Patent Publication Number: US-2010125347-A1

Title: Model-based system calibration for control systems

Description:
BACKGROUND OF THE INVENTION 
     1. Statement of the Technical Field 
     The invention concerns system calibration. More particularly, the invention concerns systems and methods for model-based calibration for control systems. 
     2. Description of the Related Art 
     In many physical systems, particularly electrical and mechanical, calibration data-based and model-based control systems are typically used. In the case of calibration data-based control systems, modern measurement tools permit precise measurements of the behavior of the physical system with reduced noise as compared to measurement systems available decades ago. In the case of model-based control systems, highly advanced mathematical descriptions of components are generally available that typically permit inclusion of effects that decades ago would have been neglected or roughly approximated due to the amount of computation intensity required. In some cases, the model predictions can be more accurate than experimental measurements of the physical system. 
     In either type of control system, the accuracy of control is limited by the accuracy of the model or the calibration data. In general, a physical system models is only as accurate as the parameters and/or assumptions initially input into the model. As a result, when a physical system is installed and used, the parameters or assumptions may no longer apply. Similarly, in the case of calibration data-based control systems, calibration measurements can become contaminated by numerous errors, which include biases and random noise. For example, inconsistencies between the actual performance of a physical system, such as a communications system, and the models or calibration data is generally due to component installation imperfections, varying signal-to-noise ratios, multipath signals, limited observation times, and non-optimum calibration signal sources. The result is a set of operational calibration measurements and/or models that are inaccurate and inaccurate operation of the physical system. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present invention systems and methods for model-based calibration of physical systems utilizing model-based control systems. In a first embodiment of the present invention, a method of using a model-based control system to control a physical system having a plurality of components is provided. The model-based control system is based on a computer simulation model of the physical system approximating operating characteristics of at least a portion of the plurality of components, the computer simulation model having one or more model parameters for adjusting a modeled operating characteristic of at least one of the plurality of components. The method includes generating at least one active input parameter for the physical system based on current values for the model parameters and the computer simulation model and obtaining at least one measured system parameter value and at least one modeled system parameter value for measuring the performance of physical system responding to the active input parameter. The method also includes evaluating a difference between the measured system parameter value and the modeled system parameter value and updating the current values for the model parameters to minimize the difference. 
     In a second embodiment of the present invention, a model-based control system for controlling a physical system having a plurality of components is provided. The control system includes a storage element for receiving a computer simulation model of the physical system, where the computer simulation model approximates operating characteristics of at least a portion of the plurality of components has one or more model parameters for adjusting a modeled operating characteristic of at least one of the plurality of components. The control system also includes a processing element for generating at least one active input parameter for physical system based on current values for the model parameters and the computer simulation model, where the processing element further includes a model-based calibration element for adjusting the current values for the model parameters based on a response of the physical system to the active input parameter. In the model-based calibration element, adjusting comprises obtaining at least one measured system parameter value and at least one modeled system parameter value for measuring the response of the physical system, evaluating a difference between the measured system parameter value and the modeled system parameter value, and updating the current values for the model parameters to minimize the difference. 
     In a third embodiment of the present invention, a communications system is provided. The communications system includes an array of antenna elements and a control system communicatively coupled to the array and generating control signals for the array. The control system includes a storage element for receiving a computer simulation model of the communications system approximating operating characteristics of the array of antenna elements and having one or more model parameters for adjusting a modeled operating characteristic of the array of antenna elements, and a processing element for generating the control signals for the array of antenna element based on current values for the model parameters and the computer simulation model. The processing element further includes a model-based calibration element for adjusting the current values for the model parameters based on a response of the array of antenna elements to the control signals. Adjusting in the model-based calibration element includes obtaining at least one measured system parameter value and at least one modeled system parameter value for measuring the response, evaluating a difference between the measured system parameter value and the modeled system parameter value, and updating the current values for the model parameters to minimize the difference based on an iterative analysis of the computer simulation model. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments will be described with reference to the following drawing figures, in which like numerals represent like items throughout the figures, and in which: 
         FIG. 1  is a schematic illustration of an exemplary model-based calibration system in accordance with an embodiment of the present invention. 
         FIG. 2  is a flowchart of steps in an exemplary method for operating an array of antenna element according to an embodiment of the present invention. 
         FIG. 3  is a schematic view of a computer system within which a set of instructions operate according to an embodiment of the present invention. 
         FIG. 4  is a schematic illustration of an exemplary communications system configured according to an embodiment of the present invention. 
         FIG. 5  is a block diagram of the element array control system shown in  FIG. 4 . 
         FIG. 6  is a block diagram of the transmit side of the system controller shown in  FIG. 5  communicatively coupled to the RF equipment shown in  FIG. 4 . 
         FIG. 7  is a block diagram of the receive side of the system controller shown in  FIG. 5  communicatively coupled to the antenna controllers shown in  FIG. 4 . 
     
    
    
     DETAILED DESCRIPTION 
     The present invention is described with reference to the attached figures, wherein like reference numerals are used throughout the figures to designate similar or equivalent elements. The figures are not drawn to scale and they are provided merely to illustrate the instant invention. Several aspects of the invention are described below with reference to example applications for illustration. It should be understood that numerous specific details, relationships, and methods are set forth to provide a full understanding of the invention. One having ordinary skill in the relevant art, however, will readily recognize that the invention can be practiced without one or more of the specific details or with other methods. In other instances, well-known structures or operations are not shown in detail to avoid obscuring the invention. The present invention is not limited by the illustrated ordering of acts or events, as some acts may occur in different orders and/or concurrently with other acts or events. Furthermore, not all illustrated acts or events are required to implement a methodology in accordance with the present invention. 
