Abstract:
The present invention provides operators the ability to follow a predetermined path and achieve desired digging depth by watching steering and elevation indicators of just one system. The indicators are activated by data derived from the interception of signals generated by a single laser transmitter and a receiver array mounted on the machine. The system according to the present invention uses the multiple, tilted fan beams provided by the laser transmitter to calculate elevation angle and azimuth of the tool carried by machine.

Description:
BACKGROUND OF THE INVENTION 
   The present invention relates generally to position indicating and guidance systems and in particular, to a control system and method providing positional and guidance information to a machine carrying a tool for movement along a predetermined path at a worksite using a single laser transmitter and a detector array. 
   Construction relies heavily on positioning data. Construction performance, in particular productivity and quality of work, is tied to the speed and accuracy of positioning methods being used. Standard surveying techniques are relatively slow, require highly skilled operators, and remain prone to human error. 
   In a prior art laser transmitter, a narrowly focused, horizontally rotating beam of laser energy is used to provide a reference plane. The rotating beam intercepts a vertically extending array of photodetectors in a laser receiver to mark the elevation of the receiver with respect to the laser beam. The array extends typically 4 to 8 inches. Accordingly, the available data is limited to elevation over a rather small vertical range, and thus due to plane tilting and alignment iteration, establishing grade with such a conventional laser system is time consuming. 
   In another prior art laser transmitter, planes of light are emitted, instead of just a line of light showing level. The planes of light provide enough angle information that an associated receiver can calculate plumb alignment, elevation, and slope to the transmitter. However, in both the former and latter systems, information regarding the relative distance and direction (azimuth) from the receiver to the transmitter is not established. 
   To establish distance and direction, machine operators typically follow pre-surveyed direction markings on the stakes, string lines, a laser beam from a pipe laser, or by triangulation using a second laser transmitter. Furthermore, in excavating operations, the conventional depth indicating system is a rotating laser plane with a single laser receiver to indicate if the vertically oriented boom and bucket are above, below or on the desired elevation, with or without grade. However, it is to be appreciated that the length of the photo-detection area of the single laser receiver limits the vertical operating range of such depth indicating systems to approximately ±2 and ±4 inches respectively. These narrow limits often result in the operator “searching for the beam” to regain depth indication. 
   Typically, direction of a machine, such as for example an excavator, is provided by pre-surveyed markings on stakes, string lines, or an additional laser transmitter, such as a pipe laser. However, these methods have known drawbacks. Line destruction resulting from construction site activity may result in digging delays, and using an additional laser is expensive. Furthermore, grade using a laser is established by sloping the laser energy plane until the sloped plane is pointed in the desired direction. This setup operation may require several checks, with an additional hand-held detector, and rotational iterations to achieve the desired grade. Accordingly, establishing distance, direction, and grade using a conventional laser system, stakes, string lines, pipe lasers, or a second transmitter is time consuming and adds additional costs. 
   SUMMARY OF THE INVENTION 
   It is against the above background, that the present invention provides a position indicating and guidance system providing at least depth and line information of a tool carried by a machine, such as for example, a scoop of an excavator or backhoe, or a bucket of a loader using a single laser transmitter and a receiver having a photodetector array. In one embodiment, the receiver provides integral grade and line indicators. Grade is simply set by entering it in the receiver, thereby eliminating the time consuming tilting and plane alignment required with conventional systems. In another embodiment, six degrees of positional information (x, y, z, pitch, roll, and yaw) is also provided by receiver from sensing the reference fans from the laser transmitter. 
   The present invention also provides the benefit of giving machine operators the ability to follow a predetermined path and achieve desired digging depth by watching steering and elevation indicators also provided to the receiver. The indicators of the position indicating system are activated by data derived from interception of signals generated by a single laser transmitter by the photodetector array. It is to be appreciated that because a photodetector array is used, the present invention provides the added benefit of increasing the vertical receiving range to meters, as opposed to the typical ±2 to 4 inches of vertical receiving range of a conventional laser receiver. As such, the present invention substantially reduces or eliminates the time need to deploy stakes and string lines, sync with the laser transmitter (i.e., beam searching), and the cost associated with using a second laser transmitter. 
