radar:measurements
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| radar:measurements [2018/05/31 10:22] – dipaolo | radar:measurements [2026/04/28 16:58] (current) – mauro | ||
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| - | >it is ok for the moment. You can start --- // | ||
| - | > Where do the figures come from? Please cite the document as decribed in [[: | ||
| ====== Radar Measurement ====== | ====== Radar Measurement ====== | ||
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| ===== Range ===== | ===== Range ===== | ||
| - | To begin our dissertation, | + | //An overall discussion about radar techniques to detect the range of a given target// |
| + | |||
| + | To start our dissertation, | ||
| <figure label> | <figure label> | ||
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| \end{equation} | \end{equation} | ||
| - | Once we know this value we can recover the value of $R_{T} + R_{R}$ that however does not give us the precise information about the distance of the target.\\ In practice, this kind of device is mainly used for weather radar. The bistatic radar technology has been in use for several years at the Institute of Atmospheric Physics at the German Aerospace Center. This system is also of some importance | + | Once we know this value we can recover the value of $R_{T} + R_{R}$ that however does not give us the precise information about the distance of the target.\\ In practice, this kind of device is mainly used for weather radar. The bistatic radar technology has been in use for several years at the Institute of Atmospheric Physics at the German Aerospace Center. This system is also important |
| On the other hand, a lot of radar systems work with the same antenna on the $Tx$ and $Rx$ side. This is made possible to the presence of a special apparatus called // | On the other hand, a lot of radar systems work with the same antenna on the $Tx$ and $Rx$ side. This is made possible to the presence of a special apparatus called // | ||
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| == CW Radar systems == | == CW Radar systems == | ||
| - | Until now it has been supposed that our radar system works with pulses of energy. Another typical waveform used by radar systems is the sinusoidal one. Radar using this approach are commonly known as //Continous Wave radar// (CW radar). It can be seen as a special type of bistatic radar because normally it uses two antennas for transmission. This radar schema was used in the first radar applications in history and nowadays it is almost deprecated because it doesn' | + | Until now it has been supposed that our radar system works with pulses of energy. Another typical waveform used by radar systems is the sinusoidal one. Radar using this approach are commonly known as //Continous Wave radar// (CW radar). It can be seen as a special type of bistatic radar because normally it uses two antennas for transmission. This radar schema was used in the first radar applications in history and nowadays it is almost deprecated because it doesn' |
| <figure label> | <figure label> | ||
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| <figure label> | <figure label> | ||
| {{ : | {{ : | ||
| - | < | + | < |
| </ | </ | ||
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| Factors affecting measurement accuracy include not only noise and resolution but also signal and target characteristics and radar hardware considerations.\\ For example, any uncertainty in the antenna boresight angle, due for example to mounting or pattern calibration errors, will affect the accuracy of a location measurement. Radiofrequency (RF) hardware or antenna gain calibration errors (gain uncertainty) will affect the accuracy of target signal power measurements.[(cite: | Factors affecting measurement accuracy include not only noise and resolution but also signal and target characteristics and radar hardware considerations.\\ For example, any uncertainty in the antenna boresight angle, due for example to mounting or pattern calibration errors, will affect the accuracy of a location measurement. Radiofrequency (RF) hardware or antenna gain calibration errors (gain uncertainty) will affect the accuracy of target signal power measurements.[(cite: | ||
| - | The accuracy | + | The accuracy |
| - | each error source. Specifically, | + | each error source. Specifically, |
| \begin{equation} | \begin{equation} | ||
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| The RSS error effectively treats each error source as independent and Gaussian. | The RSS error effectively treats each error source as independent and Gaussian. | ||
| - | Another source of accuracy and estimation error in surveillance radar is given to the fact that the received signal is sampled for further elaboration, | + | Another source of accuracy and estimation error in surveillance radar is given to the fact that the received signal is sampled for further elaboration, |
| ===== Angle ===== | ===== Angle ===== | ||
| + | |||
| + | //Angular detection of the target, starting from knowing how a given antenna is able to detect the presence of a taget in the space// | ||
