurately determine both the position and orientation of one RF device relative to the other RF device. 
     In one illustrative embodiment disclosed herein, a position determining system includes a first radio frequency (RF) device including at least one antenna configured to receive and transmit RF signals, and a first radio unit in communication with the at least one antenna. The position determining system further includes a second RF device including a constellation of antennae including at least three receiving antennae, a second radio unit in communication with the constellation of antennae; and a processor. The processor is configured to determine a three-dimensional position of the first RF device relative to the second RF device based on computing at least two of three angles in the second RF device coordinate frame (XY, XZ and YZ) computed from carrier phase difference (CPD) measurements taken between each pair of the at least three receiving antennae when receiving a single RF signal transmitted from the at least one antenna of the first RF device. 
     In another illustrative embodiment disclosed herein, a position and orientation determining system includes a first radio frequency (RF) device including at least one antenna configured to receive and transmit RF signals, a first radio unit in communication with the at least one antenna and an inertial measurement unit (IMU). The position determining system further includes a second RF device including a constellation of antennae including at least three receiving antennae, a second radio unit in communication with the constellation of antennae; and a processor. The processor is configured to determine a three-dimensional position of the first RF device relative to the second RF device based on computing at least two of three angles in the second RF device coordinate frame (XY, XZ and YZ) computed from carrier phase difference (CPD) measurements taken between each pair of the at least three receiving antennae when receiving a single RF signal transmitted from the at least one antenna of the first RF device, and further estimating a direction of a gravity vector generated by the IMU. 
     In another illustrative embodiment disclosed herein, a method of determining a three-dimensional position of a first radio frequency (RF) device relative to a second RF device. The method includes providing the first RF device including at least one antenna configured to receive and transmit RF signals, and a first radio unit in communication with the at least one antenna. The method further includes providing the second RF device including a constellation of antennae including at least three receiving antennae, a second radio unit in communication with the constellation of antennae, and a processor in communication with the second radio unit and the constellation of antennae. The method further includes determining, by the processor of the second RF device, a three-dimensional position of the first RF device relative to the second RF device based on computing at least two of three angles in the second RF device coordinate frame (XY, XZ and YZ) computed from carrier phase difference (CPD) measurements taken between each pair of the at least three receiving antennae when receiving a single RF signal transmitted from the at least one antenna of the first RF device. 
     It should be appreciated that this Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to be used to limit the scope of the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The illustrative embodiments of the invention will be better understood from the following detailed description with reference to the drawings, which are not necessarily drawing to scale and in which: 
         FIG.  1    illustrates a schematic diagram of the general context of the illustrative embodiments presented herein of a position and orientation tracking system; 
         FIG.  2    illustrates a logical element schematic of a TCR Controller device; 
         FIG.  3    illustrates a logical element schematic of a HMD device; 
         FIG.  4    illustrates a schematic diagram of one illustrative embodiment of sensor hardware on a TCR Controller device; 
         FIG.  5    illustrates a schematic diagram of one illustrative embodiment of sensor hardware on a TCR HMD device; 
         FIG.  6    illustrates a schematic antennae diagram used to calculate Carrier Phase Difference (CPD); 
         FIG.  7    illustrates example CPD data with both a Distance Difference and a Mobile Antennae Relative Angle; 
         FIG.  8    illustrates a carrier frequency for Carrier Phase Range determination; 
         FIG.  9    illustrates a signal processing schematic diagram representing signal paths of raw data observable measurements and their corresponding processing via sensor fusion algorithms into a fused data output; 
         FIG.  10    illustrates a first communication sequence between corresponding TCR devices of the position and orientation determining system; 
         FIG.  11    illustrates a second subsequent communication sequence between corresponding TCR devices of the position and orientation determining system; 
         FIG.  12    illustrates a schematic diagram of one illustrative embodiment of a position and orientation determining system comprising a TCR Transponder device and a TCR Originator device, where a position and orientation of the TCR Transponder device is calculated relative to a reference frame of the TCR Originator device; 
         FIG.  13    illustrates a logic flowchart describing a method of determining a position and orientation of the TCR Transponder device relative to the TCR Originator device; 
         FIG.  14    illustrates a schematic diagram of another illustrative embodiment of a position and orientation determining system comprising a TCR Originator device, a TCR Transponder device and an external TCR processing device; 
         FIGS.  15 - 16    illustrate a logic flowchart describing method of determining a position and orientation of an object in accordance with the illustration of and corresponding description of  FIG.  14   ; 
         FIG.  17    illustrates a schematic diagram of another illustrative embodiment of a position and orientation determining system comprising a TCR Originator device, a TCR Transponder device and an external reference frame; 
         FIGS.  18 - 19    illustrate a logic flowchart describing method of determining a position and orientation of an object in accordance with the illustration and corresponding description of  FIG.  17   ; 
         FIG.  20    illustrates a schematic diagram of an exemplary hardware environment that can be used to implement the TCR devices presented in the illustrative embodiments described in  FIGS.  1 - 19  and  21 - 33   , below; 
         FIG.  21    illustrates a second embodiment of a logical element schematic of a TCR Controller device; 
         FIG.  22    illustrates a second embodiment of a schematic diagram of an illustrative sensor hardware on a TCR Controller device; 
         FIG.  23    illustrates a second embodiment of a signal processing schematic diagram representing signal paths of raw data observable measurements and their corresponding processing via sensor fusion algorithms into a fused data output 
         FIG.  24    illustrates a second embodiment of a first communication sequence between corresponding TCR devices of the position and orientation determining system; 
         FIG.  25    illustrates a second embodiment of a second subsequent communication sequence between corresponding TCR devices of the position and orientation determining system; 
         FIG.  26    illustrates a second embodiment of a schematic diagram of one illustrative embodiment of a position and orientation determining system comprising a TCR Transponder device and a TCR Originator device, where a position and orientation of the TCR Transponder device is calculated relative to a reference frame of the TCR Originator device; 
         FIG.  27    illustrates a second embodiment of a logic flowchart describing a method of determining a position and orientation of the TCR Transponder device relative to the TCR Originator device; 
         FIG.  28    illustrates a second embodiment of a schematic diagram of another illustrative embodiment of a position and orientation determining system comprising a TCR Originator device, a TCR Transponder device and an external TCR processing device; 
         FIGS.  29 - 30    illustrate a second embodiment of a logic flowchart describing method of determining a position and orientation of an object in accordance with the illustration of and corresponding description of  FIG.  28   ; 
         FIG.  31    illustrates a second embodiment of a schematic diagram of another illustrative embodiment of a position and orientation determining system comprising a TCR Originator device, a TCR Transponder device and an external reference frame; and 
         FIGS.  32 - 33    illustrate a second embodiment of a logic flowchart describing method of determining a position and orientation of an object in accordance with the illustration and corresponding description of  FIG.  31   . 
     
    
    
