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radar:tws [2018/06/07 09:28] – georgeradar:tws [2026/04/28 18:24] (current) – mauro
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->TOC ok for now! Please use headers instead of bold!  --- //[[webmaster@localhost|DokuWiki Administrator]] 2018/04/24 16:18//+
  
 ===== TWS ===== ===== TWS =====
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 The automatic detector part of the ADT quantizes the range into intervals equal to the The automatic detector part of the ADT quantizes the range into intervals equal to the
-range resolution. At each range interval the detector integrates 11 pulses, where n is the numberof pulses expected to be returned from a target as tile antennas catis past. The integrated pulses+range resolution. At each range interval the detector integrates 11 pulses, where n is the number of pulses expected to be returned from a target as tile antennas catis past. The integrated pulses
 are compared with a threshold to indicate the presence or absence of a target. An example is are compared with a threshold to indicate the presence or absence of a target. An example is
 the commonly used moving window detector which examines continuously the last r-1 samples the commonly used moving window detector which examines continuously the last r-1 samples
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 avoiding computer overload that the radar used with ADT should be designed to exclude avoiding computer overload that the radar used with ADT should be designed to exclude
 unwanted signals, as from clutter and interference. A good ADT system therefore reqirires radar with a good-MTI and a good CEAE-(constant false alarm rate) receiver. A clutter map, unwanted signals, as from clutter and interference. A good ADT system therefore reqirires radar with a good-MTI and a good CEAE-(constant false alarm rate) receiver. A clutter map,
-generated by the radar, is sometimes used to reduce the load on thc tracking computer by blanking clutter areas and removing detections associated with large point clutter sources not+generated by the radar, is sometimes used to reduce the load on the tracking computer by blanking clutter areas and removing detections associated with large point clutter sources not
 rejected by the MTI. Slowly moving echoes that are not of interest can also be removed by the rejected by the MTI. Slowly moving echoes that are not of interest can also be removed by the
 clutter map. The availability of some distinctive target characteristic, such as its altitude, might clutter map. The availability of some distinctive target characteristic, such as its altitude, might
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 One approach is to first quantize the range and sometimes the azimuth angle.The quantization increment in range might be the pulse width and that is angle might be the azimuth beamwidth.At each range-azimuth quantization cell, the pulse received during the time the antenna scans past the target are integrated and a detection decision is made. CFAR generally is incorporated before the decision process inorder to prevent excessive false alarm due to clutter echoes. Pulse Integration is performed in some form of automatic detector,or integrator. One approach is to first quantize the range and sometimes the azimuth angle.The quantization increment in range might be the pulse width and that is angle might be the azimuth beamwidth.At each range-azimuth quantization cell, the pulse received during the time the antenna scans past the target are integrated and a detection decision is made. CFAR generally is incorporated before the decision process inorder to prevent excessive false alarm due to clutter echoes. Pulse Integration is performed in some form of automatic detector,or integrator.
  
-Another approach to automatic detection is the moving window detector which examines continuosly the last n pulses and announces the presence of a target if it at least m out of n of the pulses exceed a present threshold.A by product of the automatic detection decision with a moving window detector or something similar is an angle measurement made by beam splitting. if n pulses expected to be recieved from a target ,beam splitting involves recognizing the begining and end of the n pulses and locating their centre.Angle accuracy depends on how well the begining and end of the tram of n pulse can be determined,as well as the number of pulses available and their signal to noise ratio.The beam spltting decision logic usually has no prior knowledge of targets begining.The logic must be sufficiently sensitive to quickly recognize the increased density region that signifies the start of an echo-signal pulse train , yet it must not be so sensitive it generates false starts due to noise alone.Once a target's beginning is recognized,the device must sense the end of the increased density region .If the decision logic is too sensitive to change,it could cause a single target to split into two. A rough rule of thumb often quoted is that the accuracy of beam splitting is about one-tenth of a beamwidth when the signal to noise ratio is high enough to provide a good probability of detection.+Another approach to automatic detection is the moving window detector which examines continuosly the last n pulses and announces the presence of a target if it at least m out of n of the pulses exceed a present threshold.A by product of the automatic detection decision with a moving window detector or something similar is an angle measurement made by beam splitting. if n pulses expected to be recieved from a target ,beam splitting involves recognizing the begining and end of the n pulses and locating their centre.Angle accuracy depends on how well the begining and end of the tram of n pulse can be determined,as well as the number of pulses available and their signal to noise ratio.The beam splitting decision logic usually has no prior knowledge of targets begining.The logic must be sufficiently sensitive to quickly recognize the increased density region that signifies the start of an echo-signal pulse train , yet it must not be so sensitive it generates false starts due to noise alone.Once a target's beginning is recognized,the device must sense the end of the increased density region .If the decision logic is too sensitive to change,it could cause a single target to split into two. A rough rule of thumb often quoted is that the accuracy of beam splitting is about one-tenth of a beamwidth when the signal to noise ratio is high enough to provide a good probability of detection.
 === Track Correlation and Association === === Track Correlation and Association ===
 Target observation on each radar scan that survives hit pattern recognition and clutter rejection functions is Target observation on each radar scan that survives hit pattern recognition and clutter rejection functions is
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 tracking gates, **tracking ambiguity** results. tracking gates, **tracking ambiguity** results.
  