| To univocally identify the position of a target we must measure not only the distance but also the angle from which the scattered energy comes from. For this reason, very directive antennas are used, i.e. antennas that perform a radiation diagram with a maximum along a given direction. | To univocally identify the position of a target we must measure not only the distance but also the angle from which the scattered energy comes from. For this reason, very directive antennas are used, i.e. antennas that perform a radiation diagram with a maximum along a given direction. | ||
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| According to the requirements, | According to the requirements, | ||
| - | It is quite easy to recognize which kind of beam an antenna is using just watching to its physical dimensions. For example, if an antenna is wider than longer its beam should be a Fan Beam. Otherwise | + | It is quite easy to recognize which kind of beam an antenna is using just watching to its physical dimensions. For example, if an antenna is wider than longer its beam should be a Fan Beam. Otherwise |
| Using a Pencil Beam phased array it is possible to realize the so-called //3D Stacked Beams// radar. The electronic scanning can be performed both on elevation and azimuth planes, but usually we prefer to perform a mechanical scanning on the azimuth plane and the electronic one on the elevation plane. In this way, we are able to measure also the altitude of the target. For this reason, this radar is called 3D, because it is able to locate the target in the 3-dimensional space giving the $R, \theta$ and $\phi$ coordinates at the same time. | Using a Pencil Beam phased array it is possible to realize the so-called //3D Stacked Beams// radar. The electronic scanning can be performed both on elevation and azimuth planes, but usually we prefer to perform a mechanical scanning on the azimuth plane and the electronic one on the elevation plane. In this way, we are able to measure also the altitude of the target. For this reason, this radar is called 3D, because it is able to locate the target in the 3-dimensional space giving the $R, \theta$ and $\phi$ coordinates at the same time. | ||
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| \end{equation} | \end{equation} | ||
| - | If we take into account also antenna losses we must multiply the effective area for the loss factor $L_a$ that is less the 1. So we have: | + | If we take into account also antenna losses we must multiply the effective area for the loss factor $L_a$ that is less than 1. So we have: |
| \begin{equation} | \begin{equation} | ||
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| ===== Velocity ===== | ===== Velocity ===== | ||
| + | |||
| + | //Analysis of the velocity parameter of the target, with a main focus on the Doppler frequency// | ||
| Once we have defined the previous parameters that allow us to measure the distance from the radar, another information that can be derived from the echo signal is the radial velocity of the target. Of course, this quantity is revealed by the radar only if the target is moving. | Once we have defined the previous parameters that allow us to measure the distance from the radar, another information that can be derived from the echo signal is the radial velocity of the target. Of course, this quantity is revealed by the radar only if the target is moving. | ||
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| === Maximum unambiguous velocity === | === Maximum unambiguous velocity === | ||
| - | If a pulse radar sends a series of rectangular pulses with a period $PRT$, the output of the mixer is no more a sinusoidal signal of frequency $f_D$ as in the case of CW radar, but it is a sampling of this waveform at the instants $t_k = k \cdot PRT$. So, using a pulse radar is equivalent to introducing | + | If a pulse radar sends a series of rectangular pulses with a period $PRT$, the output of the mixer is no more a sinusoidal signal of frequency $f_D$ as in the case of CW radar, but it is a sampling of this waveform at the instants $t_k = k \cdot PRT$. So, using a pulse radar is equivalent to introduce |
| *$f_D = 3/4PRF$, so $2\pi f_D T = \frac{3}{2}\pi$.\\ In this case, the phasor that rotates counterclockwise with an angular speed of $\omega_D = 2\pi f_D$ is confused with another phasor that rotates with an angular speed $\frac{3\pi}{2T} - \frac{2\pi}{T} = -\frac{\pi}{2T}$ i.e, it seems to rotate clockwise and with a speed that is one-third of the real one. This is shown in fig.17. | *$f_D = 3/4PRF$, so $2\pi f_D T = \frac{3}{2}\pi$.\\ In this case, the phasor that rotates counterclockwise with an angular speed of $\omega_D = 2\pi f_D$ is confused with another phasor that rotates with an angular speed $\frac{3\pi}{2T} - \frac{2\pi}{T} = -\frac{\pi}{2T}$ i.e, it seems to rotate clockwise and with a speed that is one-third of the real one. This is shown in fig.17. | ||
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| </ | </ | ||
| - | In general, between the " | + | In general, between the " |
| \begin{equation} | \begin{equation} | ||
