Most tracking systems use gyroscopes of one form or another to help stabilize and control the line of sight (LOS) for the
tracking sensor. Typically, the gyroscopes may be a significant part of the cost of the tracking system and may also require
significant power which is often limited, especially for tactical applications. By optimally combining the tracking sensor's
output with that from a magnetohydrodynamic angular motion sensor (MHD AMS), a tracking system platform can be
stabilized to high bandwidths. The MHD AMS performs the same function as a gyroscope at high frequencies, but currently
lacks capability to measure very low frequency inertial angular rates.
This paper briefly reviews typical tracking systems using gyroscopes. Next, the basic characteristics and testbed capabilities
of the MHD AMS are presented. Using the predicted MHD AMS noise and that expected from the tracking sensor, the
pointing performance is estimated for several different applications. The MHD AMS has been designed in several versions
which have different sensitivity and noise characteristics. Hence, a range of MHD AMS/tracking sensor combinations may be
used to provide systems which fulfill a variety of pointing and tracking specifications. Cost and performance information is
compared with those of typical gyroscopes used in a tracking system LOS stabilization application
A Fast Steering Mirror (FSM) is a mechanism that directs an optical beam
between a source and a receiver using a reflective surface. Applications
involving target detection and tracking require rapid scanning and slewing to
maintain the line of sight (LOS). These mission requirements define the performance
of a mechanism that offers precise pointing capability and a high
level of disturbance rejection capability.
Ball Communication Systems Division (BCSD) has developed, tested and delivered
reactionless fast steering mirror/scanners (see Figure A-1) that were designed
for use in an airborne tactical environment. These mechanisms direct, scan,
and stabilize a two inch optical beam over a total angular range of eight
degrees in a triangular scan profile at a frequency of fifteen Hertz. The
absolute position of the mirror is linear to within plus or minus forty microradians
within the eight degrees of angular travel and to within thirty-four
microradians for ninety percent of the triangular wave profile while scanning.
This paper will discuss the overall mechanical and electrical design as well
as present data illustrating the performance of the FSM.
Backlash (deadzone) and gear train resonances limit geared drive accuracy and dynamic performance. Although
direct drives provide a solution, there are many applications where torque requirements, configuration,
weight, and cost prevent practical application. In the past, a number of methods have been utilized to
minimize the negative effects of backlash, usually on a specific application basis, with the results poorly
reported and correlated. Through proper characterization of the drive problem, selection of mechanical and
electrical drive components and utilization of modem control techniques, high performance zero backlash
geared servo mechanisms can be designed and manufactured with predictable results. The purpose of this
paper is to present an approach to accomplish this task. The steps in this task are listed as follows:
1 . Definition of the available methods of implementation.
2. Presentation of factors in selecting the most effective approach for the specific application.
3. Selection of drive components and definition of system parameters including the necessary control
requirements, determining performance limits, and setting the maximum backlash and torque-bias
4. Performance analysis of a representative system.
5. Generation of a simulation program representing a test system.
6. Utilization of the simulation program to determine performance of future requirements to include
capability of parameter variance to evaluate "what if" conditions.
Magnetic Bearings are being used to isolate sensors from the severe vibrational, thermal, and frictional environments encountered on airborne systems. Technology developed by Aura Systems in the design and fabrication of magnetic suspension systems shows great promise for the stabilization of airborne sensors. This paper will cover the performance results of the Magnetic Gimbal Fabrication and Test (MGFT) project, which consisted of fabrication and performance testing of a single axis magnetic bearing. The MGFT results show LINE OF SIGHT (LOS) accuracy from 3 to 8 μrad with an angular disturbance of 48 rad/sec achieving vibration rejection of up to 79 dB. Also included is the description of the Advanced Missile Technology (AMT) project, which consists of fabrication and test of a single axis magnetic arc bearing for a small diameter missile. The AMT shows the capability to miniaturize the magnets and to provide extremely low friction under thermal loading. After proving the performance of magnetic bearings with the MGFT program a vast reduction in the size and weight of the magnetic bearing and associated electronics has been achieved while maintaining performance as demonstrated in the AMT.
A new noncontact optical preview sensing technique, developed at Georgia Tech, for possible application to a robotic seam tracking system is presented in this paper. This technique uses a structured laser illumination source, SELFOC Lens Array (SLA) coupled to fiberoptic array and phototransistor (photodetector) array. The hardware and software components, and the experimental results are described in this paper.