-When a new detection is recieved that is not at the location of a clutter echo stored in the clutter map, an attempt is made to associate it with an existing track.Association with an existing track is aided by establishing for each track a small search window or gate ,within which the detction of target on the next scan of the radar antenna is predicted to appear. The gate should be as small as possible in order to avoid having more than one echo fall within it when the traffic density is high or when two tracks are close to one another. On the other hand, a large gate region is needed if the tracker is to follow target turns or maneuvers. More than one gate size is used to over come this dilemma.Figure 1 shows a small nonmaneuvering gate situated around the predicted position of the target in track. The size of the gate is determined by the estimated errors in the predicted position and the estimated errors in speed and direction of the track. The detection threshold might be lowered in the gate region to increase the probability of detection. When an echo is not found within the maneuvering gate ,the larger region encompassing the maneuvering gate is then searched. The size of the maneuvering gate is determined by the estimate of the maneuvering capability of the target under track.+When a new detection is recieved that is not at the location of a clutter echo stored in the clutter map, an attempt is made to associate it with an existing track.Association with an existing track is aided by establishing for each track a small search window or gate ,within which the detection of target on the next scan of the radar antenna is predicted to appear. The gate should be as small as possible in order to avoid having more than one echo fall within it when the traffic density is high or when two tracks are close to one another. On the other hand, a large gate region is needed if the tracker is to follow target turns or maneuvers. More than one gate size is used to over come this dilemma.Figure 1 shows a small nonmaneuvering gate situated around the predicted position of the target in track. The size of the gate is determined by the estimated errors in the predicted position and the estimated errors in speed and direction of the track. The detection threshold might be lowered in the gate region to increase the probability of detection. When an echo is not found within the maneuvering gate ,the larger region encompassing the maneuvering gate is then searched. The size of the maneuvering gate is determined by the estimate of the maneuvering capability of the target under track.
  
  
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 </figure> </figure>
  
-One reason the target might , not appear in the nonmaneuvering gate is that its radar cross secion might decrease, or fade,so that it is not detected.When this is the case, it is possible for a false track to occur when a noise spike or an echo from another target is found in the maneuvering gate.To avoid the problem caused by a target fade and a false indication appearing in the larger maneuvering gate, the tracks can be divided into two tracks.(This is known as bifurcation of the track). One in the original track with no new detection in the nonmaneuvering gate.The other is a new track based on the signal found in the maneuvering gate. After recieving the target position on the next scan of the radar (or sometimes after two scans), a decision is made as to which of two tracks should be dropped.Tracking is usually done in cartesian coordinates, but the coorelation gates are defined in polar (r,θ) coordinates.+One reason the target might , not appear in the nonmaneuvering gate is that its radar cross section might decrease, or fade,so that it is not detected.When this is the case, it is possible for a false track to occur when a noise spike or an echo from another target is found in the maneuvering gate.To avoid the problem caused by a target fade and a false indication appearing in the larger maneuvering gate, the tracks can be divided into two tracks.(This is known as bifurcation of the track). One in the original track with no new detection in the nonmaneuvering gate.The other is a new track based on the signal found in the maneuvering gate. After recieving the target position on the next scan of the radar (or sometimes after two scans), a decision is made as to which of two tracks should be dropped.Tracking is usually done in cartesian coordinates, but the coorelation gates are defined in polar (r,θ) coordinates.
  