     DETAILED DESCRIPTION 
     The illustrative embodiments presented herein for six-degrees of freedom tracking leverages previously developed and patented high accuracy and precision, high measurement rate radio frequency (RF) sensing methods. These RF sensing methods, referred to as Timing, Communications, and Ranging (TCR) technology, and previously as Distance Measuring Radio, (DMR) use several patented measurement methods. 
       FIG.  1    illustrates a schematic diagram of the general context of the illustrative embodiments presented herein of a position and orientation tracking system  100  that tracks a three-coordinate position and three-axis angular orientation or attitude of a first RF device  110  with respect to and from a second RF device  120 . In one illustrative embodiment, the first RF device  110  may be referred to as a hand-held TCR Controller device  110  that is tracked with respect to the second RF device  120  that may be referred to as an instrumented TCR HMD device  120 . 
     The illustrative embodiments presented herein build upon TCR data preprocessing, most notably the unwrapping of carrier phase raw data observables, (Carrier Phase Range (CPR), and Carrier Phase Difference (CPD), as discussed more in detail below). Some illustrative embodiments presented herein also provide sensor fusion algorithms that process the raw data observables and further process the output of the sensor fusion algorithms with an Extended Kalman Filter (EKF) to finally produce a fused data product from the TCR and an aiding Inertial Measurement Unit (IMU) sensor. The illustrative embodiments presented herein provide post-processed six-degrees of freedom results but may also be designed to be causal and support real-time processing. 
     For example, with respect to  FIG.  1   , tracking six-degrees of freedom of the TCR Controller device  110  from the TCR HMD device  120  in 3-D coordinate space includes determining: 1) a ΔX, ΔY and ΔZ position (ΔX, ΔY, ΔZ) of the TCR Controller device  110  from a position, e.g., (0,0,0) of the TCR HMD device  120 ; and 2) an angular orientation ∠ΔX, ∠ΔY and ∠ΔZ, that is, the angular difference between the coordinate frame of the TCR Controller device  110  (X2, Y2, Z2) and the TCR HMD device  120  (X1, Y1, Z1), e.g., (X2-X1), (Y2-Y1) and (Z2-Z1). 
     The illustrative embodiments presented herein are envisioned to be an ideal sensor and signal processing solution for “Inside Out”-type VR/AR tracking. “Inside Out” tracking positions a controller(s), and potentially other real objects, relative to the TCR HMD device  120 . “Inside-out” tracking is a method of positional tracking commonly used in virtual reality (VR) technologies, specifically for tracking the position of head-mounted displays (HMDs) and motion controller accessories. It differentiates itself from “outside-in” tracking by the location of the cameras or other sensors that are used to determine the object&#39;s position in space. In “inside-out” positional tracking, the camera or sensors are located on the device being tracked (e.g. HMD) while in “outside-in” the sensors are placed in a stationary location. At present, most commercially available systems, such as the Valve Lighthouse™, use “outside-in” tracking, where a HMD device and controller device are positioned relative to some fixed infrastructure sensors (not shown). 
     The illustrative embodiments presented herein currently achieves better than 1.0 cm positioning accuracy and precision, and better than one-degree angular orientation accuracy and precision for typical use cases. Key technical challenges for real-world use of the illustrative embodiments presented herein are robustness to radio frequency (RF) occlusion, multipath, and interference for the TCR measurement system. The illustrative embodiments presented herein may be capable of operation in typical office/home environments, however, additional signal processing, sensor pre-filtering, and sensor aiding are discussed herein that may further improve the technology performance, robustness and broaden applicability. 
     I. System Design 
     The six-degrees of freedom tracking illustrative embodiments presented herein are designed to solve close range six-degrees of freedom tracking between RF radio devices via a flexible system architecture. System architecture configurations may include: 1) using one or more transmit (Tx) channels per TCR device, (e.g., TCR HMD device  120  and at least one Controller device(s)  100 ; 2) using two or more receive (Rx) channels on the TCR HMD device  120  to constrain or over-constrain a two-dimension (2-D) or 3-D position of the TCR Controller device  110  with CPD measurements; and/or 3) using one or more Rx channels on the TCR Controller device  110 . 
       FIG.  2    illustrates a logical element schematic  200  of TCR Controller device  110  comprising a plurality of physical sensors  210  that collect raw data observables and include a first Rx/Tx antenna  212 , a second Rx antenna  214 , an nth numbered Rx antenna  216 , an IMU device  218  and a GPS device  220 . Reference number  230  illustrates a logical element represents sensor fusion algorithms that processes raw data observables to create fused data output  240 . 
       FIG.  3    illustrates a logical element schematic  300  of TCR HMD device  120  comprising a plurality of physical sensors  310  that collect raw data observables and include a first Tx/Rx antenna  312 , a second Rx antenna  314 , a third Rx antenna  316 , a fourth Rx antenna  318 , an IMU device  320  and a GPS device  322 . Reference number  330  illustrates a logical element represents sensor fusion algorithms that processes raw data observables to create fused data output  340 . 
     A single Tx/Rx channel, (e.g., a transceiver channel), aids in constraining the TCR Controller device  110  position via a Baseband Range, CPR, carrier phase velocity (CPV), and TDR measurements, described in more detail below. Two or more Rx channels on the TCR Controller device  110  aids in constraining the TCR Controller device  110  heading in addition to its position relative to the TCR HMD device  120  by using CPD measurements in addition to the single Tx/Rx measurements. 
     Using an IMU on the TCR Controller device  110  or optionally using an IMU on the TCR HMD device  120  improves position and orientation/attitude tracking through aiding the fusion filter and TCR carrier phase measurement unwrap. 
     Performance drivers of illustrative embodiments presented herein are TCR sensor measurement accuracy, successful unwrap of carrier phase measurements (CPR, CPD), and accurate time synchronization of IMU and TCR data. Generally, TCR data is of good quality in normal RF environmental conditions. However, in poor RF environmental conditions, the individual TCR measurements can become degraded. The biggest challenge to performance for the illustrative embodiments presented herein is the failure to properly unwrap CPR and/or CPD measurements due to degraded TCR measurement quality. TCR measurement unwrap errors can degrade system performance by introducing correlated errors into the EKF. Some of the complexity of the signal processing presented below is used for identifying and correcting unwrap issues in CPR and/or CPD. 
     I.A. Sensor and Hardware Design Parameters 
     I.A.1. Controller Device Sensors 
       FIG.  4    illustrates a schematic diagram  400  of one illustrative embodiment of sensor hardware on the TCR Controller device  110 . The TCR Controller device  110  may include a pair of antennae having a first Tx/Rx antenna  402 , and a second Rx antenna  404 . A single Tx/Rx channel, (e.g., the first antenna  402 ), may also be used without significant impact to the system positioning performance. Additional Rx channels and antennae may be used to improve system performance. The antennae also may be spaced apart from each other by an antennae baseline distance  406  of sufficient length to determine the TCR CPD measurement as described below. For example, in one illustrative embodiment, the antennae baseline distance  406  may be approximately 5 cm for a hand-held TCR Controller device  110 . The antennae baseline distance  406  may be modified accordingly based on the size of the TCR Controller device  110  and the desired accuracy of the six-degrees of freedom measurements with respect to the TCR HMD device  120 . Furthermore, the antennae baseline distance  406  may be tied to a range between 0.1 to 100 times of a radio frequency wavelength used in RF communication between the TCR devices. 
     The TCR Controller device  110  may also include an IMU  420  and magnetometer  430  for providing raw data observables to determine orientation/attitude with respect to the TCR HMD device  120  as described below. 
     I.A.2. HMD Device Sensors 
       FIG.  5    illustrates a schematic diagram  500  of one illustrative embodiment of sensor hardware on the TCR HMD device  120 . The TCR HMD device  120  may include four antennae: a first Tx/Rx antenna  502 , and a second Rx antenna  504 , a third Rx antenna  506  and a fourth antenna  508 . Additional Rx channels and antennae may be used to improve system performance. Generally, one antenna, the “primary”, may be a Tx/Rx channel. All other channels may be Rx only. The illustrated four antennas may be used to over-constrain the 3-D position of the Controller(s) device  100  in the current system. Fewer antennas may be used if additional aiding sensors are available, or only if 2-D tracking is desired. More than four antennas on the TCR HMD device  120  may also be utilized to improve the accuracy or robustness of the system. 
     The antennae also may be spaced apart from each other by antennae baseline distances of sufficient length to determine the TCR CPD measurement as described below. For example, in one illustrative embodiment, a first antennae baseline distance  510 , (measured between first Tx/Rx antenna  502  and third Rx antenna  506  pair, and between second Rx antenna  504  and fourth Rx antenna  508  pair), may be approximately 5 cm for the TCR HMD device  120 . A second antennae baseline distance  512  (measured between first Tx/Rx antenna  502  and second Rx antenna  504  pair, and between third Rx antenna  506  and fourth Rx antenna  508  pair), may be approximately 10 cm for the TCR HMD device  120 . A third antennae baseline distance  514  (measured between first Tx/Rx antenna  502  and fourth Rx antenna  508  pair, and between second Rx antenna  504  and third Rx antenna  506  pair), may be approximately 11 cm for the TCR HMD device  120 . These antennae baseline distances  510 ,  512  and  514  may be modified accordingly based on the size of the TCR HMD device  120  and the desired accuracy of the six-degrees of freedom measurements with respect to the TCR Controller device  110  and applications for which the system is intended. Furthermore, the antennae baseline distances  510 ,  512  and  514  may be tied to a range between 0.1 to 100 times of a radio frequency wavelength used in RF communication between the TCR devices. 
     The current TCR HMD device  120  hardware may include four antennae with known characteristics in a fixed, known geometric configuration. The physical relationship, particularly the baseline distances between all antennae pairs must be well known for proper utilization of TCR CPD measurements. For example, given the above described first  510 , second  512  and third  514  antennae baseline distances, CPD calculations may be made for each of the antenna pairs illustrated in  FIG.  5    based on these antennae baseline distances. For example, a first logical CPD  520  may be calculated based on RF signals received between first Tx/Rx antenna  502  and second Rx antenna  504  pair having the second antennae baseline distance  512 . A second logical CPD  522  may be calculated based on RF signals received between second Rx antenna  504  and fourth Rx antenna  508  pair having the first antennae baseline distance  510 . A third logical CPD  524  may be calculated based on RF signals received between third Rx antenna  506  and fourth Rx antenna  508  pair having the second antennae baseline distance  512 . A fourth logical CPD  526  may be calculated based on RF signals received between first Rx antenna  502  and third Rx antenna  506  pair having the first antennae baseline distance  510 . A fifth logical CPD  528  may be calculated based on RF signals received between first Rx antenna  502  and fourth Rx antenna  508  pair having the third antennae baseline distance  514  And a sixth logical CPD  530  may be calculated based on RF signals received between second Rx antenna  504  and third Rx antenna  506  pair having the third antennae baseline distance  514 . 
     The TCR HMD device  120  may also include an IMU  540  and magnetometer  550  similar to the TCR Controller device  110  for providing raw data observables to determine orientation/attitude with respect to another external TCR device as further described below. 
     I.A.3. Antennae Characteristics for Both the HMD and Controller 
     Although the antenna illustrative embodiments presented herein may work with any antenna or antenna system designs to enable the core TCR sensor measurements, particular antenna designs may impact the accuracy of the measurements and the ability to cleanly unwrap the carrier phase measurement data. An effort was made to optimize the antennae configuration resulting in two different antenna systems. Both antenna system designs featured a wide field-of-view and were well-matched to the TCR RF transmission frequency. The field of view was optimized to maintain a high signal-to-noise over as wide a range of TCR Controller device  110  positions as possible, and the antenna element load impedance was matched to the source and transmission line impedance of the RF circuitry of the TCR device. 
     I.A.3.i. Separation of Antennae 
     When properly unwrapped and bias corrected, CPD can be used to calculate the angle between a first line A defined between a transmitting antenna  610  and first receiving antenna  620  pair, and a second line B defined between the same transmitting antenna  610  and a second receiving antenna  630  pair, (e.g., given Tx antenna  610  of TCR device  110 , and Rx antennae  620  and  630  of the TCR device  120 ), using simple geometry as shown the schematic antennae diagram  600  of  FIG.  6    and the below equation. 
     Measured Variables: 
     Carrier Phase Difference (CPD)=[φ(B)−φ(A)] 
     (wherein φ is the carrier phase) 
     B=unwrapped Carrier Phase Range (CPR) 
     Constants: 
     Baseline A-B (between the phase centers of the two antennas performing the CPD measurement, i.e., antenna  620  and antenna  630 ) 
     Calculated Variables: 
     
       
         
           
             
               Carrier 
               ⁢ 
                   
               Phase 
               ⁢ 
                   
               Difference 
               ⁢ 
                   
               
                 ( 
                 CPD 
                 ) 
               
               ⁢ 
                   
               Distance 
               ⁢ 
                   
               Difference 
             
             = 
             
               
                 
                   [ 
                   
                     
                       φ 
                       ⁡ 
                       ( 
                       B 
                       ) 
                     
                     - 
                     
                       φ 
                       ⁡ 
                       ( 
                       A 
                       ) 
                     
                   
                   ] 
                 
                 [ 
                 
                   λ 
                   
                     2 
                     ⁢ 
                     π 
                   
                 
                 ] 
               
               = 
               
                 [ 
                 
                   B 
                   - 
                   A 
                 
                 ] 
               
             
           
         
       
       
         
           
             	 
             
               ( 
               
                 wherein 
                 ⁢ 
                     
                 λ 
                 ⁢ 
                     
                 is 
                 ⁢ 
                     
                 the 
                 ⁢ 
                     
                 carrier 
                 ⁢ 
                     
                 wavelength 
               
               ) 
             
           
         
       
       
         
           
             
               
                 θ 
                 ⁡ 
                 ( 
                 
                   A 
                   , 
                   B 
                 
                 ) 
               
               = 
               
                 
                   cos 
                   
                     - 
                     1 
                   
                 
                 ( 
                 
                   
                     CPD 
                     
                       
                         baseline 
                         ⁢ 
                             
                         A 
                       
                       - 
                       B 
                     
                   
                   + 
                   
                     
                       
                         baseline 
                         ⁢ 
                             
                         A 
                       
                       - 
                       B 
                     
                     
                       2 
                       * 
                       B 
                     
                   
                   - 
                   
                     
                       CPD 
                       2 
                     
                     
                       
                         2 
                         * 
                         B 
                         * 
                         baseline 
                         ⁢ 
                             
                         A 
                       
                       - 
                       B 
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
       
         
           
             	 
             or 
           
         
       
       
         
           
             
               
                 	 
                 
                   
                     
                       θ 
                       ⁡ 
                       ( 
                       
                         A 
                         , 
                         B 
                       
                       ) 
                     
                     ≈ 
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                       ( 
                       
                         CPD 
                         
                           
                             baseline 
                             ⁢ 
                                 
                             A 
                           
                           - 
                           B 
                         
                       
                       ) 
                     
                   
                   , 
                   
                     when 
                     ⁢ 
                         
                     B 
                   
                 
                  
               
               ⁢ 
               baseline 
               ⁢ 
                   
               A 
             
             - 
             
               B 
               . 
             