The manuscript is divided into five chapters as indicated below. Chapter I is the introduction, Chapter II describes the hardware while Chapter III explains the experimental procedures. The development of specialized data processing software is presented in Chapter IV. Finally, Chapter V discusses the results and conclusions.
During the last ten years the need for a new generation of star trackers emerged as the requirements for space platform attitude control became more stringent. Star trackers of the 1970's and 1980's were typically based upon image dissector tubes or P-N junction photo—diodes and could provide accuracy near 10 arc-seconds, 1-sigma, with extensive calibration. Future NASA an4 DoD spacecraft, including Space Station "Freedom" and various SDIO surveillance spacecraft, require almost a ten-fold improvement in accuracy coupled to greater sensitivity, functional versatility, and lower power and weight. lb meet these demands, a new tracker architecture is required. The Advanced Star T1acker (ASTRA) developed by Hughes Danbury Optical Systems, Inc. (formerly Perkin-Elmer's Electro-Optics Technology Division) combines the high sensitivity and resolution inherent in a modem charge coupled device detector with the versatile processing capability of a 16-bit microprocessor to achieve a level of performance surpassing existing trackers.
In this paper, we explore star tracker error sources and the design and calibration techniques utilized in ASTRA to eliminate or minimize those errors. An error tree presents high and low special frequency centroiding error sources and their influence on the tracker's design. Requirements for thermal control of the detector and for optical calibration are discussed along with an overview of the data processing function. Finally, we present hardware test results that demonstrate a significant improvement in accuracy and sensitivity relative to existing tube-type trackers.
The Weapons Lab/ARCA has developed a 1.5 meter telescope facility at Kirtland Air Force Base, New Mexico. Capabilities include tracking celestial objects and solar illuminated artificial satellites. To eliminate scheduled maintenance and minimize "down-time" due to equipment failure, only desktop computers and common optical sensors are used for pointing, acquisition, and tracking. WL/ARCA has developed in-house all of the software for the desktop computers, a tracker, and a control system for a fast steering mirror. This paper serves as a system overview which describes the telescope, the acquisition cameras, the tracker, the steering mirror control system, the software, and examples of tracking performance.
Briefly, a Macintosh lix computer interfaces to the telescope controller, to two acquisition cameras mounted on the main telescope tube, and to an Atari ST computer which controls the tracker and steering mirror. (Fig. 1) Using available ephemeris, the Macintosh dynamically points the telescope until the desired target is seen in the acquisition cameras. Video from these cameras is digitized and displayed in a rectangle on the computer monitor. If the computer "mouse" is "clicked" on the displayed target, the software modifies the ephemeris so that the target image moves to the center and illuminates the tracker. The Macintosh then accepts measurements from the Atari and holds the target to within a few arc-seconds of the boresite of the telescope. To achieve sub-microradian tracking , the Atari also sends correction signals at 300 hz to the fast steering mirror controller which causes the mirror to reduce the remaining tracking errors.
A real time image centroid tracker has been developed and is presently being used for laser beam alignment in the Aurora Laser Fusion project at Los Alamos National Laboratory. Aurora is one of the three national inertial confinement fusion energy experiments. The Aurora beam control systems are required to achieve angular beam pointing accuracy of up to 0.25 microradians by precision control of optical mirrors up to 44 inches in diameter.
The centroid tracker is part of a PS 170 video image processing system which provides the precision beam position information that is the feedback portion of a stochastic control system for beam pointing. Mechanical vibration and electronic noise inherent in the system is used to enhance, rather than degrade, positional resolution. This system is capable of yielding centroid position information accurate to within a very small fraction of one pixel.
The centroid tracker is presently implemented on one Multibus board using primarily HCT 7400 series logic and large PLDs. Digitized R5170 video is supplied as the board's input. The video image's centroid information is supplied by the board every 33 milliseconds as the board's output. A unique hardware algorithm used on the board allows very high resolution, real time tracking with a relatively small amount of electronics. Included on the board is circuitry used to distinguish image pixels from noise and background pixels.
Other applications of the centroid tracker might include pick and place robot arm control, military target tracking and pointing, intruder localization and, in general, very high resolution, real time image position tracking.