 **Resolution of track ambiguity**:Track ambiguity arises when either multiple targets appear within a single **Resolution of track ambiguity**:Track ambiguity arises when either multiple targets appear within a single
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 too slow to be used in a system where speed of operation is one of the primary goals. too slow to be used in a system where speed of operation is one of the primary goals.
  
-In principle, a track can be initiated from the target location information obtained on two successive scans of the radar antenna. In practice, however target information from three or more scans is usually needed to intiate a track.Two scans would be adequatewhen there is only one or a few aircraft within view, but when the radar has in view  a larger number of echoes, one or more additional scan may be needed to prevent false tracks from being initiated. Thus it is more usual to require three or more scan before establishing a track.A clutter map is used to store, the locations of fixed clutter echoes and prevent tracks from being initiated based on a clutter echo combined with a real target detection.Such tracks can eventually be recognized as false  and can be dropped , but it takes time and computer capacity to do so when there are a large number of them.Clutter echoes for inclusion in the clutter map are those echoes that do not change their location with time or that change loction too slowly to be targets of interest.+In principle, a track can be initiated from the target location information obtained on two successive scans of the radar antenna. In practice, however target information from three or more scans is usually needed to intiate a track.Two scans would be adequate when there is only one or a few aircraft within view, but when the radar has in view  a larger number of echoes, one or more additional scan may be needed to prevent false tracks from being initiated. Thus it is more usual to require three or more scan before establishing a track.A clutter map is used to store, the locations of fixed clutter echoes and prevent tracks from being initiated based on a clutter echo combined with a real target detection.Such tracks can eventually be recognized as false  and can be dropped , but it takes time and computer capacity to do so when there are a large number of them.Clutter echoes for inclusion in the clutter map are those echoes that do not change their location with time or that change loction too slowly to be targets of interest.
  
-The process of initiating a track in a dense environment of targets and clutter not diminated by the radar can be quite demanding in both computer software and hardware. Initiation of a new track may take more computer time  and capability than any other aspect of ADT.Requiring three scans for a civil air-traffic control radar to establish a track is usually not a burden. Wiating three scans for track establishment , however may be an excessively long time for a military  air-defense radar that has to direct weapon-control radars to defined against high speed trackers that "pop up" at short range over the horizon.it is possible to quickly aquire  the target on the basis of a sinlge scan past the target if the radar can obtain a quick second look. This might be done with a look-back beam directed to the angle of the original detection.The quick look-back can provide confirmation of detection  and an estimate of target's related velocity. A phased array radar is well suited for this purpose, but mechanical rotating radar can also be outfitted with a fixed look back beam. Look back might also be accomplished with a 3D radar whose eletronically scanning beam in elevation is returned to the elevation angle of initial detection, before the radar beam entirely scans past the target.+The process of initiating a track in a dense environment of targets and clutter not diminated by the radar can be quite demanding in both computer software and hardware. Initiation of a new track may take more computer time  and capability than any other aspect of ADT.Requiring three scans for a civil air-traffic control radar to establish a track is usually not a burden. Waiting three scans for track establishment , however may be an excessively long time for a military  air-defense radar that has to direct weapon-control radars to defined against high speed trackers that "pop up" at short range over the horizon.it is possible to quickly aquire  the target on the basis of a sinlge scan past the target if the radar can obtain a quick second look. This might be done with a look-back beam directed to the angle of the original detection.The quick look-back can provide confirmation of detection  and an estimate of target's related velocity. A phased array radar is well suited for this purpose, but mechanical rotating radar can also be outfitted with a fixed look back beam. Look back might also be accomplished with a 3D radar whose eletronically scanning beam in elevation is returned to the elevation angle of initial detection, before the radar beam entirely scans past the target.
      