           
         
       
     
     A second angular measurement may be made between the second line B defined between the transmitting antenna  610  and the second receiving antenna  630  pair, and a third line C defined between the same transmitting antenna  610  and a third receiving antenna  640  pair, (e.g., given Tx antenna  610  of TCR device  110 , and Rx antennae  630  and  640  of the TCR device  120 ), further using simple geometry as shown in  FIG.  6    and the below equation. 
     Measured Variables: 
     Carrier Phase Difference (CPD)=[φ(B)−φ(C)] 
     B=unwrapped Carrier Phase Range (CPR) 
     Constants: 
     Baseline B-C (between the phase centers of the two antennas performing the CPD measurement, i.e., antenna  630  and antenna  640 ) 
     Calculated Variables: 
     
       
         
           
             
               Carrier 
               ⁢ 
                   
               Phase 
               ⁢ 
                   
               Difference 
               ⁢ 
                   
               
                 ( 
                 CPD 
                 ) 
               
               ⁢ 
                   
               Distance 
               ⁢ 
                   
               Difference 
             
             = 
             
               
                 
                   [ 
                   
                     
                       φ 
                       ⁡ 
                       ( 
                       B 
                       ) 
                     
                     - 
                     
                       φ 
                       ⁡ 
                       ( 
                       C 
                       ) 
                     
                   
                   ] 
                 
                 [ 
                 
                   λ 
                   
                     2 
                     ⁢ 
                     π 
                   
                 
                 ] 
               
               = 
               
                 [ 
                 
                   B 
                   - 
                   C 
                 
                 ] 
               
             
           
         
       
       
         
           
             
               
                 θ 
                 ⁡ 
                 ( 
                 
                   B 
                   , 
                   C 
                 
                 ) 
               
               = 
               
                 
                   cos 
                   
                     - 
                     1 
                   
                 
                 ( 
                 
                   
                     CPD 
                     
                       
                         baseline 
                         ⁢ 
                             
                         B 
                       
                       - 
                       C 
                     
                   
                   + 
                   
                     
                       
                         baseline 
                         ⁢ 
                             
                         B 
                       
                       - 
                       C 
                     
                     
                       2 
                       * 
                       B 
                     
                   
                   - 
                   
                     
                       CPD 
                       2 
                     
                     
                       
                         2 
                         * 
                         B 
                         * 
                         baseline 
                         ⁢ 
                             
                         B 
                       
                       - 
                       C 
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
       
         
           
             	 
             or 
           
         
       
       
         
           
             
               
                 	 
                 
                   
                     
                       θ 
                       ⁡ 
                       ( 
                       
                         B 
                         , 
                         C 
                       
                       ) 
                     
                     ≈ 
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                       ( 
                       
                         CPD 
                         
                           
                             baseline 
                             ⁢ 
                                 
                             B 
                           
                           - 
                           C 
                         
                       
                       ) 
                     
                   
                   , 
                   
                     when 
                     ⁢ 
                         
                     B 
                   
                 
                  
               
               ⁢ 
               baseline 
               ⁢ 
                   
               B 
             
             - 
             
               C 
               . 
             
           
         
       
     