   In one embodiment, a method for guiding a machine carrying a tool for movement along a predetermined path at a worksite is disclosed. The method comprises placing a fan-type laser transmitter at the worksite remote from the machine. The laser transmitter has an arbitrary reference direction and generates two fan-shaped laser beams. The method also includes sensing the two fan-shaped beams with at least four photodetectors fixed arbitrarily at known positions in a detector array having a three-dimensional shape. The detector array is placed at a known position on the machine. The method further includes setting a reference azimuth angle from the arbitrary reference direction into a control unit provided on the machine, the reference azimuth angle points in a direction parallel to the predetermined path, and computing a measured azimuth angle using information provided to the control unit by the detector array sensing the two fan-shaped beams. Additionally, the method includes determining position of the machine relative to the predetermined path via the control unit comparing the measured azimuth angle to the reference azimuth angle, and generating signals which help guide the machine along the predetermined path. 
   In another embodiment, a method for guiding a machine carrying a tool for movement along a predetermined path at a worksite is disclosed. The method comprises placing a fan-type laser transmitter at the worksite remote from the machine and on a reference line offset a distance from the predetermined path, the laser transmitter having an arbitrary reference direction, and setting a reference azimuth angle from the arbitrary reference direction into a control unit provided on the machine. The reference azimuth angle points in a direction parallel to the predetermined path. The method also includes establishing a desired grade by entering into the control unit a percent slope, the control unit converting the percent slope to an equivalent reference elevation angle, and receiving a measured azimuth angle and a measured elevation angle from the fan-type laser transmitter with a detector array. The detector array has a plurality of photodetectors geometrically arranged and spaced apart at known locations, and is mounted to the machine at a known location. The method further includes comparing the measured azimuth angle to the reference azimuth angle, comparing the measured elevation angle to the reference elevation angle, and generating signals which indicate that the tool is left, right or on the predetermined path, and that the tool is above, below or on the desired grade. The comparing and generating is performed by the control unit. 
   In still another embodiment, a control system to guide a machine carrying a tool for movement along a predetermined path at a worksite is disclosed. The control system comprises a fan-type laser transmitter which when used in the control system is placed in the worksite remote from the machine on a reference line parallel to the predetermined path and set-up in an arbitrary reference direction, and at least four photodetectors fixed arbitrarily at known positions in a detector array having a three-dimensional shape. The detector array is placed at a known position on the machine and configured to receive a measured azimuth angle from the fan-type laser transmitter when in operation. The system also includes a control unit provided on the machine and configured to store a reference azimuth angle from the arbitrary reference direction. The reference azimuth angle when stored in the control unit points in a direction parallel to the predetermined path. The control unit is configured to generate signals which indicate at least a position of the tool relative to the predetermined path by comparing the measured azimuth angle to the reference azimuth angle when in use. 
   These and other features and advantages of the invention will be more fully understood from the following description of the various embodiments of the invention taken together with the accompanying drawing. It is noted that the scope of the claims is defined by the recitations therein, and not by the specific discussion of features and advantages set forth in the present description. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The organization and manner of operation of the invention, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawing in which: 
       FIG. 1  is a schematic block diagram of one embodiment of a position indication system comprising a fan type laser transmitter and a receiver having a photodetector array according to the present invention. 
       FIG. 2  is diagrammatic side view of a conventional excavator mounting a photodetector array thereon and being oriented to receive signals from a fan-type laser transmitter according to the present invention. 
       FIG. 3  is a schematic diagram of one embodiment of a control unit used in the position indication system of the present invention. 
       FIG. 4  is a block diagram showing an overhead view of an excavation operation using a system according to the present invention. 
   