     As previously described, physical systems are generally controlled using either model-based approaches or calibration data-based approaches. In the case of calibration data-based control, control signals are generated based on a table of measurement values for each measurement parameter. Typically, these would be generated using a finite set of measurements over the range of the parameter of interest after installation of the physical system allowing the physical system to be calibrated to account for systematic variations due to installation or other local factors. In operation, response of the system for a particular parameter value would be obtained by table lookup. Response values for parameter quantities not measured are typically obtained by some type of interpolation using nearby measured points (e.g., Linear Interpolation, Cubic Spline, Fourier, or Polynomial expansions). However, the accuracy of a calibration data-based approach is limited by the fact that the accuracy of measured calibration values is limited by the noise inherent in physical system and the accuracy of the interpolation method. Therefore, if a set of calibration data is obtained that has a high degree of noise in the measured values, accurate control of the system is difficult. 
     In a model-based control system, the underlying function associated with the measured parameter may be well-defined, so noise is typically not an issue. Furthermore, since the control signals are based upon the underlying function, the need for interpolation is generally reduced or eliminated. However, in a model-based control system, the underlying function is generally responsive to one or more unknown parameters, typically based on an initial set of measurements performed during installation or initial calibration of the physical system. Consequently, any error in obtaining the initial calibration data and/or configuring the model-based control system can result in an inaccurate control of the system. 
     To overcome the limitations of conventional control system methods, embodiments of the present invention provide a model-based calibration systems and methods. That is, the systems and methods described herein utilized a model-based approach for control of the physical system, as described above, but model parameters are dynamically adjusted to improve the accuracy of the model. In particular, measured output parameters of the physical system are compared with estimated output parameters and based on their difference, updated model parameters are generated. Such an approach provides the advantages of low-noise and well-defined behavior of the physical system provided by model-based approaches and the ability to account for systematic variations in the installed physical system provided by calibration-data based approaches. 
       FIG. 1  is a schematic illustration of an exemplary model-based calibration system  100  in accordance with an embodiment of the present invention. The system  100  can include a measured signal parameter estimator (SPE)  102  for receiving output signals from the physical system. In the various embodiments of the present invention, the output signal can include not only an output signal associated with an end result of the physical system, but can also input output signals associated with one or more intermediate results of the physical system and/or measurements obtained from or at various components of the system. The measured SPE  102  can also generate or compute one or more system parameters for characterizing the physical system based on the output signals received by the measured SPE  102 . For example, in a communications system using an array of antenna elements, measurements of signal phases or differences in signal phases at each of antenna elements can be received as output parameters. Consequently, the measured SPE  102  can generate system parameters based on such as signal covariance matrix coefficients, signal angle-of-arrival (AOA), or signal steering vectors, to name a few. 
     The system can also include a modeled SPE  104  for generating values for the same system parameters based on a modeled output signal generated by a system model simulation engine (SMSE)  106  in the system  100 . The SMSE  106  is also configured to receive signals indicating the input or control parameters used for generating the output signals received by the measured SPE  102  and for receiving simulation data for generating the modeled output signal. 
     Input parameters for the SMSE  106  can include active input values provided to the system by a user or a particular component or function of the system. For example, in the case of a communications system comprising an array of antenna elements, input parameters can include amplitude, phase variation, azimuth, and elevation, to name a few. The input parameters can also include passive input parameters. Such passive input parameters can include, for example, environmental parameter values, such as temperature, pressure, and humidity, or other input parameters based on conditions in or around the physical system. However, embodiments of the present invention are not limited to solely for use with physical systems having the input parameters listed above. Rather, in the various embodiments of the present invention, the SMSE  106  can be used to simulate any type of systems affected by any number and type of input parameters, including biological, mechanical, chemical, or electromagnetic parameters. 
     As shown in  FIG. 1 , the SMSE  106  can also received simulation data. The simulation data received by the SMSE  106  can include a computer simulation model of the physical system and initial model parameters for the computer simulation model. In the various embodiments of the present invention, the computer simulation model can include models for describing the behavior of any number and types of components in the physical system, including components affected by biological, mechanical, chemical, or electromagnetic parameters. Accordingly, based on the computer simulation model and the input parameters for the output signal, the SMSE  106  estimates the output signals of the physical system for the modeled SPE  104 . 
     The estimates of the system parameters generated by the measured SPE  102  and the modeled SPE  104  can then be compared in the parameter difference analyzer (PDA)  108 . The PDA  108  calculates a difference between the modeled and measured values of the system parameters and provides the difference to the parameter calculator  110 . For example, the PDA  108  may find a difference between measured and modeled signal strength and/or phase at a point between a control system and an antenna element in a communications system. The parameter calculator can then compute a new set of model parameters to minimize the differences computed at the PDA  108  so as to increase the accuracy of the model. That is, to adjust the model to improve agreement to the system parameters generated by the measured SPE  102 . In some embodiments, the new model parameters can be directly calculated if the mathematical model of the physical system is sufficiently simple and the number of model parameters is sufficiently low. For example, in a physical system including only a few components, the model parameters can be directly calculated. However, as the complexity or non-linearity of the system increases, finding a solution using a direct method becomes increasingly computationally intensive and therefore impractical even when large computing resources are available. As a result, such complex systems generally require the use of iterative methods to find an approximate value for the model components, especially when the number of model parameters is large. That is, the model parameters are computed to minimize difference between the measured and modeled system parameters. In such embodiments, numerical gradient and steepest descent algorithms can be applied, to name a few. 