     The primary design variable that drives the accuracy of the computed angle, (e.g., θ(A,B) and θ(B,C) is the “baseline” distance between the phase centers of the two antennas performing the CPD measurement. As the baseline increases, the accuracy of the angle increases. The TCR HMD device  120  angle(s) estimated from this calculation can be used to solve for the TCR Controller device  110  position by estimating the intersection of multiple bearings in different coordinate planes (XY, YZ and XZ) of the TCR HMD device  120 . Alternatively, the direct measurement of CPD can also be consumed as an aiding measurement as part of the larger position and orientation tracking filter. 
     I.A.3.ii. Number of Antennae 
     With a minimum of three antennae on the TCR HMD device  120 , enough information is available to estimate the 3-D position of the TCR Controller device  110  with respect to the TCR HMD device  120 . By using four or more antennas, an overdetermined solution may be determined to estimate the 3-D position of the Controller device  120 . The extra information resulting from the additional antenna(s) is desirable during an initialization procedure when a simultaneous estimate of the initial 3-D position and the initial integer ambiguity in CPR is needed. Also, the extra CPD measurement from an additional (fourth) antenna may be used for evaluating the internal consistency of the determined 3-D position based on the other remaining (three) antennas, which may assist in filtering out any “bad” CPD measurements. 
     The illustrative embodiments presented herein may utilize additional antennae on the Controller device(s)  110  to constrain TCR Controller device  110  angular orientation and position relative to the TCR HMD device  120 . The illustrative embodiment presented herein illustrates two antennas on the TCR Controller device  110 , (resulting in one CPD calculation between each pair of antennae), primarily to aid in TCR Controller device  110  angular orientation/attitude estimation. Adding additional antennae may improve position and angular orientation accuracy and computational robustness by further constraining those solutions, as well as offering improved antenna geometric dilution of precision (GDOP). 
     I.A.3.iii. Configuration of Antennae (Baseline) 
     Practically, it is desirable to maximize the distance, or baseline, between antennae on the TCR HMD device  120  to achieve higher accuracy angle estimates and to have at least four antennae for the reasons described above. To maximize the angle accuracy, the four antennas were placed on the four corners of the top XY plane of the TCR HMD device  120  as illustrated in  FIG.  5   . 
     Similarly, the two antennae on the TCR Controller device  110  are placed at a largest baseline separation distance on the top XY plane given the TCR Controller device  110  size as illustrated in  FIG.  4   . 
     For applications that require high accuracy and longer distances between the TCR HMD device  120  and TCR Controller device  110 , larger baselines distances would enable this. Baseline choice must also be balanced against the need to unwrap CPD measurements—larger baselines mean more possible integer ambiguities for a given CPD measurement, and a smaller angular resolution between CPD integers. 
     I.B. TCR Measurements 
     The TCR measurements made on the TCR HMD device  120  and TCR Controller device  110  are made via one-way and two-way RF transactions between corresponding “TCR devices”. For example, in  FIG.  1    an TCR Originator  100  broadcasts a preamble and data payload  130  which a TCR Transponder  110  observes, receives, and processes. The TCR Transponder  110  then responds with its own preamble and data payload  140  containing data products from its observations on the original transmission from the TCR Originator  100  and other data products. The TCR Originator  100  observes and receives TCR Transponder  110  transmission  140 , makes its own data products from its observations, and reports the following measurements: 
     Baseband Range—A baseband code phase measurement of round-trip RF time-of-flight (TOF), which represents the relative distance between transacting TCR devices; 
     Carrier Phase Range (CPR)—A carrier phase measurement of the relative distance between transacting TCR devices; 
     Carrier Phase Velocity (CPV)—A carrier phase measurement of Doppler velocity, which represents the relative speed between transacting TCR devices; 
     Carrier Phase Difference (CPD)—A carrier phase measurement of the interferometric Phase Difference of Arrival (PDoA) of a signal received on multiple coherent receive channels of a TCR device. This phase difference can be further expressed as a Time Difference of Arrival (TDoA) or a distance difference; 
     Transactional Difference Range (TDR)—A baseband code phase measurement of time difference of arrival as received on a passive observer TCR, where the observing TCR builds a TDR measurement from receiving and processing the Originator and Transponder transmissions of transacting TCRs; and 
     Wireless clock frequency, clock phase, and time synchronization—Fundamental TCR observables are used to measure and correct for frequency and phase offsets of remote clocks to achieve a synchronized network time and/or clock frequency and/or phase across transacting TCRs. 
     The illustrative embodiments presented herein utilizes the TCR measurements, most notably CPD, CPR, CPV, and wireless synchronization, in conjunction with a cell phone class, commercial inertial measurement unit (IMU) (e.g., the Bosch® Sensortec™ BMI160), also typically including an accelerometer to detect linear motion and gravitation forces, and a gyroscope that measures the rate of rotation in 3-D space, i.e., roll, pitch and yaw. 
     I.B.1. Carrier Phase Difference (CPD) 
     CPD is the backbone of the TCR data processing of the illustrative embodiments presented herein. Regarding the TCR HMD device  120  as illustrated in  FIG.  5   , six CPDs, (CPD1  520 , CPD2  522 , CPD3  524 , CPD4  526 , CPD5  528 , and CPD6  530 ), logically placed between the receiving antenna signal path of each pair of antennae on the TCR HMD device  120  over constrain the 3-D position of the TCR Controller device  110  and are primarily responsible for the accuracy and robustness of the position and orientation determine system  100  positioning performance. 
     Regarding the TCR Controller device  110 , as illustrated in  FIG.  4   , a single CPD, (CPD1  410 ), is logically placed between the receiving antenna signal path of the pair of antennae on the TCR Controller device  110  to constrain the attitude of the TCR Controller device  110 , most notably the yaw. This is especially valuable since the yaw axis (Z-axis) is not constrained by the gravity vector when the TCR Controller device  110  is held in a neutral position (i.e., when the TCR Controller device  110  antennae (e.g., ANT1  402  and ANT2  404 ), and IMU  420  are in an upward facing direction). 
     CPD is a carrier phase measurement of distance difference with an integer ambiguity. CPD unwrap challenges occur relatively frequently in challenging environments but can be identified and corrected using the other TCR/IMU observations. Properly initializing and tracking CPD integer ambiguities is relevant to using CPD data in the six-degrees of freedom sensor fusion. CPD integer ambiguity estimation and tracking is simplified somewhat by the significant position jump an incorrect ambiguity implies. For example, if two possible integer ambiguities would computationally place the TCR Controller device  110  either to the left at 45° or the right at 45° of the TCR HMD device  120 , a previous position of the Controller device&#39;s  110  position should enable proper integer ambiguity resolution by eliminating the least probably position option. 
     When properly unwrapped and bias corrected, CPD can be used to calculate the angle, by the above defined equations, between the line defined by the receiving antennae and the line defined by the receiving antenna and one of the transmitting antennae using simple geometry as defined above. 
       FIG.  7    illustrates example CPD data with both a Distance Difference  700  and a Mobile Antennae Relative Angle  710 . The TCR HMD device  120  angle(s) estimated from the above-identified CPD calculation can be used to solve for the TCR Controller device  110  position by estimating the intersection of multiple bearings in different planes (i.e., XY, YZ and XZ planes). The estimated angle(s) or the direct measurement of CPD can also be consumed as part of the larger position and attitude tracking filter. 
     I.B.2. Carrier Phase Range (CPR) 
     CPR constrains the distance between the TCR HMD device  120  and TCR Controller device  110  to better than millimeter accuracy and precision based on the measure of the range between a transmitter and receiver expressed in units of cycles of the carrier frequency. See carrier frequency illustration  800  in  FIG.  8   . This CPR measurement can be made with very high precision (of the order of millimeters), but the whole number of cycles between transmitter and receiver is typically not measurable. CPR allows for the measurement of the range between corresponding TCR devices very precisely with an ambiguity in the number of whole carrier cycles. 
     CPR integer ambiguity can be initialized and tracked via one or more of the following methods: 1) known or externally measured initial positions or distance between TCR HMD device  120  and TCR Controller device  110 ; 2) estimation of relative position of TCR Controller device  110  relative to TCR HMD device  120  using CPD measurements; and 3) estimation of relative distance for TCR Controller device  110  relative to TCR HMD device  120  using Baseband Ranging. The illustrative embodiments disclosed herein typically use approach 2). Approach 3) has also been used for applications where the distance between TCR Controller device  110  and TCR HMD device  120  is larger. 
     Once the initial ambiguity is known, raw CPR measurements are “unwrapped” using some combination of: 1) CPV—directly measured estimate of change in CPR since last measurement; 2) ΔCPR—first difference of last two unwrapped CPR samples, or some windowed and/or smoothed estimate of average change in recent CPR; 3) inertially or filter output derived expected CPR; and 4) expected CPR from CPD derived positioning. 
     The integer ambiguity initialization methods can also be used throughout the operation to check the validity of the current CPR integer ambiguity estimate, flag bad data, and potentially correct or re-initialize the CPR integer estimate. 
     I.B.3. Carrier Phase Velocity (CPV) 
     CPV is primarily used to aid in CPR unwrap, since the current CPV observation can provide an independent measurement of the expected CPR, assuming sufficiently fast sampling. CPV can also be used directly in the EKF to aid in CPR unwrapping errors but may be of limited value if CPR is available and being unwrapped properly. 
     I.B.4. Transactional Difference Range (TDR) 
     TDR measurements may be leveraged as an additional aid for measuring illustrative embodiments utilizing multiple Controller devices  120  or multiple user setups comprising multiple TCR HMD device  120  and TCR Controller device  110  pairings. 
     I.B.5. Time, Frequency, and Phase Synchronization 
     The TCR time sync capability may be used to synchronize the time scales of the TCR HMD device  120  and Controller device(s)  110  to eliminate time sync errors that would drive position/orientation errors in a final system. By synchronizing time wirelessly between corresponding TCR devices to a nanosecond level, the tracking accuracy of the system may be improved. 
     I.B.6. Baseband Range 
     Baseband ranging can be used to help constrain CPR integer ambiguities. Baseband ranging may also be used as a positioning aide for alternative applications where the distance between TCR HMD device  120  and TCR Controller device  110  is 10 meters or greater. 
     I.C. Sensor Fusion 
     Generally, the illustrative embodiments described in herein may be suitable for estimating full six-degrees of freedom position and orientation/attitude estimation, or any subset of that six-degrees of freedom. At a minimum, to achieve six-degrees of freedom tracking, two things must be estimated: 1) the position of the TCR Controller device  110  relative to the TCR HMD device  120 ; and 2) the angular orientation of the TCR Controller device  110  relative to the coordinate frame (XY, YZ, XZ) of the TCR HMD device  120 . 
     In order to relate the coordinate frame of the TCR Controller device  110  and TCR HMD device  120 , the HMD device&#39;s  120  orientation and position must be known, measured, estimated, or remain fixed relative to the local level frame. The relative position and angular orientation of the TCR Controller device  110  can be estimated separately or in a single fusion method. The minimum set of measurements necessary to estimate both is presented below, along with the relative benefits of additional measurements or sensor fusion techniques. 
     I.C.1. Positioning 
     The 3-D position of the TCR Controller device  110  relative to the TCR HMD device  120  can be calculated directly from the distance between them, and two of the three angles of the TCR HMD device  120  coordinate frame (i.e., planes XY, XZ and YZ). This is simply measuring the position via distance and bearing from a known position. The TCR measurements of CPD from three antennae and CPR, unwrapped, can be used to calculate the distance and angles, (as described above). Additional CPD measurements and antennae can be used to over constrain and improve the positioning solution. Additional TCR measurements, (e.g., Baseband Range, CPV, TDR), may optionally be used to further aid the positioning solution. 
     The addition of inertial sensing on the TCR Controller device  110  provides sensing of incremental rotations and accelerations that further improve the robustness and accuracy of the TCR Controller device  110  positioning estimate. Inertial navigation also provides holdover performance during periods of TCR measurement outage or degradation due to occlusion or environmental effects. The TCR measurements and IMU heuristic updates constrain and improve estimation of changing inertial sensor errors, which improves the accuracy and utility of the inertial sensing. 
     I.C.2. Orientation 
     The IMU is the primary sensor for estimating the orientation of the TCR Controller device  110  in its coordinate frame. Much of the orientation estimation involves estimating the direction of the gravity vector, which constrains 2 of 3 axes. Orientation estimation is accomplished through the fusion of all measurements that provide observability to TCR Controller device  110  orientation, which is primarily the IMU, position estimate, and TCR Controller device  110  CPD. Magnetic heading on the TCR Controller device  110  could also be used as a further constraint. 
     I.C.3. Signal Processing 
       FIG.  9    illustrates a signal processing schematic diagram  900  representing signal paths of raw data observable measurements  910  and their corresponding processing via sensor fusion algorithms  940  into a fused data output  960 . Software for sensor fusion for the illustrative embodiments described herein may occur on an embedded processor, digital signal processor (DSP), field programmable gate array (FPGA), or application-specific integrated circuit (ASIC) that is present on the TCR Controller device  110 , TCR HMD device  120 , and/or an external host PC or computing device. Fusion algorithms currently implemented utilize significant data prefiltering with an EKF, but numerous other options exist for data fusion. The fusion algorithms and associated preprocessing are represented in the dashed box entitled sensor fusion algorithms  940 . 
     The core processing consists of integrating raw data observable measurements and heuristic measurements derived from data supplied by the IMU  912  in an EKF  950  to estimate and correct errors in the position, velocity, attitude and sensor errors of the IMU  912  based on conventional inertial navigation. Specifically, EKF  940  state errors consist of three position errors, three velocity errors, three attitude errors, three accelerometer bias errors and three gyro bias errors, each being associated with X, Y and Z axes, respectively. 
     I.C.3.i. Raw Data Sensor Observable Measurements 