   DETAILED DESCRIPTION 
   While the invention may be susceptible to embodiment in different forms, there is shown in the drawings, and herein will be described in detail, specific embodiments with the understanding that the present disclosure is to be considered an exemplification of the principles of the invention, and is not intended to limit the invention to that as illustrated and described herein. 
   Skilled artisans appreciate that elements in the drawing are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the drawing may be exaggerated relative to other elements to help to improve understanding of the various embodiments of the present invention. 
     FIG. 1  shows generally one illustrative embodiment of a position indication system  10  according to the present invention. The present invention addresses all the problems mentioned in the background above by providing a single fan-type laser transmitter  12 , a detector array  14 , and a control unit  16 . The laser transmitter  12  is a conventional laser transmitter, such as sold by Trimble, Inc., under model number LS920, and provides a LED strobe  17  as well as at least two light planes  18   a  and  18   b , instead of just a line of light showing level. The generated LED strobe energy  17  and the light planes  18   a  and  18   b  provide enough angle information such that the control unit  16  can calculate azimuths and elevation angles to the laser transmitter  12  from detection information provided by each photodetector  20   a ,  20   b ,  20   c ,  20   d ,  20   e  of the detector array  14 . In one embodiment, the laser transmitter  12  may be self-leveling, and easily positioned at the worksite via a tripod. 
   As shown, the photodetectors  20   a - e  are spaced geometrically apart. In the illustrated embodiment shown by  FIG. 1 , the detector array  14  also comprises a mechanical mounting  22  to secure an array support frame  23  to a machine. The array support frame  23  comprising, such as for example, but not limited to, pipes  24 , pipe joiners  26 , and two-pipe cross joints  28 , for securing and maintaining the photo-detectors  20  in the desire geometrical shape are provided. The detector array  14  in the illustrated embodiment provides five photo-detectors  20   a - e , labeled as Det 1 , Det 2 , Det 3 , Det 4 , and Det 5 , respectively. In one embodiment, nominal positions of the photo-detectors  20   a - e  in x, y, and z coordinates are listed by Table 1. 
   
     
       
             
             
             
             
             
           
         
             
                 
               TABLE 1 
             
             
                 
                 
             
             
                 
               Detector 
               x 
               y 
               z 
             
             
                 
                 
             
           
           
             
                 
               Det1 
               −0.5 m 
               −0.5 m 
               0.0 m 
             
             
                 
               Det2 
                 0.5 m 
               −0.5 m 
               0.1 m 
             
             
                 
               Det3 
                 0.5 m 
                 0.5 m 
               0.0 m 
             
             
                 
               Det4 
               −0.5 m 
                 0.5 m 
               0.1 m 
             
             
                 
               Det5 
                 0.0 m 
                 0.0 m 
               1.0 m 
             
             
                 
                 
             
           
        
       
     