     The new model parameters generated by the parameter calculator  110  can then be provided to a control system (not shown) for generating new input parameters for the physical system. Additionally, the new model parameters are provided to the SMSE  106  to update the model being used for generating subsequent modeled output signals for the system  100 . As a result, the model parameters controlling for the physical system are dynamically updated as additional output signals are generated by the system. 
     As a result, control of the physical system is provided that includes the benefits of calibration data-based control techniques (i.e., accounting for systematic variations in the behavior of the physical system) and model-based control techniques (i.e., well-defined system behavior). Furthermore, if the model parameters are allowed to be dynamically updated over a period of time, the model will become increasingly accurate over time. As a result, the amount of computations required during later updates of the model is significantly reduced and the physical system effectively operates as a purely model-based control system. 
     For example, a model-based calibration control was implemented for an exemplary interferometer system consisting of two microstrip patch antenna elements mounted on a large conical ground plane. In the exemplary system, the function describing the output power of the antenna elements was the electrical sum of the output power of the two elements as the incidence angle of the source was varied over a 65 degree azimuth range. 
     When such a system is controlled using a calibration data-based method, a large number of data points (typically tens of thousands of points) would need to be taken over the elevation and azimuth space of interest, each of which contains some amount of measurement error. As a result, the calibration data-based approach, as previously described, is limited by the accuracy of the measurements. A purely model-based control approach, based solely on pre-determined knowledge of the cone angle, the location of the elements on the cone, and the element patterns on a cone also provides only limited accuracy. 
     When a pre-defined model control system was applied, the measured and modeled output results varied significantly. Two model discrepancies primarily accounted for the difference between measured and modeled results: (1) the antenna element patterns did not include the effect of a conical ground plane, and (2) the locations of the elements were inaccurate in the model. Although the locations of the element could be more precisely measured to improve accuracy of the modeled output, these measurements will always include some amount of error. Furthermore, determining a correct value for the model parameters that account of the effect of the conical ground plane is non-trivial. 
     However, when utilized with a model-based calibration system in accordance with an embodiment of the present invention, the Present Inventors found that model parameters were quickly obtained that provided good agreement between modeled and measured output. During operation, the model-based calibration system initially adjusted element position parameters for the model of the interferometer system, which provided an improved agreement between measured and model results. As the number of data samples acquired was increased, even better agreement between measured and modeled output results were obtained as the model parameters were further adjusted. After these adjustments, the calibrated model predicted array performance in two scan dimensions (elevation and azimuth) with an insignificant amount of error as compared to calibration data-based or model-based control methods. Furthermore, once the model parameters were adjusted by the model-based calibration system, little or no additional adjustments to the model parameters were needed, reducing the need for iterative computations. Accordingly, the control system for the interferometer system was provided with a model calibrated with a substantially lower number of measurements than required for a calibration data-based approach. In general, the number of measurements needed for calibrating a model is dependent on the difference between the initial set of model parameters and the final set of model parameters. Therefore, the closer the approximation provided by the computer simulation model using the initial set of model parameters is to the actual output of the physical system, the lower is the number of measurements needed to obtain a final set of model parameters. In any case, the number of measurements needed for a model-based calibration in accordance with an embodiment of the present invention is at least one order of magnitude lower than the number of measurements required for a conventional calibration-based control system. 
       FIG. 2  is a flowchart of steps in an exemplary method  200  for operating a system using a model-based calibration technique in accordance with an embodiment of the present invention. The method can begin in step  202  can continue on to step  204 . In step  204 , an initial computer simulation model of the physical system to be controlled and an initial set of model parameters can be received. Using the computer model and current model parameters, a set of active input or control signals for the physical system can be generated at step  206 . 
     At step  208 , the output signals generated by the physical system in response to the active input signals generated at step  206  and any passive input control signals are measured. Afterwards, at step  210 , the measured system parameters can be calculated from the output signals measured at step  208 . Subsequently or in combination with step  208 , modeled output signals are generated at step  212  and modeled system parameters are generated at step  214 . The modeled output signal can be generated using a computer simulation model of the physical system using the input signals generated at step  206  and any other input signals (active or passive) or parameters affecting the physical system. The modeled system parameters can be generated at step  214  in the same way the measured system parameters are generated in step  210 . 
     Once the measure and modeled system parameters are generated at steps  210  and  214 , the difference between the parameters can be computed at step  216 . That is, for each parameter being measured, the error in the model, due to the current set of model parameters, is calculated. Afterwards, in step  218 , the adjustment needed for one or more model parameters is calculated to reduce the difference at step  216  is computed. As previously described, direct or iterative methods can be used at step  218 , depending on the complexity of the physical system. The model parameters for the model of the physical system used by the control system for the physical system are then updated at step  220 . The method  200  can then repeat starting at step  206 , to provide further refinement of the model parameters based on subsequent performance of the physical system. 