     Raw data sensor observable measurements  910  at either the TCR Controller device  110  and/or the TCR HMD device  120  may be taken from three sources: an IMU  912 , TCR antenna(e) providing CPR and CPD measurements  914 , and TCR antenna(e) providing CPV measurements  924 . 
     The IMU  912  provides IMU data  912 . 1  to initialization algorithm  942  and the same IMU data  912 . 2  to heuristics pre-filter algorithm  946 . 
     CPR or Baseband Range, HMD CPD &amp; Controller CPD  914  logic element obtains CPR and CPD observable data from antenna signals on the TCR Controller device  110  and/or TCR HMD device  120 . Particularly, CPD observable data is collected from discrete CPD antenna pairs  916 , for example, represented by a first antenna  918  and a second corresponding antenna  920  of a CPD antenna pair  916 . Antennae baseline distance  922  between each corresponding antennae pair  918 ,  920  is also collected to be used to calculate the CPD observable data. CPR/CPD data  924 . 1  may be sent to initialization algorithm  942  of position and orientation/attitude and the same CPR/CPD data  914 . 2  may be sent to the TCR pre-filter algorithm  948 . 
     CPV observable data  924  may be collected from a CPV antenna pair  926  defined by a first antenna  928  of CPV antenna pair  928  being on one of the TCR devices (e.g., a TCR Controller device  110 ), and a second corresponding antenna  930  of CPV antenna pair  930  being on the other corresponding TCR device, (e.g., a TCR HMD device  120 ). CPV data  924 . 1  may be sent directly to the EKF algorithm  950  of the sensor fusion algorithms  940 . 
     I.C.3.ii. Initialization 
     Initialization algorithm  942  of position and orientation/attitude, as stated above, receives the IMU output  912 . 1  of IMU  912  and the CPR/CPD output  914 . 1  of CPR, HMD device CPD and Controller device CPD  914 . Initialization data  942 . 1  is subsequently output to the inertial navigation algorithm  944 . 1  described in more detail below. 
     There are 23 parameters that may be processed by the initialization algorithm  942 : nine parameters describing the position, velocity and attitude of the IMU in the TCR Controller device  110 ; six IMU sensor biases; seven CPD integer ambiguities; and one CPR integer ambiguity. The TCR Controller device  110  is initially stationary, so the velocity parameters may be set to zero. The roll and pitch attitude components are initialized based solely on conventional coarse alignment using the IMU data  912 . 1  to sense the direction of gravity, and the accelerometer biases are initialized based on the residual in the projected accelerometer measurements onto the known local gravity vector. The initial gyro biases are set to zero. This leaves twelve parameters to be initialized. As stated above, estimation of the CPD integer ambiguities is simplified by the significant position jump an incorrect ambiguity implies. The initial position is estimated based on minimizing the error in an iterative fit of the six TCR HMD device  120  CPD measurements and their possible integer ambiguities. Given this best position estimate, the CPR integer ambiguity is then estimated based on the expected CPR measurements for that best position estimate. Finally, the IMU heading is initialized based on the initial position and feasible TCR Controller device  110  CPD integer ambiguities during the first few measurements during motion. 
     I.C.3.iii. Inertial Navigation and Heuristic Pre-filters 
     Additional measurements to the EKF  950  are available based on the detection of any periods when the IMU  912  comes to rest by the inertial navigation pre-filter  944  where Zero Velocity Updates (ZUPTs) and Frozen Azimuth Updates (FRAZs) are detected based on empirically derived variance thresholds in the raw IMU data  912 . 1 . 
     ZUPTs constrain the velocity to zero during periods when the IMU  912  is stationary. This update directly constrains the velocity errors but also constrains position errors, some components of the IMU bias errors and the roll and pitch misalignment errors relative to gravity through the associated state covariances. FRAZs constrain the change in the yaw of the IMU  912  to zero, which allows estimation and removal of the component of the gyro bias projected along the yaw-axis during stationary periods. Inertial navigation data  944 . 1  may be sent to the EKF  950  for further filtering based on CPV data  924 . 1 . 
     Heuristics pre-filter algorithm  946  receives IMU data  912 . 2  from the IMU  912  and outputs heuristics pre-filter data  946 . 1  to the EKF  950 . 
     I.C.3.iv. TCR Pre-filters 
     The TCR pre-filter algorithms  948  reject bad TCR data and provide tracking of CPR integer ambiguities and CPD integer ambiguities by utilizing algorithms similar to the initialization algorithms  942  processing. 
     CPD integer ambiguities are unwrapped using a raw measurement project/correct style filter, with outlier checking from the inertially derived position projection. Valid and robust unwrap of CPD is integral to system stability and performance. CPR integer ambiguities are unwrapped using a raw measurement project/correct style filter, with the projection being a combination of inertially derived projection and directly measured CPV. Outlier checking for the inertial and/or CPD derived position projection is also used. Valid and robust CPR unwrap is also important to system stability and performance. 
     TCR pre-filter data  948 . 1  is subsequently sent to the EKF  950  for further filtering based on CPV data  924 . 1 . 
     I.C.3.v. Fusion EKF-Type Filter 
     As disclosed above, the specific TCR measurements are consumed directly by the fusion EKF filter  950 . However, an alternate illustrative embodiment may fuse TCR observations into Distance and Angle-of-Arrival measurements, and fuse those estimates analytically or with a very simple filter for the TCR Controller device  110  position. Different sensor fusion algorithms could be applied to the same or similar sensor data. Further, an alternative RF illustrative embodiment or different sensor modality may replace some or all the TCR observations for a similar system and sensor fusion approach. 
     The use of a magnetometer in conjunction with the IMU  912  on the TCR Controller device  110  to constrain heading and position for heading estimation and potentially as a positioning aide may additionally aid in the sensor fusion. Furthermore, a similar sensor and fusion approach may be used for “Outside In” tracking with positioning infrastructure. 
     I.C.3.vi. Fused Data Output 
     EKF filter algorithm  950  outputs EKF filtered data  950 . 1  to provide a fused data output  960  comprising six-degrees of freedom position and orientation output  962 . The fused data product is a causal position and attitude estimate that is capable of being computed in real-time or with a small, fixed lag from real-time. 
     Additional extensions possible from this approach include: 1) using known, measured, or tracked position and orientation of the TCR HMD device  120  in some other coordinate frame, such as Global Positioning System (GPS), to translate the TCR Controller device  110  and/or TCR HMD device  120  position into the GPS coordinate frame or a related frame; 2) extending tracking to additional Controller devices  110  or other tracked items, and 3) if hard real-time is not required, utilization of a windowed or full dataset smoothing algorithm to improve post processed results. 
     Alternative illustrative embodiments may provide using the above-identified inertial sensing and fusion filtering to also estimate an TCR HMD device  120  position/attitude in a local or global coordinate frame, as described below, in conjunction with the fused data output of the TCR Controller device  110 . 
     II. System Operation 
     II.A. TCR Originator to TCR Transponder 
       FIGS.  10  and  11    illustrate a communication sequence between corresponding TCR devices of the position and orientation determining system  100  as shown from  FIG.  1    to  FIG.  9   . 
       FIG.  10    illustrates a first illustrative embodiment of a communication sequence originated by a TCR Originator device  1000 , e.g., TCR HMD device  120 , and a TCR Transponder device  1060 , e.g., TCR Controller device  110 . First, the TCR Originator device  1000  activates a transmitter antenna, e.g., ANT 1 TX/RX  1012 , to transmit a preamble and a data payload via a carrier frequency at operation  1012 . 1  to the TCR Transponder  1060  for reception by any receiving antennae thereon, e.g., ANT 1 TX/RX  1072 , and ANT 2 RX  1074 . 
     Upon receiving the preamble and data payload from the TCR Originator  1000 , the TCR Transponder  1060  forwards the antennae received preamble and data payload to the raw data observable measurements unit  1080  for calculation of CPR, CPD and CPV observable measurements in addition to IMU and/or magnetometer  1076  data, and GPS  1078  data. These data are then processed by the sensor fusion algorithms  1082 , to produce baseband ranging data including master clock number counts, clock dynamic measurements and time-of-flight data, CPR data, CPV data, CPD data and orientation data based on the IMU/MAG device  1076 . The data after passing through the EKF (e.g., EKF  950  in  FIG.  9   ) is then output as fused data output  1084 . 
     II.B. TCR Transponder to TCR Originator 
       FIG.  11    illustrates a second illustrative embodiment of a communication sequence where a TCR Transponder device  1060  responds to the communication received from the TCR Originator device  1000  of  FIG.  10   . The fused data output  1084  previously output by the sensor fusion algorithms  1082  is sent as a data payload with a TCR Transponder specific preamble to the transmitter antenna of the TCR Transponder, e.g., ANT 1 TX/RX  1072 . The transmitting antenna transmits the TCR Transponder  1060  preamble and data payload  1072 . 1  to any receiving antennae of the TCR Originator device  1000 , e.g., in this illustration, ANT1 to ANT4, designated by reference numbers  1012 ,  1014 ,  1016  and  1018 . 
     The received signals at each of the respective antennae are forwarded to the raw data sensor observable measurements  1030  processor to calculate CPR, CPD and CPV solutions, in addition to IMU and/or magnetometer  1020  data, and/or GPS  1022  data. These data are then processed by the sensor fusion algorithms  1032 , as described above with respect to  FIG.  9   , to produce baseband range measurements, CPR data and integer ambiguities, and CPD distance measurements, that, after processing by the EKF  950  of  FIG.  9   , is then output as fused data output  1034 . 
     In a first illustrative embodiment, the fused data output  1034  at operation  1034 . 1  may be output to a display driver  1040  integral with the TCR Originator device  1000  to process graphic display information for presentation to a graphic display  1050  integrated with or for use in conjunction with the TCR Originator device  1000 . The graphic display  1050  may be configured for a dual-eye head mounted micro-display device. 
     In a second alternative illustrative embodiment, the fused data output  1034  at operation  1034 . 2  may be output to a remote AR/VR system processor  1090  that may further process the fused data output  1034  and at operation  1090 . 1  and return data to the display driver  1040  of the TCR Originator device  1000  for presentation to the graphic display  1050 . This illustrative embodiment may provide greater processing power to the fused data output  1034  than the TCR Originator device  1000  may be able to provide before rendering the graphics in an AR/VR environment on the graphic display  1050  of the TCR Originator device  1000 . 
     II.C. HMD Device and Controller Device 
       FIG.  12    illustrates a schematic diagram of one illustrative embodiment of a position and orientation determining system  1200  comprising a TCR Transponder device  1210  and a TCR Originator device  1220 , where a position and orientation of the TCR Transponder device  1210  is calculated relative to a reference frame of the TCR Originator device  1220 . 
     A TCR Transponder device  1210  comprises an antenna pair  1212  and IMU and/or magnetometer  1214  similar to the illustration in  FIG.  4   . A TCR Originator device  1220  comprises an antenna array  1224  similar to the illustration in  FIG.  5    and a graphical display  1226 . TCR Originator device  1220  additionally includes a TCR Originator coordinate frame  1222 , having planes XY, YZ, and XZ to which the TCR Transponder device  1210  is oriented against. 
       FIG.  13    further illustrates a logic flowchart describing a method of determining a position and orientation of the TCR Transponder device  1210  relative to the TCR Originator device  1220 , where the method comprises providing  1300  a TCR radio frequency (RF) Transponder device  1210  including a first constellation of antennae  1212  including at least two receiving antennae and at least one transmitting antenna, a first radio unit in communication with the first constellation of antennae  1212 . 
     The method further comprises  1302  providing a TCR RF Originator device  1220  including a second constellation of antennae  1224  including at least three receiving antennae and at least one transmitting antenna, a second radio unit in communication with the second constellation of antennae  1224 , a processor in communication with the second radio unit and the second constellation of antennae  1224 , and a graphical display  1226 . 
     The method further comprises determining  1304  a three-dimensional position and three-axis angular orientation of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220  based on calculating a carrier phase difference (CPD) measurement of phase difference based on signals received from the TCR RF Originator device  1220  between each discrete pair of receiving antennae of the at least three receiver antennae of the TCR RF device  1220 . 
     The method further comprises rendering  1306  an image on the graphical display  1226  of the TCR RF Originator device  1220  in one a virtual reality or an augmented realty environment based on the determined three-dimensional position and three-axis angular orientation of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220 . 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220  based on unwrapped carrier phase range (CPR) samples. 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220  device by determining at least two of three angles of the TCR RF Transponder device  1210  relative to a coordinate frame (XY, XZ, YZ) of the TCR RF Originator device  1220  based on determining CPD measurement of phase difference by subtracting: 1) a first carrier phase range (CPR) determined distance between a transmitting antenna of the TCR RF Transponder device  1210  and a first receiving antenna of a pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1220 , from 2) a second CPR determined distance between the transmitting antenna of the TCR RF Transponder device  1210  and a second receiving antenna of the pair of receiving antennae of at least three receiver antennae of the TCR RF Originator device  1220 . 
     The method further includes where determining the three-dimensional position of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220  by determining at least two of three angles of the TCR RF Transponder device  1210  relative to the coordinate frame  1222  of the TCR RF Originator device further comprises the method of calculating an angle of the TCR RF Transponder device  1210  relative to the coordinate frame  1222  of the TCR RF Originator device by determining a quotient of the determined CPD over a baseline distance between the pair of receiving antennae of the TCR RF Originator device. 
     The method further comprises providing each antenna of the TCR Transponder device  1210  and TCR Originator device  1220  constellations of antennae as circular polarized antennae. 
     The method further comprises providing the first constellation of antennae  1212  as one of linear polarized antennae or circular polarized antennae, and the second constellation of antennae  1224  as the other one of linear polarized antennae or circular polarized antennae. 
     II.D. HMD, Controller and AR/VR Controller 
       FIG.  14    illustrates a schematic diagram of another illustrative embodiment of a position and orientation determining system  1400  comprising a TCR Originator device  1410 , a TCR Transponder device  1420  and an external TCR processing device  1430 , where 1) a position and orientation of the TCR Transponder device  1420  is calculated relative to a reference frame of the TCR Originator device  1410 , and 2) a position and orientation of the TCR Originator device  1410  is further determined relative to a reference frame of the external TCR processing device  1430 . 
