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Millimeter Wave RADAR Power-Range Spectra Interpretation    85

                                   50
                                           (A) Nonmetallic pole       (C) Lamp post
                                                            (B) Fence
                                   40

                                   30

                                  Power (dB)  20


                                   10


                                    0

                                  –10


                                  –20
                                     0    20   40   60   80  100  120   140  160  180  200
                                                           Range (m)

                                                                                      ◦
                              FIGURE 2.26 A single RADAR range bin, recorded at the bearing angle 231 shown
                              in Figure 2.25, obtained from the outdoor field with multiple features down-range.


                              predicted from the predicted state in Equation (2.24). The predicted range and
                              bearing observations are similar to the ordinary SLAM formulation, that is,


                               ˆ                                 2                        2
                               R i (k + 1|k)= [ˆx p i  (k+1|k)−ˆx R (k+1|k)] +[ˆy p i (k + 1|k)−ˆy R (k + 1|k)]
                                                                                       (2.25)

                                                               (k + 1|k) −ˆy R (k + 1|k)
                               ˆ β i (k + 1|k) = ˆ θ R (k + 1|k) − tan −1  ˆ y p i     (2.26)
                                                               (k + 1|k) −ˆx R (k + 1|k)
                                                             ˆ x p i
                              The predicted power for all targets, such as those in Figure 2.26, is the
                              fundamental difference offered in this chapter.


                              2.8.2.1 Predicted power observation formulation
                              The assumptions made in the predicted power model are as follows:

                                  • The environmental features of interest are assumed to have small
                                    circular cross-sections, so that the estimated normalized RCS




                              © 2006 by Taylor & Francis Group, LLC



                                 FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 85 — #45
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