Case Studies - Digital Signal Processing: A Practitioner's Approach - page 123

underwater acoustic emitter. Monopulse radar [5] also works on the same principle,
as shown below.
To understand this in simple terms, let us consider three directional receivers as
shown in Figure 6.1. Each directional receiver consists of a set of antenna elements
and a receiver that has a definite gain pattern. The first receiver provides an output
r 1 in a given direction . To be more precise, we assume an emitter of a given power

when moved at a constant distance. Put another way, in a circle around this
directional receiver, the output r 1 follows the pattern in Figure 6.1.

Direction of interest

90

1

120 60

0.8

0.6

150 30

0.4

0.2

180 0

210 330

240 300

270

0 : 25

Figure 6.1 Directional receivers r ¼j sin j for ¼ 0to

When we have three such receivers each shifted by 45 we get a response vector
i ¼½ r i 1 r i 2 r i 3 r i 1 ; 2 ; 3 Þ

, where each element ð represents the response of each receiver.

Now we map this 3-tuple to a scalar . Let the ensemble of vectors be

A ¼ 1 2 ... N 3 matrix in this case. This data

is generated at the design time and needs to be obtained at periodic intervals. Let

½ . We can see that A is an N

be a vector obtained at a given time, then we define a function e k ¼ k ð Þ

log e k .

t . Using this we generate another function J k ¼

ð k Þ