     A TCR Transponder  1410  comprises an antenna pair  1412  and IMU and/or magnetometer  1414  similar to the illustration in  FIG.  4   . A TCR Originator  1420  comprises an antenna array  1424  similar to the illustration in  FIG.  5   , a graphical display  1426  and an IMU and/or magnetometer  1428 . TCR Originator  1420  additionally includes a TCR Originator coordinate frame  1422 , having planes XY, YZ, and XZ to which the TCR Transponder  1410  is oriented against. A reference TCR  1430  includes a reference TCR coordinate frame having axes Xref, Yref and Zref, and a reference TCR antenna array  1434 . 
       FIG.  15    and  FIG.  16    further illustrate a logic flowchart describing method of determining a position and orientation of an object comprising providing  1500  a TCR radio frequency (RF) Originator device  1410  including a first constellation of antennae  1412  including at least two receiving antennae and at least one transmitting antenna, a first radio unit in communication with the first constellation of antennae  1412 . 
     The method further comprises providing  1502  a TCR RF Originator device including a second constellation of antennae  1424  including at least three receiving antennae and at least one transmitting antenna, a second radio unit in communication with the second constellation of antennae  1424 , a processor in communication with the second radio unit and the second constellation of antennae  1424 , and a graphical display  1426 . 
     The method further comprises determining  1504  a first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device relative to the TCR RF Originator device  1420  based on calculating a first carrier phase difference (CPD) measurement of phase difference based on signals received from the TCR RF Transponder device  1410  between each discrete pair of receiving antennae of the at least three receiver antennae of the TCR RF Origination  1420  device. 
     The method further comprises providing  1506  a reference TCR RF device  1430  including a third constellation of antennae  1434  including at least three receiving antennae and at least one transmitting antenna, a third radio unit in communication with the third constellation of antennae, a processor in communication with the third radio unit and the third constellation of antennae  1434 . 
     The method further comprises determining  1508  a second three-dimensional position and second three-axis angular orientation of the TCR RF Origination device  1420  relative to the reference TCR RF device  1430  based on calculating a second CPD measurement of phase difference based on signals received from the TCR RF Origination device  1420  between each discrete pair of receiving antennae of the at least three receiver antennae of the reference TCR RF device  1430 . 
     The method further comprises rendering  1510  an image on the graphical display  1426  of the TCR RF Origination device  1420  in one a virtual reality or an augmented realty environment based on the determined first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1410  relative to the TCR RF Origination device  1420 , and the second determined three-dimensional position and second three-axis angular orientation of the TCR RF Origination device  1420  relative to the reference TCR RF device  1430 . 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1410  relative to the TCR RF Origination device  1420  based on unwrapped carrier phase range (CPR) samples. 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1410  relative to the TCR RF Originator device  1420  by determining at least two of three angles of the TCR RF Transponder device relative to a coordinate frame (XY, XZ, YZ) of the TCR RF Originator device  1420  based on determining CPD measurement of phase difference by subtracting 1) a first carrier phase range (CPR) determined distance between a transmitting antenna of the TCR RF Transponder device and a first receiving antenna of a pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1420 , from 2) a second CPR determined distance between the transmitting antenna of the TCR RF Transponder device  1410  and a second receiving antenna of the pair of receiving antennae of at least three receiver antennae of the TCR RF Originator device  1420 . 
     The method of determining a position and orientation of an object wherein determining the three-dimensional position of the TCR RF Transponder device relative to the TCR RF Originator device  1420  by determining at least two of three angles of the TCR RF Transponder device  1410  relative to the coordinate frame of the TCR RF Originator device  1420  further comprises calculating an angle of the TCR RF Transponder device  1410  relative to the coordinate frame of the TCR RF Originator device  1420  by determining a quotient of the determined CPD over a baseline distance between the pair of receiving antennae of the TCR RF Originator device  1420 . 
     The method further comprises providing each antenna of the first  1412  and second  1424  constellations of antennae as circular polarized antennae. 
     The method further comprises providing the first constellation of antennae  1412  as one of linear polarized antennae or circular polarized antennae, and the second constellation of antennae  1424  as the other one of linear polarized antennae or circular polarized antennae. 
     II.E. HMD, Controller and GPS Constellation 
       FIG.  17    illustrates a schematic diagram of another illustrative embodiment of a position and orientation determining system  1700  comprising a TCR Originator device  1710 , a TCR Transponder device  1720  and an external reference frame  1730 , where 1) a position and orientation of the TCR Transponder device  1720  is calculated relative to a reference frame of the TCR Originator device  1710 , and 2) a position and orientation of the TCR Originator device  1710  is further determined relative to the external reference frame  1730 . 
     A TCR Transponder  1710  comprises an antenna pair  1712  and IMU and/or magnetometer  1714  similar to the illustration in  FIG.  4   . A TCR Originator  1720  comprises an antenna array  1724  similar to the illustration in  FIG.  5   , a graphical display  1726 , an IMU and/or magnetometer  1728  and a GPS receiver  1730 . TCR Originator  1720  additionally includes a TCR Originator coordinate frame  1722 , having planes XY, YZ, and XZ to which the TCR Transponder  1710  is oriented against. The position and orientation determining system  1700  additionally includes an external coordinate frame  1740  having axes Xext, Yext and Zext against which the TCR Originator device  1720  is positioned and oriented with respect to. The external coordinate frame  1740  may include a Global Positioning System (GPS) coordinate reference frame. 
       FIG.  18    and  FIG.  19    further illustrate a logic flowchart describing method of determining a position and orientation of an object comprising providing  1800  a TCR radio frequency (RF) Transponder device  1710  including a first constellation of antennae  1712  including at least two receiving antennae and at least one transmitting antenna, a first radio unit in communication with the first constellation of antennae  1712 . 
     The method further comprises providing  1802  a TCR RF Originator device  1720  including a second constellation of antennae  1724  including at least three receiving antennae and at least one transmitting antenna, a second radio unit in communication with the second constellation of antennae  1724 , a processor in communication with the second radio unit and the second constellation of antennae  1724 , a graphical display  1726 , a global positioning system (GPS) receiver  1730 . 
     The method further comprises determining  1804  a first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1710  relative to the TCR RF Originator device  1720  based on calculating a first carrier phase difference (CPD) measurement of phase difference based on signals received from the TCR RF Transponder device  1710  between each discrete pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1720 . 
     The method further comprises determining  1806  a second three-dimensional position of the TCR RF Originator device  1720  relative to an external coordinate system based on receiving a signal at the GPS receiver. 
     The method further comprises determining  1808  a second three-axis angular orientation of the TCR RF Originator device  1720  based on receiving a signal from the IMU  1714  of the TCR RF Originator device  1720 . 
     The method further comprises rendering  1810  an image on the graphical display  1826  of the TCR RF Originator device  1720  in one a virtual reality or an augmented realty environment based on the determined first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1710  relative to the TCR RF Originator device  1720 , and the second determined three-dimensional position and second three-axis angular orientation of the TCR RF Originator device  1720 . 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1710  relative to the TCR RF Originator device  1720  based on unwrapped carrier phase range (CPR) samples. 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1710  relative to the TCR RF Originator device  1720  by determining at least two of three angles of the TCR RF Transponder device  1710  relative to a coordinate frame (XY, XZ, YZ) of the TCR RF Originator device  1720  based on determining CPD measurement of phase difference by subtracting 1) a first carrier phase range (CPR) determined distance between a transmitting antenna of the TCR RF Transponder device  1710  and a first receiving antenna of a pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1720 , from 2) a second CPR determined distance between the transmitting antenna of the TCR RF Transponder device  1710  and a second receiving antenna of the pair of receiving antennae of at least three receiver antennae of the TCR RF Originator device  1720 . 
     The method of determining a position and orientation of an object where determining the three-dimensional position of the TCR RF Transponder device  1710  relative to the TCR RF Originator device  1720  by determining at least two of three angles of the TCR RF Transponder device  1710  relative to the coordinate frame of the TCR RF Originator device  1720  further comprises calculating an angle of the TCR RF Transponder device  1710  relative to the coordinate frame  1722  of the TCR RF Originator device  1720  by determining a quotient of the determined CPD over a baseline distance between the pair of receiving antennae of the TCR RF Originator device  1720 . 
     The method further comprises providing each antenna of the first  1714  and second  1724  constellations of antennae as circular polarized antennae. 
     The method further comprises providing at least one but not all of the first  1714  or second  1724  constellations of antennae as linear polarized antennae, and providing the remainder of the first  1714  or second  1724  constellations of antennae as circular polarized antennae. 
     Regarding the routines presented in the methods illustrated in  FIG.  13   ,  FIGS.  15 - 16   , and  FIGS.  18 - 19   , it should be appreciated that while they are expressed with discrete steps, these steps should be viewed as being logical in nature and may or may not correspond to any actual, discrete steps. Moreover, while these routines are set forth in a particular order in carrying out various functionality, the order that these steps are presented should not be construed as the only order in which the various steps may be carried out in their respective routines. Further, those skilled in the art will appreciate that logical steps may be combined together or be comprised of multiple steps. 
     Still further, while novel aspects of the disclosed subject matter are expressed in routines or methods, this functionality may also be embodied on computer-readable media. As those skilled in the art will appreciate, computer-readable media can host computer-executable instructions for later retrieval and execution. When executed on a computing device, the computer-executable instructions carry out various steps or methods. Examples of computer-readable media include, but are not limited to: optical storage media such as digital video discs (DVDs) and compact discs (CDs); magnetic storage media including hard disk drives, floppy disks, magnetic tape, and the like; memory storage devices such as random access memory (RAM), read-only memory (ROM), memory cards, thumb drives, and the like; cloud storage (i.e., an online storage service); and the like. For purposes of this document, however, computer-readable media expressly excludes carrier waves and propagated signals. 
       FIG.  20    is a block diagram illustrating an exemplary computer system configured to determine a position and orientation of an object. In particular, in order to provide additional context for aspects of the disclosed subject matter,  FIG.  20    and the following description are intended to provide a brief, general description of a suitable computing system  2000  in which the various aspects may be implemented. 
     The computing system  2000  includes a processor (or processing unit)  2002  and a memory  2004  interconnected by way of a system bus  2010 . As those skilled in the art will appreciate, the processor executes instructions retrieved from the memory  2004  in carrying out various functions and, particularly, determine a position and orientation of an RF Controller device with respect to an RF Originator device. The processor may be comprised of any of various commercially available processors such as single-processor, multi-processor, single-core units, and multi-core units. Moreover, those skilled in the art will appreciate that the novel aspects of the disclosed subject matter may be practiced with other computer system configurations, including but not limited to: mini-computers; mainframe computers, personal computers (e.g., desktop computers, laptop computers, tablet computers, etc.); handheld computing devices such as smartphones, personal digital assistants, and the like; microprocessor-based or programmable consumer electronics; and the like. 
     The memory  2004  may be comprised of both volatile memory  2006  (e.g., random access memory or RAM) and non-volatile memory  2008  (e.g., ROM, EPROM, EEPROM, etc.) Moreover, the memory  2004  may obtain data and/or executable instructions (especially within the volatile memory  2006 ) from the data storage subsystem  2018  by way of the system bus  2010 . Moreover, a basic input/output system (BIOS) can be stored in the non-volatile memory  2008  and conclude the basic routines that facilitate the communication of data and signals between complements within the computing system  2000 , such as during startup of the computing system. The volatile memory  2006  may also include a high-speed RAM such as static RAM for caching data. 
     The system bus  2010  provides an interface for system components to enter communicate. The system bus  2010  can be of any of several types of bus structures that can interconnect the various components (both internal and external components). The computer system  2000  further includes a network communication subsystem  2012  for interconnecting with other computers and devices on a computer network. The network communication subsystem  2012  may be configured to communicate with an external network via a wired connection, a wireless connection, or both. The network communication subsystem  2012  may additionally be configured to communicate with an IMU, a magnetometer, and/or a GPS receiver (not shown in  FIG.  20   ). 
     Also included in the computer system  2000  is a display subsystem  2014 . It is through the display subsystem  2014  that the computer system presents a graphical display in an AR/VR environment. Further still, the computer system  2000  includes a user interface subsystem  2016  through which the computer system obtains user input. The user interface subsystem  2016  provides the interface with various user interface mechanisms including, but not limited to: voice input/output; visual recognition systems; keyboards; touchpads; touch- or gesture-based enabled surfaces (including display surfaces); pointing devices; and the like. Indeed, while the display subsystem  2014  has been individually called out as part of the computer system  2000 , those skilled in the art will appreciate that in many configurations the display subsystem  2014  is part of the user interface subsystem  2016 . 