   
   It is to be appreciated that the positions of the photo-detectors  20   a - e  are within 0.2 mm one sigma tolerance in the x, y and z coordinates, or have a displacement of 0.3 mm one sigma tolerance from the nominal position by the design and construction method. Such tolerance is checked with a surveying instrument of the same accuracy of displacement of 0.3 mm one sigma tolerance or better. If desired, the surveyed positions may be used as nominal positions in the setup procedure of the position indication system  10 . 
   In the illustrated embodiment, the shape of the array support frame  23  and nominal positions of the detectors  20   a - e  are such that the line of sight view of more than one detector at any detector array orientation within x-axis rotation of ±45° and y-axis rotation of ±45° and z-axis rotation of ±180° will always be unblocked. It is to be appreciated that the detector  20   e  designated Det  5  will remain unblocked in all orientations of the detector array  14 . However, the differential displacement of detector on average per detector should not be more than 0.3 mm one sigma tolerance from the nominal position between 1 Hz and 80 Hz due to the vibration, resonance and flexure of the array when the array is subjected to the typical vibrations experienced on an excavating machine. In addition, the common displacement of detector should not be more than 10.0 mm one sigma tolerance from the nominal position between 0.1 Hz and 1 Hz due to the vibration, resonance and flexure of the array when the array is subjected to the typical vibrations experienced on an excavating machine. The photo-detectors  20   a - e  are also fixed to the array support frame  23  in a vertical orientation within ±3° accuracy. 
   The array support frame  23  should be mounted on a machine so as to allow unobstructed view of the detector array  14  at any orientation of excavating machine within x-axis rotation of ±45° and y-axis rotation of ±45° and z-axis rotation of ±180°. In one particular embodiment, which is illustrated by  FIG. 2 , the detector array  14  is mounted to a machine carrying a working implement or tool such as, for example, a bucket or backhoe. In the illustrated embodiment, it is to be appreciated that the pyramid if mounted on the cab, care must be taken to ensure that the roof will not block the lower rear detectors when the excavator is tilted upward in the direction of transmitter. In one embodiment, the array should be mounted at least 0.7 m above the roof of the cab to prevent blocking of the lower detector  20   a.    
   Referring now to  FIG. 3 , the control unit  16  is provided with integral detection and calculation electronics  30 , as well as position indication processing, hardware and software, which are generally indicated by symbol  32 . The control unit  16  provides pulse detection, azimuth and elevation angle processing, position determination, and display processing. A user-interface  34 , providing display and control input functions, is either integral with the control unit  16  or remotely connected thereto. A power supply  36 , either an integral battery or a machine power connection, powers the control unit  16  and all connected peripheral devices. Line and grade indicators  38  are also provided to the control unit  16  either on an integral display or on an optional remote display (not shown) via remote connections  40 . 
   As mentioned previously, the information provided from the combination of the laser transmitter  12 , detector array  14 , and control unit  16  are position, orientation, azimuth (heading), and elevation angles with the origin of the coordinate system centrally located in the rotor of the laser transmitter. As illustrated in  FIG. 2 , the LED generated strobe energy  17  and each laser fan beam  18  emanating from the laser transmitter  12  diverges with distance. This divergence provides a wide vertical operating range of a boom or dipper  42  of a machine or excavator  44  carrying a tool or bucket  46  which is measured in meters, not just a few inches, thereby eliminating the requirement of having to search for the beam in order to setup the position indication system  10 . 
   In the embodiment shown by  FIG. 2 , the system  10  is provided with a 0% grade setting, which represents a typical excavation operation working the ground  48 . It is to be appreciated that other grades settings typical in the art may also be used with the system. The dipper  42  of the excavator  44  is vertically oriented with the bucket  46  in the measurement position at the proper depth. Next, with reference made also to  FIG. 4  showing an overhead view of the excavation operation illustrated in  FIG. 2 , with the laser transmitter  12  arbitrarily (no rotational orientation required) positioned on a control line  50 , an azimuth angle  52  from an arbitrary reference direction  54  is set that points in the direction of the desired heading. One approach for setting the azimuth angle  52  is to position the detector array  14  over a distant point that is on the desired control line  50 , and press an ‘Establish Line’ button  56  on the control unit  16  ( FIG. 3 ). The control unit  16  stores the measured azimuth as the reference azimuth angle for the desired heading, which is displayed on a display  57  provided to the user interface  34 . The control unit  16  then compares the measured azimuth to the reference azimuth and error signals are sent to the indicators  38  to inform the operator that the machine is left, right or on line. The operator manually steers to correct the machine heading if it is not on line. Accordingly, the present invention eliminates the need for pre-surveyed stakes, string lines, and an additional laser. 
   To establish grade, the customer simply enters the percentage slope (grade) he wishes to follow using input buttons  59  provided also to the user interface  34 . The control unit  16  converts the grade setting to the equivalent reference elevation angle. The equivalent reference elevation angle is calculated as follows:
 
Elevation Angle=tan −1 (% Slope/100)  (1)
 