 === Generation of tracking "gates" === === Generation of tracking "gates" ===
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 ground-based system consisting of a pencil-beam antenna mounted on a rotatable ground-based system consisting of a pencil-beam antenna mounted on a rotatable
 platform which is caused by motor drive of its azimuth and elevation position to platform which is caused by motor drive of its azimuth and elevation position to
-follow a target in Figure 5. Errors in pointing direction are determined by sensing+follow a target in Figure 6. Errors in pointing direction are determined by sensing
 the angle of arrival of the echo wavefront and corrected by positioning the antenna the angle of arrival of the echo wavefront and corrected by positioning the antenna
 to keep the target centered in the beam. to keep the target centered in the beam.
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 produced it. Thus, position reports are used as they occurred in real time, and no position report is accepted produced it. Thus, position reports are used as they occurred in real time, and no position report is accepted
 out of order. IADT reduces loss of data due to individual radar propagation and lobing characteristics while allowing quality weighting of data relative to it source. IADT systems can accept the output of TWS or non- out of order. IADT reduces loss of data due to individual radar propagation and lobing characteristics while allowing quality weighting of data relative to it source. IADT systems can accept the output of TWS or non-
-TWS radars as well as that derived from IFF transponders.When multiple radar view a common volume, there can be improved tracking , the data rate can be greater than any of the radar acting alone ,there is less vulnerability to electronic countermeasures, and lesslikelihood of having missed detection due to reduced echo-signal strength caused by null in one of the antenna pattern or changes in the target aspect.+TWS radars as well as that derived from IFF transponders.When multiple radar view a common volume, there can be improved tracking , the data rate can be greater than any of the radar acting alone ,there is less vulnerability to electronic countermeasures, and less likelihood of having missed detection due to reduced echo-signal strength caused by null in one of the antenna pattern or changes in the target aspect.
  
-**Integrated Tracking From Collocated Radar at a Single Site**:When more than one radar covering approximately the same volume in space, are located in the same vicinity , their individual output can be combined to form  a single track.The radar might operate in different frequency bands, have different antenna characteristics , and diferent data rates. There is more than one way to combine the output of multiple radars.A good approach is to combine all the detections from each radar  to form a single track and to update the track rather than develop seperate tracks at each radar  and either select the best track or combine them is some other manner.The data from the various radars do not arrive at the tracker at a uniform rate.The development of a single track file by the use of the total data available from all radars produce a better track than combining thetracks developed individually at each radar.it reduces the likelihood of a loss of data as might be caused by antenna lobing, target feeding, interference, and clutter since integrated processing permits the favourable weighting of the better data and lesser weighting of poorer data. This method of combining data from multiple radar has been known as either **automatic detection and integrated Tracking (ADIT) or integrated automatic detection and Tracking (IADT)**.+**Integrated Tracking From Collocated Radar at a Single Site**:When more than one radar covering approximately the same volume in space, are located in the same vicinity , their individual output can be combined to form  a single track.The radar might operate in different frequency bands, have different antenna characteristics , and diferent data rates. There is more than one way to combine the output of multiple radars.A good approach is to combine all the detections from each radar  to form a single track and to update the track rather than develop seperate tracks at each radar  and either select the best track or combine them is some other manner.The data from the various radars do not arrive at the tracker at a uniform rate.The development of a single track file by the use of the total data available from all radars produce a better track than combining the tracks developed individually at each radar.it reduces the likelihood of a loss of data as might be caused by antenna lobing, target feeding, interference, and clutter since integrated processing permits the favourable weighting of the better data and lesser weighting of poorer data. This method of combining data from multiple radar has been known as either **automatic detection and integrated Tracking (ADIT) or integrated automatic detection and Tracking (IADT)**.
  