The board can be modified relatively easily to allow real time, multiple object centroid tracking and we expect to do this in the future. The first of the Aurora beam control systems requires that 96 laser beams be simultaneously controlled. The multiple centroid tracker board will make it possible to do image processing at a higher rate, leading to increased position resolution, while still maintaining control system bandwidth.
Electro-optical systems which are physically distributed over significant space and mounted on separateOptical benches require an optical alignment mechanism. Beamwalk control provides optical alignment by actively compensating for physical translation and rotations between separate optical support structure. Beam steering mirrors, mounted on the separate benches, are used to maintain optical alignment. A set of special optical detectors is used to measure the relative translation of a reference beam and the net angular deflection of that beam. These signals are fed back to the steering mirrors so that the mirrors can re-align the optical path.
This paper describer the beamwalk system of the Starlab experiment. A functional description is followed by a brief description of the optical layout. The control system is covered in more detail. The Stralab beamwalk control system commands one mirror servo with feedback from the beamwalk translation sensor and commands the other mirror servo with feedback from the beamwalk angle sensor. Servo Compensation is applied to each loop to achieve the desired stability. The advantage and disadvantage of controlling both mirrors with combined angle and translation sensor signals is addressed.
In Optical Target Tracking Systems (TTS) the problem of Line Of Sight (LOS) stabilization plays a key role in overall TTS performance. The Stabilization Mechanism is required to compensate for disturbances arising from various parts of the TTS These disturbances arise from the servomechanism, the electronics, the optics and the imaging parts of the TTS. While in every part of the TTS an effort is made to minimize these disturbances there still exists the need for the Closed Loop Stabilization. The Closed Loop Stabilization (CLS) is implemented in various structures. It can be implemented using either Inertial Devices, such as Rate Gyros or by the use of optical methods In each case, the goal of the design is to compensate dynamically for any LOS error. The method of LOS error measurement can vary depending on system requirements and budget. The CLS design is dependent on the overall TTS performance parameters. The parameters of the TTS that influence the Stabilization Loop Structure are : pointing accuracy, target acceleration, target velocity and target maneuvering. Once system performance is presented in the frequency domain, it is possible to deal with the preferred architecture of the system. This results in a particular loop structure: the Stabilization loop being an inner loop of the pointing loop. After the Stabilization Loop location in the TTS is decided, the design parameters of the Stabilization loop are derived.
The estimation of the angular position of an object and the evaluation of image quality are considered for an active tracking system consisting of an agile scanning transmitter and an imaging receiver. In many applications (e.g. imaging at long ranges) transmitter energy/pulse requirements are stressing, and flood illumination of targets will result in images that are severely degraded due to photon shot noise. In order to achieve better image quality and tracking accuracy, it may be preferable to scan a narrow beam over the entire object or an object feature. This may reduce the effects of shot noise, but would magnify the effects of beam jitter. In this paper, we examine the effects of these two sources of image degradation, and introduce various measures of image quality. The quality of the restoration of the degraded image is evaluated, showing the extent to which the effects of beam jitter and shot noise can be reduced. There exists an optimum beam size for which the quality of the restored image is best. The sensitivity of image quality to the selection of beam size is examined, and the effect of narrow beam illumination on the performance of various algorithms is discussed.
The employment of a large telescope with a high lateral resolution imposes a high pointing precision of a generic sky target measurement. The paper describes the design of two motor servo—loops for a azimuth stabilization (single axis) of a gondola. This is the first and the most important step in pointing because it is the only one action that moves the whole flight structure and it has the task of controlling the non linear friction of the suspension bearing in order to isolate the instrumentation from the cruise balloon as much as possible. The servo—system is theoretically capable of 1 arc mm of absolute accuracy through two subsequent steps: a first one (the lower accuracy) is performed with magnetometer sensor and a second one (the highest accuracy) is led by a rate integrating gyro sensor or a high definition CCD camera. The system proposed makes use of two DC torque motors. One for any motion of the platform around the vertical axis and one strategically placed at the interconnecting point balloon—payload (Pivot) for attenuating the friction bearing. Some mechanical non—linearities, localized exactly at this point, impose a time domain design for any settling time control whenever the gondola experiences a new step in azimuth coordinate. The work points out as it is possible to control this settling time of the gondola, by means of simplified equations of motion in the time domain, tested in open loop conditions. A mechanical approach of an active Pivot to avoid the disturbance of balloon rotation on the current tracking of the sky azimuthal target is reported. This is the most important goal in order to achieve the highest precision of the action pointing without slowly cancelling the control of the motor devoted to that task. Some results of a true simulation program tailored on the mechanical approach proposed in parametric form are shown. Therefore for any combination of weight and inertia moment this program, tested on a flight prototype, can be an effective simple tool for designing pointing systems where a forecast of a final accuracy either absolute or as root—mean— square (RMS) is requested. The program can also tell us the amount of power supply consumption according either to peak or average current for some possible flight operations for remote sensing. The work suggests also some possible hardware and software solutions that interface a dedicated computer card and analog I/O signals. Finally some results of the last Italy—Spain flight (1988), in order to test the first step of the pointing precision, according to accuracy of an 8 bit A/D converter, is also shown.