   During operation, the measured elevation angle is compared to the reference elevation angle by the control unit  16 . With the link lengths a, b, and c of the dipper stick  42  and buck  46  known, and their relative orientations α 1 , α 2 , and α 3  to each other and the machine  44  known via encoders  45 , providing angular and/or linear measurements therebetween, and being provided to the control unit  16  through the remote connections  40 , the bucket vertical position is computed and displayed on the indictors  38  by the control unit  16  as above, on or below grade. Accordingly, the operator increases or decreases the digging depth as required to achieve an “on grade” indication. 
   After line and grade have been set in the control unit  16 , the only remaining setup is to ‘Bench’ the system. This process calibrates the machine on grade elevation indication to be truly on grade. The dipper  42  is vertically positioned over a known elevation reference with the bucket  46  oriented for measurement. For example, an elevating tripod  60  may be used to support the transmitter  12 , wherein the transmitter&#39;s elevation is changed to achieve a detector “on grade” indication. After the above set procedures, the system  10  is now ready to use. 
   Experimental Test Data 
   The practically of using a single laser transmitter to determine location of the tool carried for movement on the excavator in a work environment is illustrated in the following experimental test data. It is to be appreciated that the test setup is one illustrative embodiment implementing the present invention. In the illustrated embodiment of  FIG. 3 , the laser transmitter  12  puts out fans  18   a  and  18   b  of light, instead of just a line of light showing level. The fans of light provide enough angle information that a receiver can calculate azimuth and elevation angles to the transmitter. For the test and in the illustrated embodiment, the detector array  14 , with the photo-detectors  20   a - e  ( FIG. 1 ), was provided in the shape of a pyramid where all sides are of a known equal length. However, it is to be appreciated that the photodetectors in other embodiments may be fixed arbitrarily at known positions in a detector array having any three-dimensional shape. To reduce eclipsing one detector by another, two opposite detectors on the bottom were 0.1 m higher than the other two detectors. Using azimuth and elevation angles from the five photo-detectors, mathematical theory shows that position from the transmitter is determined to within 6″ over 300 feet. 
   The RS232 port of each receiver was connected to a serial port to USB adaptor. The USB port of the adaptor was then connected to the laptop PC. This allows the angle data from the transmitter to the receiver detector to be concurrently collected and sent to the PC through the serial ports. Additionally, the transmitter used was a LS920 LaserStation3D self-leveling transmitter sold by Trimble, Sunnyville Calif. A program running in the control unit  16  was written to collect angle and position data from the pyramid detectors to display and store that data. 
   Test 
   During a test to determine feasibility and accuracy of the system, the pyramid array was mounted on a cart, and moved to a number of surveyed point locations. A transmitter, ATX2021A, was placed at a first origin plate of a known location. The transmitter characteristics are provided in Table 2. 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
               ATX2O21A transmitter file: ASD 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               PHI 1: 
               −0.5344294 
             
             
                 
               PHI 2: 
               0.5360861 
             
             
                 
               ALPHA 1: 
               1.5704627 
             
             
                 
               ALPHA 2: 
               1.5664547 
             
             
                 
               THETA OFFSET: 
               1.5657921 
             
             
                 
               SPEED: 
               40.5000000 
             
             
                 
               X: 
               0.0000000 
             
             
                 
               Y: 
               0.0000000 
             
             
                 
               Z: 
               0.0000000 
             
             
                 
               RX: 
               0.0000000 
             
             
                 
               RY: 
               0.0000000 
             
             
                 
               RZ: 
               −1.330782 
             
             
                 
                 
             
           
        
       
     
   
   During an initial setup at a second origin plate of a known position from the first origin plate, the measured position showed a difference of 0.2 m in x from the surveyed position. In order to absorb this error, the size of array was increased by 1.0044 m, wherein the transformed detector positions are provided in Table 3. 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 3 
             
             
                 
             
             
               Transformed Detector Positions 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               D1X: 
               −0.005089497 
             
             
                 
               D1Y: 
               0.010946387 
             
             
                 
               D1Z: 
               −0.003872116 
             
             
                 
               D2X: 
               0.706862597 
             
             
                 
               D2Y: 
               −0.726671158 
             
             
                 
               D2Z: 
               0.099140237 
             
             
                 
               D3X: 
               1.434281058 
             
             
                 
               D3Y: 
               0.005010147 
             
             
                 