 The **Integrated Automated Detection and Tracking (IADT) System AN/SYS-2** is a computer-based radar data processor with automated radar target detection, tracking, and correlation capabilities. The AN/SYS-2 correlates contact data from the 2-D and 3-D air-search radars to provide a single, unduplicated, highly-accurate, surveillance picture output in various operational environments, including clutter and electronic countermeasures. The AN/SYS-2 accomplishes this by taking advantage of the mutually supporting aspects of the 2-D and 3-D radars surveillance volume of coverage and by exploiting their special modes of radar operation. The AN/SYS-2 is designed to enhance significantly the effectiveness of the combat system by reducing reaction time, improving threat assessment, providing earlier warning, and providing a prompt and reliable detection capability in the presence of high target density and electronic countermeasures. The **Integrated Automated Detection and Tracking (IADT) System AN/SYS-2** is a computer-based radar data processor with automated radar target detection, tracking, and correlation capabilities. The AN/SYS-2 correlates contact data from the 2-D and 3-D air-search radars to provide a single, unduplicated, highly-accurate, surveillance picture output in various operational environments, including clutter and electronic countermeasures. The AN/SYS-2 accomplishes this by taking advantage of the mutually supporting aspects of the 2-D and 3-D radars surveillance volume of coverage and by exploiting their special modes of radar operation. The AN/SYS-2 is designed to enhance significantly the effectiveness of the combat system by reducing reaction time, improving threat assessment, providing earlier warning, and providing a prompt and reliable detection capability in the presence of high target density and electronic countermeasures.
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 where  $x_{pn}$ = predicted position of the target on the nth scan, $x_{n}$ = measured position on the nth scan, α = position smoothing parameter, β = velcity smoothing parameter , and $T_{s}$ = time between observations. where  $x_{pn}$ = predicted position of the target on the nth scan, $x_{n}$ = measured position on the nth scan, α = position smoothing parameter, β = velcity smoothing parameter , and $T_{s}$ = time between observations.
  
-if α = β = 0, the tracker uses no current target information, only yhe smoothed data from prior observations. When α = β = 1, no smoothing of the data is included at all.Thus the closer α and β are to zero, the more important is the track in determining the predicted track. The closer they are to 1, the more important is the currently measured data.if target acceleration is significant , a third equation can be added to describe an α,β,γ tracker , where γ = acceleration smoothing parameter.+if α = β = 0, the tracker uses no current target information, only the smoothed data from prior observations. When α = β = 1, no smoothing of the data is included at all.Thus the closer α and β are to zero, the more important is the track in determining the predicted track. The closer they are to 1, the more important is the currently measured data.if target acceleration is significant , a third equation can be added to describe an α,β,γ tracker , where γ = acceleration smoothing parameter.
  
 Benedict and Border show that if the transient response to a maneuvering target can be modeled by a ramp function , the output noise variance at steady state is minimized in an α - β tracker when $ β = \frac {α^{2}}{2-α}$. it was stated that the analysis does not , and cannot , specify the optimum value of α. The value of α is determined by the bandwidth and will depend on the system application. In selecting α, a compromise usually must be made between good smoothing of the random measurement errors (requiring a narrow bandwidth) and a rapid response to maneuvering target (wide bandwith). Trunk states that an α and a β satisfying the above relation can be chosen so that  the tracking filter will follow a specified g turn. Benedict and Border show that if the transient response to a maneuvering target can be modeled by a ramp function , the output noise variance at steady state is minimized in an α - β tracker when $ β = \frac {α^{2}}{2-α}$. it was stated that the analysis does not , and cannot , specify the optimum value of α. The value of α is determined by the bandwidth and will depend on the system application. In selecting α, a compromise usually must be made between good smoothing of the random measurement errors (requiring a narrow bandwidth) and a rapid response to maneuvering target (wide bandwith). Trunk states that an α and a β satisfying the above relation can be chosen so that  the tracking filter will follow a specified g turn.
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 where n is the number of the scan or target obsrevation(n>2). The above equations for α and β are also called the kalman gain components. where n is the number of the scan or target obsrevation(n>2). The above equations for α and β are also called the kalman gain components.
  