       FIG. 3  is a schematic diagram of a computer system  300  for executing a set of instructions that, when executed, can cause the computer system to perform one or more of the methodologies and procedures described above. For example, the computer system can include functional or processing blocks associated with the various components in  FIG. 1  or can include instructions for performing the various steps in  FIG. 2 . In some embodiments, the computer system  300  operates as a standalone device. In other embodiments, the computer system  300  can be connected (e.g., using a network) to other computing devices. In a networked deployment, the computer system  300  can operate in the capacity of a server or a client developer machine in server-client developer network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. 
     The machine can comprise various types of computing systems and devices, including a server computer, a client user computer, a personal computer (PC), a tablet PC, a laptop computer, a desktop computer, a control system, a network router, switch or bridge, or any other device capable of executing a set of instructions (sequential or otherwise) that specifies actions to be taken by that device. It is to be understood that a device of the present disclosure also includes any electronic device that provides voice, video or data communication. Further, while a single computer is illustrated, the phrase “computer system” shall be understood to include any collection of computing devices that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. 
     The computer system  300  can include a processor  302  (such as a central processing unit (CPU), a graphics processing unit (GPU, or both), a main memory  304  and a static memory  306 , which communicate with each other via a bus  308 . The computer system  300  can further include a display unit  310 , such as a video display (e.g., a liquid crystal display or LCD), a flat panel, a solid state display, or a cathode ray tube (CRT)). The computer system  300  can include an input device  312  (e.g., a keyboard), a cursor control device  314  (e.g., a mouse), a disk drive unit  316 , a signal generation device  318  (e.g., a speaker or remote control) and a network interface device  320 . 
     The disk drive unit  316  can include a computer-readable storage medium  322  on which is stored one or more sets of instructions  324  (e.g., software code) configured to implement one or more of the methodologies, procedures, or functions described herein. The instructions  324  can also reside, completely or at least partially, within the main memory  304 , the static memory  306 , and/or within the processor  302  during execution thereof by the computer system  300 . The main memory  304  and the processor  302  also can constitute machine-readable media. 
     Dedicated hardware implementations including, but not limited to, application-specific integrated circuits, programmable logic arrays, and other hardware devices can likewise be constructed to implement the methods described herein. Applications that can include the apparatus and systems of various embodiments broadly include a variety of electronic and computer systems. Some embodiments implement functions in two or more specific interconnected hardware modules or devices with related control and data signals communicated between and through the modules, or as portions of an application-specific integrated circuit. Thus, the exemplary system is applicable to software, firmware, and hardware implementations. 
     In accordance with various embodiments of the present disclosure, the methods described herein can be stored as software programs in a computer-readable storage medium and can be configured for running on a computer processor. Furthermore, software implementations can include, but are not limited to, distributed processing, component/object distributed processing, parallel processing, virtual machine processing, which can also be constructed to implement the methods described herein. 
     The present disclosure contemplates a computer-readable storage medium containing instructions  324  or that receives and executes instructions  324  from a propagated signal so that a device connected to a network environment  326  can send or receive voice and/or video data, and that can communicate over the network  326  using the instructions  324 . The instructions  324  can further be transmitted or received over a network  326  via the network interface device  320 . 
     While the computer-readable storage medium  322  is shown in an exemplary embodiment to be a single storage medium, the term “computer-readable storage medium” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and/or associated caches and servers) that store the one or more sets of instructions. The term “computer-readable storage medium” shall also be taken to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure. 
     The term “computer-readable medium” shall accordingly be taken to include, but not be limited to, solid-state memories such as a memory card or other package that houses one or more read-only (non-volatile) memories, random access memories, or other re-writable (volatile) memories; magneto-optical or optical medium such as a disk or tape; as well as carrier wave signals such as a signal embodying computer instructions in a transmission medium; and/or a digital file attachment to e-mail or other self-contained information archive or set of archives considered to be a distribution medium equivalent to a tangible storage medium. Accordingly, the disclosure is considered to include any one or more of a computer-readable medium or a distribution medium, as listed herein and to include recognized equivalents and successor media, in which the software implementations herein are stored. 
     Although the present specification describes components and functions implemented in the embodiments with reference to particular standards and protocols, the disclosure is not limited to such standards and protocols. Each of the standards for Internet and other packet switched network transmission (e.g., TCP/IP, UDP/IP, HTML, and HTTP) represent examples of the state of the art. Such standards are periodically superseded by faster or more efficient equivalents having essentially the same functions. Accordingly, replacement standards and protocols having the same functions are considered equivalents. 
       FIG. 4  shows an exemplary communications system  400  configured according to an embodiment of the present invention. As shown in  FIG. 4 , the communication system  400  comprises a multi-element antenna system (MEAS)  450  for transmitting signals to and receiving signals from at least one object of interest  408  remotely located from the multi-element antenna system. In  FIG. 4 , the object of interest  408  is shown as airborne or space borne object, such as an aircraft, spacecraft, a natural or artificial satellite, or a celestial object (e.g., planets, moons, asteroids, comets, etc. . . . ). However, the present invention is not limited in this regard and the MEAS  450  can also be used for transmitting and receiving signals from an object of interest  408  that is not airborne or space borne but is still remotely located with respect the MEAS  450 . For example, a ground-based MEAS  450  can be used to provide communications with objects of interest  408  at other ground-based or sea-based locations. 
