IEEE Signal Processing - July 2018 - 119

The approach can be applied to sensor/processor systems
involved not only in tracking but in detection, localization, classification, and imaging. The appropriate processor cost function
would need to be specified and the PC Bayes risk evaluated. In
most problems, the PC Bayes risk is intractable to evaluate, and
it would need to be replaced by a suitable surrogate information measure. For example, joint tracking and classification was
considered in [37], and the information measure used was the
expected Renyi divergence.

5

0

5

10
Time (s)
(a)

A PR system is a bistatic radar that makes use of emissions
from a noncooperative transmitter of opportunity, such as
broadcast, communications, or radio-navigation transmitters,
rather than a dedicated, cooperative radar transmitter. Such systems have a number of potential advantages over conventional
active systems. The receiver is passive and so potentially undetectable. Many illumination sources can be used, and many of
them are high power and favorably sited. PR receiver systems

40

Measured
Tracked

2.5
0
-2.5
-5

15

0

5

10
Time (s)
(b)

0.6

0.5
0.4
0.3

Velocity Standard
Deviation (m/s)

Maximum Goal
Maximum Predicted
Target Predicted
Target Goal

0.2
0.1
5

10
Time (s)
(d)

0.4
0.3
0.2
0.1

15

0

5

10
Time (s)
(e)

8,000

1,000

6,000

800
Np

0

4,000
2,000
0

20
10

Measured
Tracked
0

5

10
Time (s)
(c)

15

0.6
Velocity Standard
Deviation Predicted
Velocity Standard
Deviation Actual
Goal

0.5

0

30

0

15

Range Standard
Deviation (m)

0.6

0

Cognitive PRs

SINR (dB)

Measured
Tracked

Velocity (m/s)

14
12
10
8
6
4
2
0

PRF (Hz)

Doppler Frequency/PRF

Range (m)

the desired effect of controlling the velocity error RMSE so
that it barely exceeded the prescribed performance level. This
time, on the two occasions where the SINR started to fall, the
number of integrated pulses was increased so that the effect
on the range error as well as the velocity error was controlled
and the achieved performance in the red curve was very close
to that predicted in the green curve. The plots demonstrating
the velocity and range errors now showed a velocity performance within the specified performance limit, with a range
just exceeding it on a couple of occasions.
These results indicate the power of a cognitive approach
to radar sensing for maintaining a desired level of tracking
performance. Indeed, instead of designing a radar by specifying the system parameters and then developing sophisticated
tracking algorithms to cope with Doppler ambiguities and target fading, we are now able to design a cognitive tracking radar
by specifying the performance and allowing the system to set
the transmit waveform parameters adaptively to achieve the
desired performance.

0.4
0.3
0.2
0.1
0

15

Range Standard
Deviation Predicted
Range Standard
Deviation Actual
Goal

0.5

0

5

10
Time (s)
(f)

15

600
400
200

0

5

10
Time (s)
(g)

15

0

0

5

10
Time (s)

15

(h)

FiguRe 9. The experimental results for a cognitively adapted PRF and number of pulses: the (a) range track, (b) velocity track, (c) SINR track, (d) normalized Doppler frequency, (e) velocity standard deviation, (f) range standard deviation, (g) PRF, and (h) number of pulses.
IEEE Signal Processing Magazine

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July 2018

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119
Table of Contents for the Digital Edition of IEEE Signal Processing - July 2018
