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--- radar:tws [2018/06/08 07:13] – [ALPHA – BETA FILTER] george
+++ radar: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 =====
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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.
-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 ===
 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.
-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>
-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
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 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" ===
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  </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.
-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
 estimated error covariance—when some presumed conditions are met. Since the time of