     The MEAS  450  can generally include an array control system (ACS)  402  for controlling the operation of multiple antenna elements. In the exemplary system  400 , the ACS  402  can include model-based calibration system for controlling operation of the MEAS  450 , as described below in  FIG. 5 . 
     In  FIG. 4 , the ACS  402  is shown as controlling the operation of antenna elements  406   a ,  406   b ,  406   c  and associated RF equipment  404   a ,  404   b ,  404   c . The antenna elements  406   a ,  406   b ,  406   c  provide wireless communications. For example, if the MEAS  450  is in a transmit mode, then each antenna element  406   a ,  406   b ,  406   c  converts electrical signals into electromagnetic waves. The radiation pattern  411  resulting from the interference of the electromagnetic waves transmitted by the different antenna elements  406   a ,  406   b ,  406   c  can then be adjusted to provide a central beam  412  in the radiation pattern  411  aimed in a direction  416  of the object of interest  408 . The radiation pattern  411  of the antenna elements  406   a ,  406   b ,  406   c  also generates smaller side beams (or side lobes)  414  pointing in other directions with respect the direction of the central beam  412 . However, because of the relative difference in magnitude between the side beams  414  and the central beam  412 , the radiation pattern preferentially transmits the signal in the direction of the central beam  412 . Therefore, by varying the phases and the amplitudes of the signals transmitted by each of antenna elements  406   a ,  406   b , and  406   c , the magnitude and direction of the central beam  412  can be adjusted. If the MEAS  450  is in a receive mode, then each of antenna elements  406   a ,  406   b , and  406   c  captures energy from passing waves propagated over transmission media (e.g., air or space) in the direction  420  and converts the captured energy to electrical signals. In the receive mode, the MEAS  450  can be configured to combined the electrical signals according to the radiation pattern  411  to improve reception from direction  420 , as described below. 
     In  FIG. 4 , the antenna elements  406   a ,  406   b , and  406   c  are shown as reflector-type (e.g., dish) antenna elements, which generally allow adjustment of azimuth (i.e., lateral or side-to-side angle) and elevation (angle with respect to a local horizontal reference plane). Therefore, in addition to adjustment of phase and amplitude of the signal transmitted by each of antenna elements  406 , the azimuth and elevation of each of antenna elements  406   a ,  406   b , and  406   c  can also be used to further steer the central beam  412  and to further adjust the radiation pattern  411 . However, the present invention is not limited in this regard and antenna elements  406  can comprise either directional or omni-directional antenna elements. 
     Although three (3) antenna elements  406   a ,  406   b ,  406   c  are shown in  FIG. 4 , the various embodiments of the present invention are not limited in this regard. Any number of antenna elements can be used without limitation. Furthermore, the spacing between the antenna elements  406   a ,  406   b , and  406   c  with respect to each other can vary. Accordingly, the antenna elements  406   a ,  406   b , and  406   c  can be widely or closely spaced to form an MEAS  450  that has a width of up to several kilometers. The antenna elements  406   a ,  406   b ,  406   c  can also be regularly spaced (not shown) with respect to one another to form a two dimensional (2D) grid of antenna elements or arbitrarily spaced (or non-linearly spaced) with respect to one another (as shown in  FIG. 4 ) to form a three dimensional (3D) irregular array of antenna elements. As shown in FIG.  4 , an arbitrary spacing for the antenna elements  406   a ,  406   b ,  406   c  can include providing varying elevation as well as varying lateral spacing between the antenna elements  406   a ,  406   b ,  406   c.    
     As shown in  FIG. 4 , each of antenna elements  406   a ,  406   b ,  406   c  is communicatively coupled to a respective RF equipment  404   a ,  404   b ,  404   c  via a respective cable assembly  410   a ,  410   b ,  410   c  (collectively  410 ). Each of the cable assemblies  410   a ,  410   b ,  410   c  can have the same or different lengths. As used herein, the term “cable assembly” refers to any number of cables provided for interconnecting two different components. In the various embodiments of the present invention, the cables in the cable assembly can be bundled or unbundled. 
     The RF equipment  404   a ,  404   b ,  404   c  control the antenna elements  406   a ,  406   b ,  406   c , respectively. For example, the RF equipment  404   a ,  404   b ,  404   c  can include hardware entities for processing transmit signals and receive signals. The RF equipment  404   a ,  404   b ,  404   c  will be described in more detail below in relation to  FIGS. 6-4 . Additionally, for directional antenna elements, as shown in  FIG. 4 , the RF equipment  404   a ,  404   b ,  404   c  are configured to provide control signals for control antenna motors (not shown), antenna servo motors (not shown), and antenna rotators (not shown) in antenna elements  406   a ,  406   b ,  406   c  to provide, for example, azimuth and elevation control. 
     As shown in  FIG. 4 , each of the RF equipment  404   a ,  404   b , and  404   c  is communicatively coupled to the ACS  402  via a respective communications links  418   a ,  418   b ,  418   c . Generally such communications links are provided via a cable assembly, however the present invention is not limited in this regard. In the various embodiments of the present invention, communications links  418  can comprise wire line, optical, or wireless communications links. The cable assemblies for the communications links  418   a ,  418   b ,  418   c  can have the same or different lengths. Furthermore, although the communications links  418   a ,  418   b , and  418   c  are shown to be arranged to couple the RF equipment  404  to the ACS  402  in parallel, in other embodiments of the present invention, they can be connected in a series arrangement, such as that shown by communications links  419   a ,  419   b , and  419   c.    