-The classical α - β tracker is designed to minmise the mean - square error in the smoothed position and velocity. This type of tracker is said to be relatively easy to implement , but it does not handle the maneuvering target. Some means has to be included to detect maneuvers and change the values of  α and β accordingly.The two tracking gate described in connection with Fig 1 is one example of how to deal with a large maneuvers. Another example is an adaptive α - β tracker which varies the smoothing parameter to achieve a variable  bandwidth that allows the radar to follow target maneuvers. When the target is not maneuvering the adaptive tracking algorithm provides heavy smoothing. if the target maneuvers or makes a turn , the filter bandwidth is widened so as to allow the track filter to follow. As the selection of the values of α and β becomemore sophesticated and requires knowledge of the statistics fo the measurement errors and the prediction errors, the α - β tracker approaches the Kalman Filter.The selection of (α , β) is a design tradeoff. Small gains make a small correction in the direction of each detection.As a result ,the tracking filter is less sensitive to noise but is more sluggist to respond to maneuvers - deviation from the assumed target model. Conversily, large gains produce more tracking noise but quicker response to maneuvers. These errors are readly calculated as a function of α and β using formula's shown in Table 1. +The classical α - β tracker is designed to minmise the mean - square error in the smoothed position and velocity. This type of tracker is said to be relatively easy to implement , but it does not handle the maneuvering target. Some means has to be included to detect maneuvers and change the values of  α and β accordingly.The two tracking gate described in connection with Fig 1 is one example of how to deal with a large maneuvers. Another example is an adaptive α - β tracker which varies the smoothing parameter to achieve a variable  bandwidth that allows the radar to follow target maneuvers. When the target is not maneuvering the adaptive tracking algorithm provides heavy smoothing. if the target maneuvers or makes a turn , the filter bandwidth is widened so as to allow the track filter to follow. As the selection of the values of α and β become more sophesticated and requires knowledge of the statistics fo the measurement errors and the prediction errors, the α - β tracker approaches the Kalman Filter.The selection of (α , β) is a design tradeoff. Small gains make a small correction in the direction of each detection.As a result ,the tracking filter is less sensitive to noise but is more sluggist to respond to maneuvers - deviation from the assumed target model. Conversily, large gains produce more tracking noise but quicker response to maneuvers. These errors are readly calculated as a function of α and β using formula's shown in Table 1. 
  
  
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  </table>  </table>
  
-To tune the α - β filter for radar tracking , one uses the radar parametrs to calculate the tracking errors listed in Table 1 as a function of the tracking gain α and β. Then one selects the gains that best meet the needs of the application. For eample, consider a radar that has 50 - meter range measurement accuracy and a two second constant update interval.The application of this radar system is to track a target that moves linearly but with occasional unpredictable maneuvers of up to 1g ($9.8 m/s^2$).+To tune the α - β filter for radar tracking , one uses the radar parameters to calculate the tracking errors listed in Table 1 as a function of the tracking gain α and β. Then one selects the gains that best meet the needs of the application. For example, consider a radar that has 50 - meter range measurement accuracy and a two second constant update interval.The application of this radar system is to track a target that moves linearly but with occasional unpredictable maneuvers of up to 1g ($9.8 m/s^2$).
  
  
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 mean square error in the smoothed position and velocity. mean square error in the smoothed position and velocity.
  
-When the Kalman filter is modeled with the target trajectory as a straight line , and the measurement noise and the trajectory disturbance are modeled as white , guassian noise with zero mean , the kalamn filter equations reduce to the α - β tracker equations with  α and  β computed sequentially by the kalman filter procedure.Blackman states that " Experience with airborne radars has shown the versatility of kalman filter to be almost indespensable when dealing with problems presented by missing data and variable measurement noise statics" . The kalman filter has better performance than the  α - β tracker since it utilizes more information. The  α - β tracker, however might be considered when the target's maneuver statistics are not known or in a dense target environment where computational simplicity is important. The Kalman filterand the  α - β tracker also can be applied to control digitally the feedback loop in the single target tracker. The Kalman filter is essentially a set of mathematical equations that implement a+When the Kalman filter is modeled with the target trajectory as a straight line , and the measurement noise and the trajectory disturbance are modeled as white , guassian noise with zero mean , the kalamn filter equations reduce to the α - β tracker equations with  α and  β computed sequentially by the kalman filter procedure.Blackman states that " Experience with airborne radars has shown the versatility of kalman filter to be almost indespensable when dealing with problems presented by missing data and variable measurement noise statics" . The kalman filter has better performance than the  α - β tracker since it utilizes more information. The  α - β tracker, however might be considered when the target's maneuver statistics are not known or in a dense target environment where computational simplicity is important. The Kalman filter and the  α - β tracker also can be applied to control digitally the feedback loop in the single target tracker. The Kalman filter is essentially a set of mathematical equations that implement a
 predictor-corrector type estimator that is optimal in the sense that it minimizes the predictor-corrector type estimator that is optimal in the sense that it minimizes the
 estimated error covariance—when some presumed conditions are met. Since the time of estimated error covariance—when some presumed conditions are met. Since the time of
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