               D3Z: 
               −7.03108E−06 
             
             
                 
               D4X: 
               0.700926356 
             
             
                 
               D4Y: 
               0.709703153 
             
             
                 
               D4Z: 
               0.098171957 
             
             
                 
               D5X: 
               0.714250253 
             
             
                 
               D5Y: 
               0.001011471 
             
             
                 
               D5Z: 
               1.011894954 
             
             
                 
                 
             
           
        
       
     
   
   The control line angle was adjusted to give 0.0 m in y at the first point location. The cart was then moved to the various surveyed point locations and the detector  1  position was vertically aligned to the plate on the floor visually by eye. At each surveyed point location, the detected output was then compared to survey information. The results are shown below in Table 4, where the surveyed point locations are labeled pt 91 , pt 41 , pt 24 , pt 115 , and pt 76  (in meters). As shown, the xy distance error ranges 2 to 5 cm (1-2″), and the z values were confirmed to be within a few millimeters. 
   
     
       
             
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 4 
             
             
                 
             
             
               in meter 
               x by pyra 
               y by pyra 
               z by pyra 
               plate x 
               plate y 
               plate z 
               dif x 
               dif y 
               xy dist 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               pt91 
               32.01 
               15.07 
               −0.34 
               31.997 
               15.084 
               −0.016 
               0.013 
               −0.014 
               0.019164 
             
             
               pt47 
               35.96 
               7.06 
               −0.34 
               36 
               7.086 
               −0.014 
               −0.039 
               −0.026 
               0.047344 
             
             
               pt24 
               35.98 
               3.04 
               −0.34 
               36.003 
               3.086 
               −0.012 
               −0.023 
               −0.046 
               0.051117 
             
             
               pt115 
               23.98 
               19.09 
               −0.33 
               23.9968 
               19.083 
               −0.006 
               −0.017 
               0.007 
               0.018317 
             
             
               pt76 
               7.983 
               11.071 
               −0.35 
               7.999 
               11.083 
               −0.018 
               −0.016 
               −0.012 
               0.01972 
             
             
                 
             
           
        
       
     
   
   A second transmitter, ATX2021B, was then placed on the second origin plate location to compare the accuracy of the present invention to the conventional and more expensive two transmitter system. The transmitter characteristics are provided in Table 5. 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 5 
             
             
                 
             
             
               ATX2O21B transmitter file: ASD 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               PHI 1: 
               −0.5193683 
             
             
                 
               PHI 2: 
               0.5160458 
             
             
                 
               ALPHA 1: 
               1.5712155 
             
             
                 
               ALPHA 2: 
               1.5715426 
             
             
                 
               THETA OFFSET: 
               1.5744753 
             
             
                 
               SPEED: 
               40.0000000 
             
             
                 
               X: 
               36.0089858 
             
             
                 
               Y: 
               0.0000000 
             
             
                 
               Z: 
               −0.0955599 
             
             
                 
               RX: 
               0.0000000 
             
             
                 
               RY: 
               0.0000000 
             
             
                 
               RZ: 
               −0.2971674 
             
             
                 
                 
             
           
        
       
     
   
   Simultaneous position measurements were then performed by the receiver of present invention (Pyramid) and a receiver of the two-transmitter system (LS920). About 200 samples were extracted from recorded data of each system collected at three different points. Blocked and spiky position data were eliminated. The spikes are caused by laser pulse collisions from the two different transmitters in the same window for the pulse tracker function. Since there will be no spikes in the one transmitter system, they were removed. The comparison on the three points is shown in Table 6. 
   