A data fusion processor which combines information from a platform scanned line array of detectors and an imaging JR sensor has been developed to detect, identify, and track ship targets. The sensors, scanning platform, and image processor are integrated into an experimental system which is tested on a Navy P3 aircraft. The processor operates in real time to select targets based on a programmable classification criteria.
The vertically stacked detector array is mounted on an inertially stabilized platform which is horizontally scanned at an operator selectable rate. The processing of each detector in the array is set by the operator and may be considered separately or combined with other elements in the array to produce a synthetic large instantaneous field of view. The scan rate and processing selection is made on the basis of the search area of interest, atmospheric conditions, the target data, and other factors. The JR imaging camera provides scene images at a 30 hertz rate which are combined with the line array data in the classification processor. Multiple digital signal processors are used in the classification processor to achieve the required data throughput rates. The system configuration, the requirements on the platform scanner, the classification processor algorithms, and the classification processor architecture are discussed. Data from the field tests will also be presented.
The Infrared High-Value Target Acquisition (IRHVTA) program demonstrated autonomous acquisition and tracking of large fixed high-value targets with an airborne imaging-infrared seeker. This paper describes the use of the terminaltracking subsystem during the autonomous-acquisition phase of each mission to improve the acquisition performance. After defining the IRHVTA program, the paper completes its introduction by describing the system, trking, and acquisition algorithms and their architecture to give the required background for understanding how the system functioned.
The paper describes how the IRHVTA tracker subsystem autonomously selected and tracked points throughout the infrared (IR) sensor's field of view to maintain geometry stabilization relative to the ground. It explains how the acquisition subsystem used this stabilization to interrelate sequential snapshots. This allowed later snapshots to use the acquisition information from earlier ones to reduce the weapon to target uncertainty. The reduced uzxertainty Permitted the searching of smaller areas of the imagery for the later acquisitions. The paper also SCribeS the use of the groundstabilized geometry to transition from acquisition of large landmark objects early in the mission to smaller targets later in the mission with minimized probability of false alarm. The paper concludes with an explanation of the benefits of this design on probability of detection and on operation in the presence of camouflage and decoys. The extension of this design to the attack of invisible aim points is also explained.
Star-tracking systems, optical communication systems, and infrared tracking systems are examples in which the measurement and correction of alignment errors between the optical source and receiver must be made. In this paper, we develop a new position estimator that retains curacy even under poor SNR conditions. This estimator is derived using an estimation theoretic approach to the problem of tracking a quasi-stationary object given photoevent data in a continuously distributed detector. We derive a maximum likelihood position estimator via application of the expectation-maximization (EM) algorithm. Simulation results are given to show that under low SNR conditions, the estimator performance is superior to that of the commonly used centroid estimator.
This paper summarizes the development, structure, verification, and applications of the Multi-Target Acquisition System (MTAS) Fire Control (FC) simulation. Development of the simulation began in 1982 as part of the Center for Night Vision and Electro-Optics (CNVEO) "Search and Target Acquisition Radar for Target Location and Engagement" (STARTLE) Program. Originally, a milli-meter wave radar sensor was employed to locate and tract multiple targets. Since then, the simulation has been extended to include a FLIR/ electro-optical sensor, a manual tracking system, and more sophisticated FC algorithms applicable to multiple targets. The purpose of this paper is to describe the beginnings of a generic, multi-target fire control structure that is applicable to armored vehicles, and to illustrate the key error contributors of accurate target location and subsequent motion prediction.