     Additionally, a Radio Frequency (RF) transceiver unit  2030  may additionally be in communication with the system bus  2010  and/or network communication subsystem  2012  to communicate and receiver information to and from the antenna array  2032 . 
     The data storage subsystem  2018  provides an additional storage system in addition to the memory  2004 . Within the data storage subsystem  2018  can be found the operating system  2020  for the computer system  2000 , applications  2024  (which may include one or more applications that are configured to render a graphical image in a display device based on the position and orientation of the TCR Transponder device); executable modules  2022 ; as well as data  2026 . Indeed, the determination of a position and an orientation, is not limited to the instructions necessary to implement the functionality outlined in regard to routines illustrated in  FIGS.  13 ,  15 - 16  and  18 - 19    described above, and  FIGS.  27 ,  29 - 30  and  32 - 33    described below. 
     It should be appreciated, of course, that many of the components and/or subsystems described as being part of the computer system  2000  should be viewed as logical components for carrying out various functions of a suitably configured computer system. As those skilled in the art appreciate, logical components (or subsystems) may or may not correspond directly in a 1:1 manner to actual components. Moreover, in an actual illustrative embodiment, these components may be combined together or broke up across multiple actual components. 
     The illustrative embodiments presented herein to enable six-degrees of freedom tracking for AR/VR environments provide for the following key features: smooth and accurate tracking of the controller&#39;s position and attitude relative to another sensor system, e.g., the TCR HMD device  120 , and/or relative to the world and real objects in the immediate environment; low latency and real-time tracking; robustness of tracking performance when line of sight between the TCR HMD device  120  and controller is obscured or blocked; and lower system and component cost and complexity suitable for commercial applications. 
     By utilizing RF sensing, the above presented illustrative embodiments improve upon existing location determining systems by 1) reducing dependence on strict line of sight, as RF line of sight is more forgiving than that required by camera, optical, and laser based approaches; 2) improving performance in different environments, as camera, optical, and laser based approaches are sensitive to ambient lighting conditions and sunlight; 3) combining wireless data communications between Controller(s) and TCR HMD device  120  with sensor measurements, thereby reducing the need for a separate data communication link; and 4) improves location and orientation tracking by providing simpler, lower power sensor fusion resulting in better performance sensor observations rather than computational heavy camera/vision location determining systems. 
     In a second embodiment, illustrated in the following  FIGS.  21 - 33   , three degree-of-freedom positioning may be accomplished using a single antenna in the TCR Controller device  110 ′ rather than a pair of antennae in the TCR Controller device  110  as described in  FIGS.  1 - 19   . In the following description, similar reference numbers will be used in the description of the second embodiment to identical elements described in the first embodiment for consistency. 
     Generally, the second embodiment is suitable for estimating full 3-DOF position estimation of a second embodiment TCR Controller  110 ′ relative to the TCR HMD  120  given a single RX/TX antenna on the TCR Controller  110 ′. To relate the coordinate frames of the TCR Controller  110 ′ and TCR HMD  120 , the position of the TCR HMD  120  must be known, measured, estimated, or remain fixed relative to a given local coordinate frame. For example, a single TCR Controller antenna is measured by a plurality of pairs of antennae on the TCR HMD  120  to obtain CPD measurements between discrete antenna pairs as previously disclosed above in the first embodiment illustrated in  FIGS.  1 - 19   . 
     The three-dimensional (3D) position of the TCR Controller  110 ′ relative to the TCR HMD  120  may be calculated by two methods: 
     1) Triangulation: a 3D-position of the TCR Controller  110 ′ may be computed by simply calculating the intersection of three planes passing through the TCR HMD  120  antenna locations at angles computed from CPD measurements taken between each pair of antennae on the TCR HMD  120 ; or 
     2) Triangulateration: a 3D-position may be computed directly from the distance between the TCR Controller  110 ′ and TCR HMD  120  (CPR or baseband range measurement), and two of the three angles in the TCR HMD  120  coordinate frame (XY, XZ, YZ) that can be computed from the CPD measurements taken between each pair of antennae on the TCR HMD  120 . This latter method simply measures the position via a distance and a bearing from a known position. 
     The TCR HMD  120  measurements of CPD from 3 antennae on the TCR HMD  120  and CPR measurement between the antennae on the TCR HMD  120  and the single antenna on the TCR Controller  110 ′ may be used to calculate the distance and angles. 
     Additional CPD measurements and antennas may be used to over-determine and improve the positioning solution. Additional TCR measurements (Baseband Range, CPV, TDR, etc.) may be used to further aid the positioning solution but are not required. 
     Furthermore, in an additional alternative embodiment, if the orientation of the TCR HMD  120  is known, may be measured or estimated, or remains fixed relative to the local level frame, then by adding an IMU to the TCR Controller  110 ′, the 3D-orientation of the TCR Controller  110 ′ may be estimated separately or together with the above-identified determined position in a single fusion method to obtain a full six degree-of-freedom determination of the TCR Controller  110 ′ with respect to the TCR HMD  120 . 
       FIG.  21   , similar to  FIG.  2   , illustrates a second embodiment of a logical element schematic of a TCR Controller device  100 ′. Particularly,  FIG.  21    illustrates a logical element schematic  200 ′ of a TCR Controller device  110 ′ of the second embodiment comprising a plurality of physical sensors  210  that collect raw data observables and includes a single Rx/Tx antenna  212 ′, an IMU device  218  and/or a GPS device  220 . 
       FIG.  22   , similarly to  FIG.  4   , illustrates a second embodiment of a schematic diagram of an illustrative sensor hardware on a TCR Controller device  100 ′. Particularly,  FIG.  22    illustrates a schematic diagram  400 ′ of the second embodiment of sensor hardware on the TCR Controller device  110 ′. The TCR Controller device  110 ′ may include a single Tx/Rx antenna  402 ′. The TCR Controller device  110  may also include an IMU  420  and magnetometer  430  for providing raw data observables to determine orientation/attitude with respect to the TCR HMD device  120  as described above. 
       FIG.  23   , similarly to  FIG.  9   , illustrates a second embodiment of a signal processing schematic diagram representing signal paths of raw data observable measurements and their corresponding processing via sensor fusion algorithms into a fused data output. Particularly,  FIG.  23    illustrates a signal processing schematic diagram  900 ′ representing signal paths of raw data observable measurements  910 ′ and their corresponding processing via sensor fusion algorithms  940  into a fused data output  960 . Software for sensor fusion for the illustrative embodiments described herein may occur on an embedded processor, digital signal processor (DSP), field programmable gate array (FPGA), or application-specific integrated circuit (ASIC) that is present on the TCR Controller device  110 ′, TCR HMD device  120 , and/or an external host PC or computing device. 
     Raw data sensor observable measurements  910 ′ at either the TCR Controller device  110 ′ and/or the TCR HMD device  120  may be taken from three sources: an IMU  912 , TCR antenna(e) providing CPR and CPD measurements  914 ′, and TCR antenna(e) providing CPV measurements  924 . 
     CPR or Baseband Range and HMD CPD  914 ′ logic element obtains CPR and CPD observable data from antenna signals on the TCR HMD device  120  based on signals received from the single RX/TX antenna of the TCR Controller  110 ′. Particularly, CPD observable data is collected from discrete CPD antenna pairs  916  of the TCR HMD device  120 , for example, represented by a first antenna  918  and a second corresponding antenna  920  of a CPD antenna pair  916 . Antennae baseline distance  922  between each corresponding antenna pair  918 ,  920  of the TCR HMD device  120  is also collected to be used to calculate the CPD observable data. CPR/CPD data  924 . 1 ′ may be sent to initialization algorithm  942  of position and orientation/attitude and the same CPR/CPD data  914 . 2 ′ may be sent to the TCR pre-filter algorithm  948 . TCR pre-filter data  948 . 1 ′ is subsequently sent to the EKF  950  for further filtering based on CPV data  924 . 1 . Thereafter, EKF filter algorithm  950  outputs EKF filtered data  950 . 1 ′ to provide a fused data output  960  comprising six-degrees of freedom position and orientation output  962 . 
       FIGS.  24  and  25   , similar to  FIGS.  10  and  11   , illustrate a second embodiment of a communication sequence between corresponding TCR devices of the position and orientation determining system  100 ′ as shown from  FIGS.  21  to  23   . 
       FIG.  24   , similarly to  FIG.  10   , illustrates a second embodiment of a first communication sequence between corresponding TCR devices of the position and orientation determining system. Particularly,  FIG.  24    illustrates a second illustrative embodiment of a communication sequence originated by a TCR Originator device  1000 , e.g., TCR HMD device  120 , and a TCR Transponder device  1060 ′, e.g., TCR Controller device  110 ′ having a single antenna. First, the TCR Originator device  1000  activates a transmitter antenna, e.g., ANT 1 TX/RX  1012 , to transmit a preamble and a data payload via a carrier frequency at operation  1012 . 1  to the TCR Transponder  1060 ′ for reception by the single receiving antenna thereon, e.g., ANT TX/RX  1072 ′. 
     Upon receiving the preamble and data payload from the TCR Originator  1000 , the TCR Transponder  1060 ′ forwards the antenna received preamble and data payload to the raw data observable measurements unit  1080  for calculation of CPR, CPD and CPV observable measurements in addition to IMU and/or magnetometer  1076  data, and/or GPS  1078  data. These data are then processed by the sensor fusion algorithms  1082 , to produce baseband ranging data including master clock number counts, clock dynamic measurements and time-of-flight data, CPR data, CPV data, CPD data and orientation data based on the IMU/MAG device  1076 . The data after passing through the EKF (e.g., EKF  950  in  FIG.  23   ) is then output as fused data output  1084 . 
       FIG.  25   , similarly to  FIG.  11   , illustrates a second embodiment of a second subsequent communication sequence between corresponding TCR devices of the position and orientation determining system. Particularly,  FIG.  25    illustrates a second illustrative embodiment of a communication sequence where a TCR Transponder device  1060 ′ responds to the communication received from the TCR Originator device  1000  of  FIG.  24   . The fused data output  1084  previously output by the sensor fusion algorithms  1082  is sent as a data payload with a TCR Transponder specific preamble to the transmitter antenna of the TCR Transponder, e.g., ANT TX/RX  1072 ′. The transmitting antenna transmits the TCR Transponder  1060  preamble and data payload  1072 . 1 ′ to any receiving antennae of the TCR Originator device  1000 , e.g., in this illustration, ANT1 to ANT4, designated by reference numbers  1012 ,  1014 ,  1016  and  1018 . 
     In a manner similar to the first embodiment illustrated in  FIG.  9   , the fused data output  1034  at operation  1034 . 1 ′ may be output to a display driver  1040  integral with the TCR Originator device  1000  to process graphic display information for presentation to a graphic display  1050  integrated with or for use in conjunction with the TCR Originator device  1000 . 
     In an alternative illustrative embodiment, the fused data output  1034  at operation  1034 . 2 ′ may be output to a remote AR/VR system processor  1090  that may further process the fused data output  1034  and at operation  1090 . 1 ′ and return data to the display driver  1040  of the TCR Originator device  1000  for presentation to the graphic display  1050 . 
       FIG.  26   , similarly to  FIG.  12   , illustrates a second embodiment of a schematic diagram of one illustrative embodiment of a position and orientation determining system comprising a TCR Transponder device and a TCR Originator device, where a position and orientation of the TCR Transponder device is calculated relative to a reference frame of the TCR Originator device. Particularly,  FIG.  26    illustrates a schematic diagram of one illustrative embodiment of a position and orientation determining system  1200 ′ comprising a TCR Transponder device  1210 ′ and a TCR Originator device  1220 , where a position and orientation of the TCR Transponder device  1210 ′ is calculated relative to a reference frame of the TCR Originator device  1220 . 
     A TCR Transponder device  1210 ′ comprises a single antenna  1212 ′ and IMU and/or magnetometer  1214  similar to the illustration in  FIGS.  21 - 22   . A TCR Originator device  1220  comprises an antenna array  1224  similar to the illustration in  FIG.  5    and a graphical display  1226 . TCR Originator device  1220  additionally includes a TCR Originator coordinate frame  1222 , having planes XY, YZ, and XZ to which the TCR Transponder device  1210 ′ is oriented against. 
       FIG.  27   , similarly to  FIG.  13   , illustrates a second embodiment of a logic flowchart describing a method of determining a position and orientation of the TCR Transponder device relative to the TCR Originator device. Particularly,  FIG.  27    further illustrates a logic flowchart describing a method of determining a position and orientation of the TCR Transponder device  1210 ′ (substantially equivalent to the TCR controller  110 ′ of illustrated in  FIGS.  21 - 22  and  24 - 25   ), relative to the TCR Originator device  1220 , where the method comprises providing  2700  a TCR radio frequency (RF) Transponder device  1210  including a first constellation of antennae  1212  including at least two receiving antennae and at least one transmitting antenna, a first radio unit in communication with the first constellation of antennae  1212 . 
     The method further comprises  2702  providing a TCR RF Originator device  1220  including a second constellation of antennae  1224  including at least three receiving antennae and at least one transmitting antenna, a second radio unit in communication with the second constellation of antennae  1224 , a processor in communication with the second radio unit and the second constellation of antennae  1224 , and a graphical display  1226 . 
     The method further comprises determining  2704  a three-dimensional position and three-axis angular orientation of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220  based on calculating a carrier phase difference (CPD) measurement of phase difference based on signals received from the TCR RF Originator device  1220  between each discrete pair of receiving antennae of the at least three receiver antennae of the TCR RF device  1220 . 
     The method further comprises rendering  2706  an image on a graphical display  1226  of the TCR RF Originator device  1220  in one a virtual reality or an augmented realty environment based on the determined three-dimensional position of the TCR RF Transponder device  1210  relative to the TCR RF Originator device  1220 . 
     Wherein the method including determining, by the processor of the second RF device  1220 , the three-dimensional position of the first RF device  1210 ′ relative to the second RF device, further includes computing an intersection of three planes passing through each of the at least three receiving antenna locations  1224  based on computing three angles in the second RF device  1220  coordinate frame (XY, XZ and YZ)  1222 . 