     
       
             
             
             
             
           
             
             
             
             
             
             
           
         
             
                 
               TABLE 6 
             
             
                 
                 
             
             
                 
               x (m) 
               y (m) 
               z (m) 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
                 
               point 106 
               Pyramid 
               17.948 
               17.058 
               −0.334 
             
             
                 
                 
               LS920 
               17.956 
               17.07 
               −0.337 
             
             
                 
                 
               Diff 
               −0.008 
               −0.012 
               0.003 
             
             
                 
               point 91 
               Pyramid 
               32.018 
               15.125 
               −0.343 
             
             
                 
                 
               LS920 
               32.004 
               15.093 
               −0.347 
             
             
                 
                 
               Diff 
               0.014 
               0.032 
               0.004 
             
             
                 
               Point 47 
               Pyramid 
               36.01 
               7.086 
               −0.342 
             
             
                 
                 
               LS920 
               35.978 
               7.06 
               −0.349 
             
             
                 
                 
               Diff 
               0.032 
               0.026 
               0.007 
             
             
                 
                 
             
           
        
       
     
   
   The vector length error was shown to be between the predicted typical and predicted max. The z-error seemed to exceed the max but it is suspected that the LS920 setup might have shifted overnight because it was not repeated the next day. The comparison of standard deviation is shown below in Table 7. 
   
     
       
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE 7 
             
             
                 
             
             
               stddev 
               pyra x 
               pyra y 
               pyra z 
               LS x 
               LS y 
               LS z 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               point 106 
               0.013 
               0.013 
               0.000 
               0.003 
               0.001 
               0.000 
             
             
               point 91 
               0.014 
               0.010 
               0.002 
               0.001 
               0.006 
               0.000 
             
             
               point 47 
               0.032 
               0.006 
               0.001 
               0.000 
               0.001 
               0.000 
             
             
                 
             
           
        
       
     
   
   It is noted that the x and y standard deviation of the pyramid measurement are closely proportional to the x and y coordinates, indicating the standard deviation is in radial direction. The comparison of standard deviation in Table 7 shows that the conventional two-transmitter system (LS920) was an order of magnitude better than the present invention (Pyramid), thereby justifying its use as a reference instrument. 
   Long Range Test 
   A long-range test was also conducted to check the worst-case error. The test was set up on a level ground with a long-range transmitter placed 100 m away from the pyramid array. The transmitter characteristics are provided in Table 8. 
   
     
       
             
           
             
             
           
         
             
               TABLE 8 
             
             
                 
             
             
               Laser Transmitter Characterization at 100 METERS 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               Characterization Fixture: 1, 
             
             
                 
               Phi 1 = −0.508985 radians, 
             
             
                 
               Phi 2 = 0.534927 radians, 
             
             
                 
               Theta Offset 1.569711 radians, 
             
             
                 
               Alpha 1 = 1.570061 radians, 
             
             
                 
               Alpha 2 = 1.567711 radians, 
             
             
                 
               Calculated Speed 39.999952 Hz. 
             
             
                 
                 
             
           
        
       
     
   
   Measurements from 100 meter were attempted but the photo detectors would not pick up the signal from the transmitter at that distance. It is believed that the 100 m range is out of reach due to a threshold adjustment in the photodetectors being set too low but such range could easily be achieved if the threshold levels were factory set. The transmitter was then gradually moved closer toward the pyramid until the pyramid detected the laser. The range obtained was 74 m with the long-range transmitter. 
   Since the characterization of the above transmitter was not available at the time of testing, only the raw angle data was recorded. The angle data was later converted to position data after the correct transmitter parameters were provided. The pyramid position calculation simulator was run on the theta data of 192 measurements. The mean and standard deviation of xyz position, distance and angles were computed and shown in the following Table 9. 
   
     
       
             
           
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE 9 
             
           
           
             
                 
             
             
               At 74 m point 
             
           
        
         
             
                 
               x 
               y 
               z 
               distance 
               azimuth 
               elevation 
             
             
                 
               (m) 
               (m) 
               (m) 
               (m) 
               (rad) 
               (rad) 
             
             
                 
                 
             
           
        
         
             
                 
               stddev 
               0.01 
               0.103 
               0.001 
               0.103 
               0.000031 
               0.0000141 
             
             
                 
               mean 
               7.528 
               73.697 
               −0.932 
               74.087 
               1.469001 
               −0.01257 
             
             
                 
                 
             
           
        
       
     
