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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.
Range and velocity can both be identified using medium PRF, but neither one can be identified directly. Medium PRF is from 3 kHz to 30 kHz, which corresponds with radar range from 5 km to 50 km. This is the ambiguous range, which is much smaller than the maximum range. Range ambiguity resolution is used to determine true range in medium PRF radar.
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.
In the cross-range coordinate, the similar resolution is mainly proportional to the bandwidth of the Doppler shift of the signal returns within the beamwidth. Since Doppler frequency depends on the angle of the scattering point's direction from the broadside direction, the Doppler bandwidth available within the beamwidth is the same at all ranges.
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]
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The tracking problem is made particularly difficult for targets with unpredictable movements (i.e. unknown target movement models), non-Gaussian measurement or model errors, non-linear relationships between the measured quantities and the desired target coordinates, detection in the presence of non-uniformly distributed clutter, missed ...
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