Descriptions of the key FC algorithms are provided. Sample results for stationary firer/maneuvering multiple targets for different tracking systems are presented. Also, the timeline characteristics of addressing three targets in succession is presented to illustrate the multi-target analysis capability of the simulation. Finally, applications to current and future Army programs are discussed.
Inertial stabilization systems are designed to maintain the angular orientation of an optical system or other device in inertial space. Applications include surveillance, target tracking, flight control, weapon pointing, navigation, communication and others. Typically, some variation of a closed loop control system is employed which uses feedback from a gyro. The object of this paper is to consider the potential benefits and some approaches to adaptive control algorithms.
Ideally, an adaptive control system would adjust itself to achieve "optimal performance" with respect to some criteria in the presence of changing plant characteristics, changing noise characteristics and a changing disturbance environment. Potentially, such a design could provide robust control for a variety of system configurations, mission conditions and applications resulting in significant reductions in both development and production costs as well as improved performance.
First, the general stabilization problem and some conventional control system designs are briefly reviewed. Then a variety of adaptive techniques are surveyed. Finally, the current status and results of a joint research project between Texas Instruments and the University of Texas at Arlington whose goal is to develop an adaptive stabilization control system is discussed.
Mobile platforms with heavy, high powered payloads, such as long range laser designators and directed energy weapons, require precision control of pointing in the presence of base motion disturbances. Wideband motion stabilization and target traking control systems with high dynamic gain are required. Cascading multiple integrators in the forward loop, for example, is a direct, commonly used technique for obtaining the loop gain required to achieve stabilization accuracy. This often leads, however, to stability problems and constraints on system bandwidth. The motion stabilized EO tracking and pointing control system design described in this paper uses a unique, supervisory control approach to achieve wideband pointing accuracy. The control system described is an extension of previously developed and fielded weapon pointing control systems.
The model based tracking and feed forward methods, used to achieve high dynamic pointing and tracking accuracy without the destabilizing effect of excessive gain, are presented. The basic system configuration and the concept of a central electro—optical Stable Sensor System controller are described and demonstrated with a simple tracking scenario.
Line-of-Sight (LOS) stabilization of a two axis gimbal (i.e., Elevation and Cross-Elevation) can be improved considerably with the addition of a second set of gimbals (inner and outer) mounted on the X-EL gimbal via flex pivots rather than bearings. With this configuration, a position loop is closed around the inner set for two main functions: 1) stabilize the inner set from a control systems point of view and 2) provide one—to—one coupling between the inner and outer gimbal sets at low frequencies for tracking purposes (less than 2 Hz).
Flex pivots introduce very low coulomb and viscous friction coupling making possible a -40 dB/dec roll-off in the position closed loop (mass stabilization) . This roll-off, beginning at about 2 Hz, increase possible the increase in stabilization from the outer to the inner set. However, special attention must be given to the effects of the relatively large spring rate coupling associated with flex pivots. For the system considered, the flex pivot gimbal resonance limits the minimum bandwidth to 3.5 Hz using conventional derivative control.
This paper discusses a positive feedback solution implementing band limited derivative control to compensate for the flex pivot resonance while minimizing the bandwidth to 2.0 Hz for an additional 11 dB of attenuation above 3 Hz. Trade-off studies are discussed and a closed form solution is presented which solves for the compensator parameters as a function of flex pivot stiffness, plant characteristics, and desired bandwidth. Three examples are presented.
The technology of testing to determine system level performance of tracking and pointing systems has evolved in recent years. Modern multichannel data acquisition, processing, and analysis systems have allowed development of new test methods that significantly increase our ability to understand and quantify system performance and the sources of performance limitations. Pointing and tracking systems control the inertial orientation of a variety of critical payloads in applications such as weapons delivery, surveillance, target discrimination, missile guidance, communication, gunnery, directed energy systems, and many others. In systems with stringent performance requirements, it is necessary to accurately identify, measure, and account for test environment effects and associated induced disturbances on the errors of the pointing and tracking system.