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| \end{equation} | \end{equation} | ||
| - | where $v_{max}$ is the maximum value of the target' | + | where $v_{max}$ is the maximum value of the target' |
| \begin{equation} | \begin{equation} | ||
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| ===== Ambiguity cases ===== | ===== Ambiguity cases ===== | ||
| + | |||
| + | //According to the characteristics of our radar system, we can incur some troubles about the accuracy of the measurements. Let's see it in detail// | ||
| We can now understand that when we have to define the working characteristics of our radar system, we have to take into account the right choice of the $PRF$ value. According to its value, we have pointed out the following: | We can now understand that when we have to define the working characteristics of our radar system, we have to take into account the right choice of the $PRF$ value. According to its value, we have pointed out the following: | ||
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| If we choose a value for the $PRT$ like in the last equation and the maximum radial velocity of the target $v_{rlim}$ is greater than the value $v_{max}$, we have realized a system that is unambiguous in distance but not in velocity. | If we choose a value for the $PRT$ like in the last equation and the maximum radial velocity of the target $v_{rlim}$ is greater than the value $v_{max}$, we have realized a system that is unambiguous in distance but not in velocity. | ||
| - | So if we put on the plane in the next figure the distance and velocity values that identify the position of a given target in a given instant of time (points A, B, C), the radar will detect the situation showed in fig.b. | + | So if we put on the plane in the next figure the distance and velocity values that identify the position of a given target in a given instant of time (points A, B, C), the radar will detect the situation showed in fig.19b. |
| <figure label> | <figure label> | ||
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| </ | </ | ||
| - | Fig.19b is obtained by " | + | Fig.19b is obtained by " |
| === Velocity unambiguous Radar === | === Velocity unambiguous Radar === | ||
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| </ | </ | ||
| - | Fig.20b is obtained by a " | + | Fig.20b is obtained by a " |
| === Distance and velocity ambiguous Radar === | === Distance and velocity ambiguous Radar === | ||
| - | Now suppose to choose a PRF value such that called $R_{max} = c/(2PRF)$ and $v_{rmax} = \lambda PRF/4$ the maximum unambiguous distance and velocity | + | Now suppose to choose a PRF value such that called $R_{max} = c/(2PRF)$ and $v_{rmax} = \lambda PRF/4$ the maximum unambiguous distance and velocity |
| - | This situation does not fit very well with our purposes to use the radar, because it is clear that we can easily incur in some error during the measurements. Once again it is shown that the choice of a right value for the $PRF$ is a key aspect when a radar system is developed | + | This situation does not fit very well with our purposes to use the radar, because it is clear that we can easily incur in some errors |
| === RVP === | === RVP === | ||
| - | We can now define a value that can help us to rightly choose the value of the $PRF$ in order to better satisfy the user requirements. It is the product of the maximum unambiguous | + | We can now define a value that can help us to rightly choose the value of the $PRF$ in order to better satisfy the user requirements. It is the product of the maximum unambiguous |
| \begin{equation} | \begin{equation} | ||
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| ===== Dwell Time ===== | ===== Dwell Time ===== | ||
| + | |||
| + | //Analysis of the Dwell time and the corresponding number of pulses available for the eleboration// | ||
| Assume to work with a pulse radar whose beam is able to move to scan all the space. If there is an object that can be approximated by a point at a certain distance it will be lighted up by the -3dB beamwidth of the antenna for a certain period of time. This target will be hit by a certain number $N$ of pulses transmitted by the radar. Consequently, | Assume to work with a pulse radar whose beam is able to move to scan all the space. If there is an object that can be approximated by a point at a certain distance it will be lighted up by the -3dB beamwidth of the antenna for a certain period of time. This target will be hit by a certain number $N$ of pulses transmitted by the radar. Consequently, | ||
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| \end{equation} | \end{equation} | ||
| - | This new variable $t_D$ is defined as //Dwell Time// and is the timeframe during which the object is lighted up by the -3dB beamwidth.\\ If we perform an azimuthal scanning with a constant angular speed $\dot{\theta}$ and the width of the beam is equal to $\theta_B$, the definition of the dwell time is the sequent: | + | This new variable $t_D$ is defined as //Dwell Time// and is the timeframe during which the object is lighted up by the -3dB beamwidth.\\ If we perform an azimuthal scanning with a constant angular speed $\dot{\theta}$ and the width of the beam is equal to $\theta_B$, the definition of the dwell time is the following: |