     In operation, the ACS  402  modulates signals to be transmitted by the antenna elements  406   a ,  406   b ,  406   c . The ACS  402  also demodulates signals received from other antenna systems. The ACS  402  further controls beam steering. The ACS  402  will be described in more detail below in relation to  FIGS. 5-7 . 
     Referring now to  FIG. 5 , there is provided a more detailed block diagram of the ACS  402  in  FIG. 4 . As shown in  FIG. 5 , the ACS  402  includes a transmit side  502  and a receive side  504 . The ACS  402  is be configured to manage both transmission and reception operations of the MEAS  450  based on signals for transmission and control signals. In particular, the transmit side  502  can generate signals to be transmitted by the RF equipment  404   a ,  404   b ,  404   c  via antenna elements  406   a ,  406   b ,  406   c . Additionally or alternatively, the transmit side  502  can receive one or more signals from one or more signal generators (not shown) or receive external control signals. The transmit side  502  is also configured for modulating each of the generated or received signals and communicating the modulated signals to the RF equipment  404   a ,  404   b ,  404   c  for transmission. The transmit side  502  will be described in more detail below in relation to  FIG. 6 . 
     The receive side  504  is configured for receiving electrical signals generated by the RF equipment  404   a ,  404   b ,  404   c  based on the energy captured by the antenna elements  406   a ,  406   b ,  406   c  from passing waves. The receive side  504  is also configured for demodulating the electrical signal and communicating the demodulated electrical signal to an output device (not shown). The receive side  504  will be described below in more detail in relation to  FIG. 7 . 
     The exemplary ACS  402 , as shown in  FIG. 5 , also includes a model-based calibration system (MBCS)  512  and an element input parameter control system (EIPCS)  508 . The MBCS  512  in  FIG. 5  is configured to receive simulation data, as previously described with respect to  FIG. 1 , including a computer simulation model of the MEAS  450  and an initial set of model parameters for the computer simulation model. The MBCS  512  in  FIG. 5  can be configured to receive the signal received by the antenna elements before and/or after beamforming in the receive side. Additionally, the MBCS  512  can be configured to receive other input data from the MEAS  450  to utilize during modeling of output signals. For example, in the case of the MEAS  450 , such measurements can include temperature measurements, signal phase measurements, or signal phase differences along different portions of the MEAS  450 , to name a few. However, the other input data received by the MBCS  512  can also include any type of environmental, mechanical, or electromagnetic measurements performed in the MEAS  450 . The MBCS  512  can be operated, as previously described with respect to  FIG. 1 , to provide updated model parameters for the EIPCS  506 . 
     The EIPCS  506 , operates as a model-based control system utilizing the model parameters provided by the MBCS  512  to control operation of the transmit side  502 , the receive side  504 , and other operations of the MEAS  450 . The EIPCS  506  can receive control signals defining how the MEAS  450  is to be operated. For example, signals indicating a direction, frequency, or other transmission or reception parameters for the MEAS  450 . Based on the control signals, the computer simulation model for the MEAS  450 , and the current model parameters computed by the MBCS  512 , the EIPCS  506  can generate the appropriate signals for the MEAS  450 . For example, as shown in  FIG. 5 , the EIPCS  506  can include a mechanical parameter calculator  508  for generating signals for adjusting mechanical motion of components in the MEAS  450 , such as an azimuth and elevation for the antenna elements  406   a ,  406   b ,  406   c . The EIPCS  506  can also include a beamforming weight calculator  510  for computing weights for the transmit side  502  and/or the receive side  504 . Operation of a beamforming weight calculator  510 , based antenna system information from a model or calibration data is well-known to those of ordinary skill in the art and will not be described herein. Additionally, as the EIPCS  506  adjusts operation of the MEAS  450 , the control signals generated by the EIPCS  506  can also be provided to the MBCS  512  in order to adjust the model parameters. 
     Referring now to  FIG. 6 , there is provided a block diagram of the transmit side  502  of  FIG. 5  communicatively coupled to the RF equipment  404   a ,  404   b ,  404   c  of  FIG. 4 . As shown in  FIG. 6 , the transmit side  502  is comprised of a Transmit Radio Signal Generator (TRSG)  602 , hardware entities  604   a ,  604   b ,  604   c , and beamformers  608   a ,  608   b ,  608   c . The TRSG  602  generates signals to be transmitted from the array of antenna elements  406   a ,  406   b ,  406   c . The TRSG  602  is communicatively coupled to the hardware entities  604   a ,  604   b ,  604   c . Each of the hardware entities  604   a ,  604   b ,  604   c  is communicatively coupled to a respective one of the beamformers  608   a ,  608   b ,  608   c.    