The keys to the improved approach to testing complex pointing and tracking systems are the coherence analysis algorithms developed in recent years by Dr. Julius Bendat et a!. The underlying concept is that all environmental and test induced disturbances are instrumented and simultaneously recorded with the signals that characterize the pointing and tracking system performance. The hypothesis on which data analysis is predicated is that a set of measured disturbances (or inputs) accounts for the measured performance error (output). The coherence analysis algorithms permit the test analyst to break up the performance signal into components caused by each of the input paths and to quantify that part of the performance not allocatable to any of the measured disturbances.
The authors have exploited the coherence analysis methods to accurately characterize the tracking and stabilization performance of equipment being prepared for a space experiment. The environment in the ground test facilities is significantly different from that expected in the space environment and would have obscured the true system performance. Therefore, vibration signals acquired on a high bandwidth, simultaneous data collection computer were analyzed using the multiple input coherence analysis algorithm to accurately determine influences of each disturbance input on the performance. This paper presents a tutorial on the advanced testing methodology and illustrates how significant testing challenges were addressed. The ability to confirm the adequacy of the system performance would not be possible without the use of the advanced tools. The techniques are applicable to system level performance testing of a broad range of complex pointing and tracking systems.
The Extended Kalman filter has been applied to track low SNR, subpixel targets and more recently for SDI applications. This approach has also been considered in long range tracking of spot targets. However the computational requirements do not fit well within the typical processing timelines of high speed missile applications therefore computationally faster but less optimal algorithms are usually selected. The computational complexity of the Extended Kalman tracking algorithm is closely related to the number of pixel observables for IR imagery. For missile closure scenarios as the target size grows so does the observation space. The Hadamard domain Extended Kalman Tracking approach first transforms IR image pixels into the Hadamard domain. A reduced set of observations in the Hadamard domain representing most of the target energy are selected to be processed by the Extended Kalman Tracker. With a significant reduction in the number pixels the Extended Kalman filter becomes computationally competitive With less optimal algorithms while preserving the optimal performance properties of Kalman filtering. This concept has been demonstrated on both synthetic and real IR imagery and shows expected improved tracking accuracy relative to the less optimal tracking algorithms. This approach is also superior to other observation space reduction techniques which do not possess the target energy preserving properties of image transforms such as the Hadamard transform
In order to meet the performance contraints imposed on modern stabilization and tracking systems, a wide variety of gimbal and optical configurations are required. As mechanisms become more complex, understanding the kinematic relationships within the assemblies becomes less intuitive. Therefore careful analysis is needed to insure the mechanisms operate properly and to identify appropriate means for control. The analysis should include the development of kinematics for transforming vectors through the gimbal set. Such vectors could be vehicle angular rate, target position, and gravity. This paper outlines the general steps to be followed in such a development and then presents a specific gimballed mirror system to serve as an example for other development of this type. This system uses a strapdown detector and mounts the optics (two front-surface flat mirrors and a derotation prism) on gimbals to stabilize and point the Line-of-Sight. Finally, this system is also used to illustrate the analysis of the kinematics necessary for maintaining the target image upright in the displayed field-of-view.
This paper addresses the use of pulse width modulation (PWM) amplifiers to drive brushless direct current (D.C.) motors in either a trapezoidal or sinusoidal commutation control scheme. A review of amplifier classifications and a comparison of the linear amplifier performance with that of the PWM amplifier is presented. Illustrations show the operational flow of two common power stages (T-bridge and H-bridge) when used with PWM and the resulting electrical equations of current flow are shown. A summary of the advantages and disadvantages of the classes of amplifiers is given. The amplifier discussion is then directed to the comparison of trapezoidal and sinusoidal commutation of the brushless D.C. motor with PWM. The electrical equations and waveforms associated with each method are developed to stress the differences between the two methods. Two servo control loop block diagrams illustrate the differences in electronics required by the two methods.
We are developing a real-time-multiple-target-tracking system using a wide-field-of-view (WFOV) camera The high resolution WFOV camera was conceived as part of the Strategic Defense Initiative Research at Lawrence Livermore National Laboratory. The camera system consists of a lens made of concentric solid blocks of index matching glasses, CCDs arrayed on the focal plane, and a custom VLSI image processor to extract the targets. References 1 and 2 describe the basic design of the WFOV camera and the prototype system that we have constructed. In this paper, we will briefly review the existing prototype system, the on-going effort to cover the full field of view using digital CCD cameras, the production of custom VLSI chips developed to extract centroids in real time, and the implementation of transputers to run the tracking algorithms.