| \begin{equation} | \begin{equation} | ||
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| ===== Temporal scales for radar signal ===== | ===== Temporal scales for radar signal ===== | ||
| - | In this chapter all the measurements that a radar system is able to perform have been defined, taking into account the presence of a target approximable to a point, i.e. the object is very small with respect to the dimensions of the radar cell.\\ They are the sequent: | + | //A brief recall of all the temporal concepts seen up to now// |
| + | |||
| + | In this chapter all the measurements that a radar system is able to perform have been defined, taking into account the presence of a target approximable to a point, i.e. the object is very small with respect to the dimensions of the radar cell.\\ They are the following: | ||
| -Range; | -Range; | ||
| -Elevation angle; | -Elevation angle; | ||
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| -Doppler frequency and radial velocity. | -Doppler frequency and radial velocity. | ||
| - | The results that we can obtain with respect to angular measurements depend substantially on the width of the antenna beam, so they can be optimized by a further improving the antenna requirements obtaining narrower lobes. On the other hand, when we talk about range and velocity we can incur in some ambiguity related to multiples of $v_{rmax}$ and $R_{max}$. | + | The results that we can obtain with respect to angular measurements depend substantially on the width of the antenna beam, so they can be optimized by further improving the antenna requirements obtaining narrower lobes. On the other hand, when we talk about range and velocity we can incur in some ambiguity related to multiples of $v_{rmax}$ and $R_{max}$. |
| If we analyze the reception phenom about the pulses that were previously transmitted by the radar, we can divide the temporal axis into three different scales used to better understand the radar behaviour.\\ The first one is the one related to the pulse length, of the order of microseconds; | If we analyze the reception phenom about the pulses that were previously transmitted by the radar, we can divide the temporal axis into three different scales used to better understand the radar behaviour.\\ The first one is the one related to the pulse length, of the order of microseconds; | ||
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| </ | </ | ||
| - | If we use a pulse radar we can observe the received signal only in time instants associated to the pulse coming from a given echo. It is like to assume to cut the signal off with a temporal window equal to $t_D$ with $N$ pulses, and so the spectrum in fig.23 makes a convolution with the Fourier transform of the temporal window that we can suppose to have a gaussian shape (and so its Fourier transform has a gaussian shape that lasts for $1/t_D$): in the next and last figure it is shown the spectrum of $R(f)$ that is the transform of each $r(n)$ obtained from eq.29. | + | If we use a pulse radar we can observe the received signal only in time instants associated to the pulse coming from a given echo. It is like to assume to cut the signal off with a temporal window equal to $t_D$ with $N$ pulses, and so the spectrum in fig.24 makes a convolution with the Fourier transform of the temporal window that we can suppose to have a gaussian shape (and so its Fourier transform has a gaussian shape that lasts for $1/t_D$): in the next and last figure it is shown the spectrum of $R(f)$ that is the transform of each $r(n)$ obtained from eq.29. |
| <figure label> | <figure label> | ||
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| </ | </ | ||
| - | This is just to say that if we consider that the Dwell time is finite and so also the number of pulses bumping into the target is limited, we cannot consider at the receiving side the whole spectrum resulting by the Fourier transform of the transmitted pulse. The window used to cut the signal lasts for a time equal to the Dwell time $t_D.$ This is why the resulting received signal has a shape like the one in fig.24: the result of the convolution between the sampled signal and the window implies a widening of every line in the spectrum equal to $1/t_d$. | + | This is just to say that if we consider that the Dwell time is finite and so also the number of pulses bumping into the target is limited, we cannot consider at the receiving side the whole spectrum resulting by the Fourier transform of the transmitted pulse. The window used to cut the signal lasts for a time equal to the Dwell time $t_D.$ This is why the resulting received signal has a shape like the one in fig.25: the result of the convolution between the sampled signal and the window implies a widening of every line in the spectrum equal to $1/t_d$. |
| More info in lecture notes FDR1 in diddatticaweb | More info in lecture notes FDR1 in diddatticaweb | ||
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