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In pulsed radar and sonar signal processing, an ambiguity function is a two-dimensional function of propagation delay and Doppler frequency, (,).It represents the distortion of a returned pulse due to the receiver matched filter [1] (commonly, but not exclusively, used in pulse compression radar) of the return from a moving target.
Pulse-Doppler signal processing separates reflected signals into a number of frequency filters. There is a separate set of filters for each ambiguous range. The I and Q samples described above are used to begin the filtering process. These samples are organized into the m × n matrix of time domain samples shown in the top half of the diagram.
Range ambiguity resolution is a technique used with medium pulse-repetition frequency (PRF) radar to obtain range information for distances that exceed the distance between transmit pulses. This signal processing technique is required with pulse-Doppler radar .
Pulse-Doppler systems measure the range to objects by measuring the elapsed time between sending a pulse of radio energy and receiving a reflection of the object. Radio waves travel at the speed of light , so the distance to the object is the elapsed time multiplied by the speed of light, divided by two – there and back.
Other difficulties arise when the interference covariance matrix is ill-conditioned, making the inversion numerically unstable. [5] In general, this adaptive filtering must be performed for each of the unambiguous range bins in the system, for each target of interest (angle-Doppler coordinates), making for a massive computational burden. [4]
When the PRF of the "jamming" radar is very similar to "our" radar, those apparent distances may be very slow-changing, just like real targets. By using stagger, a radar designer can force the "jamming" to jump around erratically in apparent range, inhibiting integration and reducing or even suppressing its impact on true target detection.
That is the source of the term "synthetic aperture," giving it the property of an imaging radar. [5] The range direction is perpendicular to the flight track and perpendicular to the azimuth direction, which is also known as the along-track direction because it is in line with the position of the object within the antenna's field of view.
If the radar was locked on to the aircraft, it will hopefully remain locked to this second pulse as the aircraft moves away from the original location. Eventually, the aircraft will fall outside the range gate and disappear, while the radar continues tracking the false signal. Thus, the false signal is said to "pull the range gate off the target".