     Wherein the method including determining; by the processor of the second RF device  1220 , the three-dimensional position of the first RF device  1210 ′ relative to the second RF device  1220  further includes computing a distance between the first RF device  1210 ′ and the second RF device  1220 . 
     Wherein the method of computing the distance between the first RF device  1210 ′ and the second RF device  1220  further includes measuring a carrier phase range (CPR) measurement of the distance between the transacting first RF  1210 ′ and second RF  1220  devices. 
     Wherein the method of computing the distance between the first RF device  1210 ′ and the second RF device  1220  further includes measuring a baseband code phase range measurement of round-trip RF time-of-flight (TOF) representing the distance between the transacting first RF  1210 ′ and second RF  1220  devices. 
     Wherein the method of determining CPD measurement of phase difference further includes subtracting a first carrier phase measured from the at least one antenna  1212 ′ of the first RF device  1210 ′ at a first receiving antenna of a pair of the at least three receiving antennae  1224  of the second RF device  1220 , from a second carrier phase measured from the at least one antenna  1212 ′ of the first RF device at a second receiving antenna of the pair of the at least three receiving antennae  1224  of the second RF device  1220 . The method further includes calculating an angle of bearing to the first RF device  1210 ′ relative to the coordinate frame  1222  of the second RF device  1220  by determining a quotient of the determined CPD measurement over a baseline distance between the pair of the at least three receiving antennae  1224  of the second RF device  1220 . 
     The method of determining the three-dimensional position further includes providing the first RF device  1210 ′ with an inertial measurement unit (IMU)  1214 ; and determining a three-axis angular orientation of the first RF device  1210 ′ relative to the second RF device  1220  based on estimating a direction of a gravity vector generated by the IMU  1214 . 
       FIG.  28   , similarly to  FIG.  14   , illustrates a second embodiment of a schematic diagram of another illustrative embodiment of a position and orientation determining system comprising a TCR Originator device  1420 , a TCR Transponder device  1410 ′, (substantially equivalent to the TCR controller  110 ′ of illustrated in  FIGS.  21 - 22  and  24 - 25   ), and an external TCR processing device  1430 . Particularly,  FIG.  28    illustrates a schematic diagram of another illustrative embodiment of a position and orientation determining system  1400 ′ comprising a TCR Originator device  1410 ′, a TCR Transponder device  1420  and an external TCR processing device  1430 , where 1) a position and orientation of the TCR Transponder device  1420  is calculated relative to a reference frame of the TCR Originator device  1410 ′, and 2) a position and orientation of the TCR Originator device  1410 ′ is further determined relative to a reference frame of the external TCR processing device  1430 . 
     A TCR Transponder  1410 ′ comprises a single antenna  1412 ′ and IMU and/or magnetometer  1414  similar to the illustration in  FIGS.  21 - 22   . A TCR Originator  1420  comprises an antenna array  1424  similar to the illustration in  FIG.  5   , a graphical display  1426  and an IMU and/or magnetometer  1428 . TCR Originator  1420  additionally includes a TCR Originator coordinate frame  1422 , having planes XY, YZ, and XZ to which the TCR Transponder  1410 ′ is oriented against. A reference TCR  1430  includes a reference TCR coordinate frame having axes Xref, Yref and Zref, and a reference TCR antenna array  1434 . 
       FIGS.  29 - 30   , similarly to  FIGS.  15 - 16   , illustrate a second embodiment of a logic flowchart describing method of determining a position and orientation of an object in accordance with the illustration of and corresponding description of  FIG.  28   . Particularly,  FIGS.  29 - 30    further illustrate a logic flowchart describing method of determining a position and orientation of an object comprising providing  2900  a TCR radio frequency (RF) Transponder device  1410 ′ including an antenna  1412 ′ that may be both a receiving and a transmitting antenna, and a first radio unit in communication with the first antenna  1412 ′. 
     The method further comprises providing  2902  a TCR RF Originator device  1420  including a second constellation of antennae  1424  including at least three receiving antennae and at least one transmitting antenna, a second radio unit in communication with the second constellation of antennae  1424 , a processor in communication with the second radio unit and the second constellation of antennae  1424 , and a graphical display  1426 . 
     The method further comprises determining  2904  a first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1410 ′ relative to the TCR RF Originator device  1420  based on calculating a first carrier phase difference (CPD) measurement of phase difference based on signals received from the TCR RF Transponder device  1410 ′ between each discrete pair of receiving antennae of the at least three receiver antennae of the TCR RF Origination  1420  device. 
     The method further comprises providing  2906  a reference TCR RF device  1430  including a third constellation of antennae  1434  including at least three receiving antennae and at least one transmitting antenna, a third radio unit in communication with the third constellation of antennae, a processor in communication with the third radio unit and the third constellation of antennae  1434 . 
     The method further comprises determining  2908  a second three-dimensional position and second three-axis angular orientation of the TCR RF Origination device  1420  relative to the reference TCR RF device  1430  based on calculating a second CPD measurement of phase difference based on signals received from the TCR RF Origination device  1420  between each discrete pair of receiving antennae of the at least three receiver antennae of the reference TCR RF device  1430 . 
     The method further comprises rendering  2910  an image on the graphical display  1426  of the TCR RF Origination device  1420  in one a virtual reality or an augmented realty environment based on the determined first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1410 ″ relative to the TCR RF Origination device  1420 , and the second determined three-dimensional position and second three-axis angular orientation of the TCR RF Origination device  1420  relative to the reference TCR RF device  1430 . 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1410 ′ relative to the TCR RF Origination device  1420  based on unwrapped carrier phase range (CPR) samples. 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1410 ′ relative to the TCR RF Originator device  1420  by determining at least two of three angles of the TCR RF Transponder device relative to a coordinate frame (XY, XZ, YZ) of the TCR RF Originator device  1420  based on determining CPD measurement of phase difference by subtracting 1) a first carrier phase range (CPR) determined distance between a transmitting antenna of the TCR RF Transponder device and a first receiving antenna of a pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1420 , from 2) a second CPR determined distance between the transmitting antenna of the TCR RF Transponder device  1410 ′ and a second receiving antenna of the pair of receiving antennae of at least three receiver antennae of the TCR RF Originator device  1420 . 
     The method of determining a position and orientation of an object wherein determining the three-dimensional position of the TCR RF Transponder device relative to the TCR RF Originator device  1420  by determining at least two of three angles of the TCR RF Transponder device  1410 ′ relative to the coordinate frame of the TCR RF Originator device  1420  further comprises calculating an angle of the TCR RF Transponder device  1410 ′ relative to the coordinate frame of the TCR RF Originator device  1420  by determining a quotient of the determined CPD over a baseline distance between the pair of receiving antennae of the TCR RF Originator device  1420 . 
     The method further comprises providing each antenna of the first  1412 ′ and second  1424  constellations of antennae as circular polarized antennae. 
     The method further comprises providing the first constellation of antennae  1412 ′ as one of linear polarized antennae or circular polarized antennae, and the second constellation of antennae  1424  as the other one of linear polarized antennae or circular polarized antennae. 
       FIG.  31   , similarly to  FIG.  17   , illustrates a second embodiment of a schematic diagram of another illustrative embodiment of a position and orientation determining system comprising a TCR Originator device, a TCR Transponder device and an external reference frame. Particularly,  FIG.  31    illustrates a schematic diagram of another illustrative embodiment of a position and orientation determining system  1700 ′ comprising a TCR Transponder device  1710 ′, (substantially equivalent to the TCR controller  110 ′ of illustrated in  FIGS.  21 - 22  and  24 - 25   ), a TCR Originator device  1720  and an external reference frame  1740 , where 1) a position and orientation of the TCR Transponder device  1710 ′ is calculated relative to a reference frame of the TCR Originator device  1720 , and 2) a position and orientation of the TCR Originator device  1720  is further determined relative to the external reference frame  1740 . 
     A TCR Transponder  1710 ′ comprises a single antenna  1712 ′ and an IMU and/or magnetometer  1714  similar to the illustration in  FIGS.  21 - 22   . A TCR Originator  1720  comprises an antenna array  1724  similar to the illustration in  FIG.  5   , a graphical display  1726 , an IMU and/or magnetometer  1728  and a GPS receiver  1730 . TCR Originator  1720  additionally includes a TCR Originator coordinate frame  1722 , having planes XY, YZ, and XZ to which the TCR Transponder  1710 ′ is oriented against. The position and orientation determining system  1700 ′ additionally includes an external coordinate frame  1740  having axes Xext, Yext and Zext against which the TCR Originator device  1720  is positioned and oriented with respect to. The external coordinate frame  1740  may include a Global Positioning System (GPS) coordinate reference frame. 
       FIGS.  32 - 33   , similarly to  FIGS.  18 - 19   , illustrate a second embodiment of a logic flowchart describing method of determining a position and orientation of an object in accordance with the illustration and corresponding description of  FIG.  31   . Particularly,  FIGS.  32  and  33    further illustrate a logic flowchart describing method of determining a position and orientation of an object comprising providing  3200  a TCR radio frequency (RF) Transponder device  1710 ′ including an antenna  1712 ′ that may be both a receiving and a transmitting antenna, and a first radio unit in communication with the antenna  1712 ′. 
     The method further comprises providing  3202  a TCR RF Originator device  1720  including a second constellation of antennae  1724  including at least three receiving antennae and at least one transmitting antenna, a second radio unit in communication with the second constellation of antennae  1724 , a processor in communication with the second radio unit and the second constellation of antennae  1724 , a graphical display  1726 , a global positioning system (GPS) receiver  1730 . 
     The method further comprises determining  3204  a first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1710 ′ relative to the TCR RF Originator device  1720  based on calculating a first carrier phase difference (CPD) measurement of phase difference based on signals received from the TCR RF Transponder device  1710 ′ between each discrete pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1720 . 
     The method further comprises determining  3206  a second three-dimensional position of the TCR RF Originator device  1720  relative to an external coordinate system based on receiving a signal at the GPS receiver. 
     The method further comprises determining  3208  a second three-axis angular orientation of the TCR RF Originator device  1720  based on receiving a signal from the IMU  1714  of the TCR RF Originator device  1720 . 
     The method further comprises rendering  3210  an image on the graphical display  1826  of the TCR RF Originator device  1720  in one a virtual reality or an augmented realty environment based on the determined first three-dimensional position and first three-axis angular orientation of the TCR RF Transponder device  1710 ′ relative to the TCR RF Originator device  1720 , and the second determined three-dimensional position and second three-axis angular orientation of the TCR RF Originator device  1720 . 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1710 ′ relative to the TCR RF Originator device  1720  based on unwrapped carrier phase range (CPR) samples. 
     The method further comprises determining the three-dimensional position of the TCR RF Transponder device  1710 ′ relative to the TCR RF Originator device  1720  by determining at least two of three angles of the TCR RF Transponder device  1710 ′ relative to a coordinate frame (XY, XZ, YZ) of the TCR RF Originator device  1720  based on determining CPD measurement of phase difference by subtracting 1) a first carrier phase range (CPR) determined distance between a transmitting antenna of the TCR RF Transponder device  1710 ′ and a first receiving antenna of a pair of receiving antennae of the at least three receiver antennae of the TCR RF Originator device  1720 , from 2) a second CPR determined distance between the transmitting antenna of the TCR RF Transponder device  1710 ′ and a second receiving antenna of the pair of receiving antennae of at least three receiver antennae of the TCR RF Originator device  1720 . 
     The method of determining a position and orientation of an object where determining the three-dimensional position of the TCR RF Transponder device  1710 ′ relative to the TCR RF Originator device  1720  by determining at least two of three angles of the TCR RF Transponder device  1710 ′ relative to the coordinate frame of the TCR RF Originator device  1720  further comprises calculating an angle of the TCR RF Transponder device  1710 ′ relative to the coordinate frame  1722  of the TCR RF Originator device  1720  by determining a quotient of the determined CPD over a baseline distance between the pair of receiving antennae of the TCR RF Originator device  1720 . 
     The method further comprises providing each antenna of the first  1714  and second  1724  constellations of antennae as circular polarized antennae. 
     The method further comprises providing at least one but not all of the first  1714  or second  1724  constellations of antennae as linear polarized antennae, and providing the remainder of the first  1714  or second  1724  constellations of antennae as circular polarized antennae. 
     Regarding the routines presented in the methods illustrated in  FIG.  13   ,  FIGS.  15 - 16   ,  FIGS.  18 - 19   ,  FIG.  27   ,  FIGS.  29 - 30    and  FIGS.  32 - 33    it should be appreciated that while they are expressed with discrete steps, these steps should be viewed as being logical in nature and may or may not correspond to any actual, discrete steps. Moreover, while these routines are set forth in a particular order in carrying out various functionality, the order that these steps are presented should not be construed as the only order in which the various steps may be carried out in their respective routines. Further, those skilled in the art will appreciate that logical steps may be combined together or be comprised of multiple steps. 
     While certain features of the described illustrative embodiments have been illustrated as described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the scope of the illustrative embodiments. It should be understood the illustrative embodiments described herein have been presented by way of example only, not limitation, and various changes in form and details may be made. Any portion of the apparatus and/or methods described herein may be combined in any combination, except mutually exclusive combinations. The illustrative embodiments described herein can include various combinations and/or sub-combinations of the functions, components and/or features of the different illustrative embodiments described.