   
   The standard deviations of measurements in lateral direction are given by range times angle standard deviation. So, 74 m×30.9E-06=2 mm in azimuth and 74 m×14.1E-06=1 mm in elevation. These values are much smaller than the radial direction standard deviation of 0.103 m. This means the measurement noise is mostly in radial direction and the angles were very tight and accurate. The mean of the measured slant distance of the transmitter was 74.087 m, wherein the mean of the z height measured by transmitter was −0.932 m. These mean measurements matches very well with a conventional two transmitter system readings, 74.124 m slant distance and −0.974 in the z position, wherein in the differences between the two systems are 0.037 m in slant distance and 0.042 m in z height. 
   Next, the transmitter was moved to provide a separation of 62 meters to the array. The mean and standard deviation of xyz position, distance and angles detected by the system at 62 meters were computed and shown in the following Table 10. 
   
     
       
             
           
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE 10 
             
           
           
             
                 
             
             
               At 62 m point 
             
           
        
         
             
                 
               x (m) 
               y (m) 
               z (m) 
               distance (m) 
               azimuth (rad) 
               elevation (rad) 
             
             
                 
                 
             
           
        
         
             
               Stddev 
               0.005005 
               0.067273 
               0.001049 
               0.067446 
               0.000026 
               0.000010 
             
             
               Mean 
               4.578071 
               62.145910 
               −0.981490 
               62.322040 
               1.497263 
               −0.015750 
             
             
                 
             
           
        
       
     
   
   The mean of the measured slant distance of the transmitter was 62.322 m, wherein the mean of the z height measured by transmitter was −0.981 m. The slant distance measured by the conventional two laser transmitter system is 62.377 m, and the z height −1.019 m, wherein in the differences between the two systems are 0.055 m in slant distance and 0.038 m in z height. This data is similar to the 74 m data except the distance standard deviation improved more than the range ratio. The ratio of the measured distance by the pyramid to that of the conventional two-laser transmitter system is 1.0005 at 74 m, and 1.0009 at 62 m. 
   During the position measurement test, the pyramid size was rescaled to compensate the error component proportional to the range. This is acceptable only if the array is always in the same orientation. If the array is viewed in different directions, the array should be measured in many perspective angles and should be averaged so that the scale factor difference is minimized from the mean scale factor. In one embodiment, the averaged array size for distance scaling is used, where position measurement testing such as described above has been completed in all direction of array while keeping photo-detector  20   a  at one fixed location. Ideally, the measured position remains the same regardless of the array orientation, which shows that the array was measured perfectly. 
   A simple error model of the detector array is given by a radial distance error formula: 
                   e     max   ,   radial       =       2   L     ⁢     (         n   θ     ⁢     R   2       +       n   array     ⁢   R       )               (   2   )               
where e max, radial  is maximum radial distance error, L is the nominal detector array size, n θ  is the theta noise level in rad, n array  is the detector array differential position error and R is the range. All dimensional units are in meters. The first term is the error due to the theta noise and is quadratic in range, and the second term is the error due to the detector array measurement error and is proportional to the range. By averaging the pyramid position for a prolonged time, the first term error is made smaller, and the second term, although cannot be time-averaged, is reduced by array rotation averaging. For error prediction the following values were used:
 
   a. L=1 m 
   b. n θ =10e-5 rad 
   c. n array =5.0e−4/sqrt(3) m 
   Other Polyhedron: 
   To improve the accuracy of the array further and to reduce the theta noise to minimal as possible, there are two options: increase the array size or throw in more detectors. With one more detector, a hexahedron shaped array is provided. The next best shape is an octahedron or cube that requires 8 detectors. The 1 m cube will reduce the error to 18 cm max. 
   The above-described embodiments are intended to illustrate the principles of the invention, not to limit its scope. Other embodiments in variations to these preferred embodiments will be apparent to those skilled in the art and may be made without departing from the spirit and scope of the invention as defined in the following claims. For example, any type of wave energy, be it sonic, ultrasonic, laser or infrared, may be used to provide the above non-contact measurement of displacement, position, and heading.