     Each of the beamformers  608   a ,  608   b ,  608   c  can be utilized to control the phase and/or the amplitude of transmit signals for each antenna element  406   a ,  406   b ,  406   c . In general, the respective phase shifts (Ø 1 , Ø 2 , Ø 3 ) and/or amplitude adjustments (a 1 , a 2 , a 3 ) for the antenna elements  406   a ,  406   b ,  406   c  can be used to adjust formation of the central beam  412 , the side beams (or side lobes)  414  and nulls in the radiation pattern  411  of the MEAS  450 . Nulls correspond to directions in which destructive inference results in a transmit signals strength that is significantly reduced with respect to the directions of the central beam  412  and the side beams  414 . The combined amplitude adjustments a 1 , a 2 , a 3  and phase shift adjustments Ø 1 , Ø 2 , Ø 3  are referred to herein as a complex weight W 1 , W 2 , W 3 . Each of the beamformers  608   a ,  608   b ,  608   c  combines a respective complex weight W 1 , W 2 , W 3  with the transmit signals to be provided to a respective RF equipment  404   a ,  404   b ,  404   c . For example, as shown in  FIG. 6 , each beamformer  608   a ,  608   b ,  608   c  includes respective amplitude adjusters  610   a ,  610   b ,  610   c  for adjusting an amplitude of the transmit signals from hardware entities  604   a ,  604   b ,  604   c , respectively, based on an amplitude a 1 , a 2 , a 3  Each beamformer  608   a ,  608   b ,  608   c  also includes phase adjusters  612   a ,  612   b ,  612   c  for applying adjusting a phase of the transmit signals from hardware entities  604   a ,  604   b ,  604   c , respectively, based on a respective phase shift Ø 1 , Ø 2 , Ø 3 . The amplitude a 1 , a 2 , a 3  and phase shift Ø 1 , Ø 2 , Ø 3  can be generated by the EIPCS  506 . 
     In some embodiments of the present invention, the phase and amplitude adjusted signals from beamformers  608   a ,  608   b ,  608   c  can be communicatively coupled to the RF equipment  404   a ,  404   b ,  404   c  via one or more respective hardware entities  614   a ,  614   b ,  614   c . The weighted transmit signals from beamformers  608   a ,  608   b ,  608   c  are received at a respective hardware entity  628   a ,  628   b ,  628   c  of the RF equipment  404   a ,  404   b ,  404   c . The hardware entities  628   a ,  628   b ,  628   c  are communicatively coupled to a respective high power amplifier (HPA)  630   a ,  630   b ,  630   c . HPAs are well known to those having ordinary skill in the art, and therefore will not be described herein. However, it should be understood that the HPAs  630   a ,  630   b ,  630   c  communicate signals to the antenna elements  406   a ,  406   b ,  406   c  for transmission therefrom in the direction  416  of an object of interest  408 . 
     The term “hardware entity”, as used herein, refers to signal processing components, including but not limited to filters and amplifiers, and/or measurement components, such as environmental, physical, or electromagnetic sensor. In some embodiments of the present invention, hardware entities comprising measurement components can be coupled to the ACS  402  to provide input parameters for the MBCS  512  to generate system parameters. For example, hardware entities  614   a ,  614   b ,  614   c  and hardware entities  628   a ,  628   b ,  628   c  can comprise components for measuring a phase of the weighted signals at beamformers  608   a ,  608   b ,  608   c  and RF equipment  404   a ,  404   b ,  404   c , respectively. The MBCS  512  can then adjust the model parameters based on a difference between measured differences and the modeled differences between the weighted signal phases at beamformers  608   a ,  608   b ,  608   c  and RF equipment  404   a ,  404   b ,  404   c  to provide a predictable weighted signal phase difference to improve operation of the EIPCS  506 . 
     Referring now to  FIG. 7 , there is provided a block diagram of the receive side  504  of  FIG. 5  communicatively coupled to the RF equipment  404   a ,  404   b ,  404   c  of  FIG. 4 . As shown in  FIG. 7 , each of the RF equipment  404   a ,  404   b ,  404   c  further comprises a Radio Frequency (RF) translator  702   a ,  702   b ,  702   c  and a Low Noise Amplifier (LNA)  704   a ,  704   b ,  704   c . Each of the RF translators  702   a ,  702   b ,  702   c  performs signal frequency translation of receive signals from a respective antenna element  406   a ,  406   b ,  406   c  in the respective antenna controller  404   a ,  404   b ,  404   c . The translation function of the RF translators  702   a ,  702   b ,  702   c  generally converts the received signal at a respective antenna element  406   a ,  406   b ,  406   c  from an RF to an intermediate frequency (IF). The LNAs  704   a ,  704   b ,  704   c  generally amplify the IF signals output from the RF translators  702   a ,  702   b ,  702   c , respectively. Each of the LNAs  704   a ,  704   b ,  704   c  is communicatively coupled to the receive side  504  of the ACS  402 . In some embodiments, the LNAs  704   a ,  704   b ,  704   c  are communicatively coupled to the receive side  504  of the ACS  402  via one or more hardware entities  705   a ,  705   b ,  705   c.    
     The receive side  504  further includes a plurality of beamformers  708   a ,  708   b ,  708   c  and a signal combiner  714 . The receive side can further include input hardware entities  720   a ,  720   b ,  720   c  and output hardware entities  712   a ,  712   b ,  712   c  for the beamformers  708   a ,  708   b ,  708   c . As shown in  FIG. 7 , the input hardware entities  720   a ,  720   b ,  720   c  are communicatively coupled between the LNAs  704   a ,  704   b ,  704   c  and beamformers  708   a ,  708   b ,  708   c . Each of the beamformers  708   a ,  708   b ,  708   c  can include a down converter  706   a ,  706   b ,  706   c , a filter  722   a ,  722   b ,  722   c , and a combiner  710   a ,  710   b ,  710   c . Embodiments of the present invention are not limited in this regard. For example, the beamformers  708   a ,  708   b ,  708   c  can be absent of the down converters  706   a ,  706   b ,  706   c  and filters  722   a ,  722   b ,  722   c.    
     Each down converter  706   a ,  706   b ,  706   c  can convert a digitized real signal centered at an IF to a basebanded complex signal centered at zero (0) frequency. The down converters  706   a ,  706   b ,  706   c  can share a common clock (not shown), and therefore receive the same clock (CLK) signal. The CLK signal can be generated within the receive side  504 , elsewhere in the ACS  402 , or external to the ACS  402 . The down converters  706   a ,  706   b ,  706   c  can be set to the same center frequency and bandwidth. The down converters  706   a ,  706   b ,  706   c  can also comprise local oscillators that are in-phase with each other. This in-phase feature of the down converters  706   a ,  706   b ,  706   c  ensures that the down converters  706   a ,  706   b ,  706   c  shift the phases of signals by the same amount. After converting the digitized real signals to basebanded complex signals, the down converters  706   a ,  706   b ,  706   c  communicate the basebanded complex signals to the filters  722   a ,  722   b ,  722   c , respectively. The filters  722   a ,  722   b ,  722   c  filter the basebanded complex signals and forward the same to the combiners  710   a ,  710   b ,  710   c.    
     Each of the combiners  710   a ,  710   b ,  710   c  combines a basebanded complex signal with a complex weight W 1 , W 2 , W 3  for a particular antenna element  406   a ,  406   b ,  406   c . The complex weights W 1 , W 2 , W 3  are selected to combine the receive signals according to a particular radiation pattern. That is, complex weights W 1 , W 2 , W 3  are selected to provide a central beam  412 , side beams  414 , and nulls, as described above, so as to preferentially receive signals from one or more preferred directions. The combiners  710   a ,  710   b ,  710   c  can include, but are not limited to, complex multipliers. Thereafter, the combiners  710   a ,  710   b ,  710   c  communicate the signals to the hardware entities  712   a ,  712   b ,  712   c , respectively. The hardware entities  712   a ,  712   b ,  712   c  can further process the signals received from the beamformers  708   a ,  708   b ,  708   c . The hardware entities  712   a ,  712   b ,  712   c  communicate the processed signals to the signal combiner  714 . 
     At the signal combiner  714 , the processed signals are combined to form a combined signal. The signal combiner can include, but is not limited to, a signal adder. Subsequent to forming the combined signal, the signal combiner  714  communicates the same to the hardware entities  716  for further processing. The hardware entities  716  can include, but are not limited to, filters and amplifiers. After processing the combined signal, the hardware entities  716  communicate the same to the demodulator for demodulation. 
     As previously described for  FIG. 6 , in some embodiments of the present invention, hardware entities comprising measurement components can be coupled to the ACS  402  to provide input parameters for the MBCS  512  to generate system parameters. For example, hardware entities  705   a ,  705   b ,  705   c  and hardware entities  720   a ,  720   b ,  720   c  can comprise components for measuring a phase of the weighted signals at RF equipment  404   a ,  404   b ,  404   c  and beamformers  708   a ,  708   b ,  708   c , respectively. The MBCS  512  can then adjust the model parameters based on a difference between measured differences and the modeled differences between the weighted signal phases at beamformers  708   a ,  708   b ,  708   c  and RF equipment  404   a ,  404   b ,  404   c  to provide a predictable weighted signal phase difference to improve operation of the EIPCS  506 . 
     Additionally, the receive signals can be utilized by the MBCS  512  to update model parameters to correct for errors in differential distances for the antenna elements. That is, individual variation in transmission path length for the antenna elements for a particular AOA with respect to a reference location. For example, based on the signal data associated with received signals, the MBCS  512  can be configured to calculate differential distances for the antenna elements for the AOA relative to a reference location. The MBCS  512  can also calculated the differential distances based on the configuration data and the AOA. The error between the values can then be used by the MBCS  512  to adjust the model parameters. Such errors can occur due to variations in the troposphere, errors in the placement of the antenna elements, or errors in the configuration data for the antenna elements. As a result, the analysis of such errors can lead to improved location information for the antenna elements or generation of addition phase and/or amplitude corrections during beamforming for transmitted signals. 
     Applicants present certain theoretical aspects above that are believed to be accurate that appear to explain observations made regarding embodiments of the invention. However, embodiments of the invention may be practiced without the theoretical aspects presented. Moreover, the theoretical aspects are presented with the understanding that Applicants do not seek to be bound by the theory presented. 
     While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Numerous changes to the disclosed embodiments can be made in accordance with the disclosure herein without departing from the spirit or scope of the invention. Thus, the breadth and scope of the present invention should not be limited by any of the above described embodiments. Rather, the scope of the invention should be defined in accordance with the following claims and their equivalents. 
     Although the invention has been illustrated and described with respect to one or more implementations, equivalent alterations and modifications will occur to others skilled in the art upon the reading and understanding of this specification and the annexed drawings. In addition, while a particular feature of the invention may have been disclosed with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Furthermore, to the extent that the terms “including”, “includes”, “having”, “has”, “with”, or variants thereof are used in either the detailed description and/or the claims, such terms are intended to be inclusive in a manner similar to the term “comprising.” 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.