Radar fusion to detect targets. Part III
Section snippets
Problem statement
High-velocity ballistic targets may be characterised by rather low RCS (radar cross section) in the order of 0.1– when viewed under nose-on aspect at microwaves. A microwave radar would have to spend a long time on target integrating enough echo signal energy to detect a low RCS ballistic target. With a narrow beam antenna to achieve sufficient angular resolution, such integration time can hardly be achieved with acceptable update rates for the whole search volume. Hence the radar
Track initiation of a ballistic target during gravitational flight from satellite observations
This section describes the gravitational model of the ballistic target and the MLE procedure to estimate the target state at a specified time instant; also the corresponding CRLB is determined. This section exploits the work reported in [6]; in the following we will summarise the main results.
The MLE of ballistic target trajectory is based on the solution of a non-linear least-squares minimization problem. The cost function to be minimised is the quadratic norm of measurement errors. Ballistic
Assumptions and results from previous work
Much of the hypotheses in the present work derive by the analysis done in [3]; here we summarise the main hypotheses and the related changes with respect to [3].
- •
The MR and LFR are placed in the same site.
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The MR is a multifunction phased-array operating at . Its antenna rotates mechanically in azimuth; the beam can be pointed electronically in both azimuth and elevation. Azimuth pointing is within +/−45° off the current bore sight azimuth. When operating in a stand alone mode, the radar
Detection range without and with cueing
We will compare the performance of the following system configurations:
- (i)
two satellites for initial detection plus LFR and MR; this is the most complete sensor suite,
- (ii)
one satellite for initial detection plus LFR and MR,
- (iii)
MR cued by LFR,
- (iv)
MR alone.
Track initiation without and with cueing
The tracking performance during the initiation phase is reported in Fig. 6, Fig. 7. The track initiation range vs. frequency of LFR for the system configurations above is displayed in Fig. 6. Note that these curves mimic the corresponding curves of Fig. 4 with a range reduction corresponding to the time delay in establishing the initiation conditions of the track. A suitable number of scans are needed to reach the N/M track initiation condition (e.g.: two detections over three scans logic as in
Track accuracy without and with cueing
The performance of the firm track is reported in Fig. 8, Fig. 9, Fig. 10. Track range, at which a specified location accuracy is reached, vs. frequency of LFR is displayed in Fig. 8 for the four system configurations. This figure clearly shows the advantage brought by the use of the satellites to initiate the target track. In fact, if the LFR has a carrier frequency of , the configuration i forms a track with of location accuracy at while configuration ii provides the track
Concluding remarks
In this paper, we have extended the analysis of search and track a ballistic target presented in [3]. In the previous publication, the analysis was focused on the exploitation of measurements provided by two ground based radar: a low-frequency radar and a microwave radar. In this paper, we use the measurements provided by sensors on board of satellites; the sensors provide just the bearings of target. Furthermore, the target trajectory includes also the exo-atmospheric cruise and not only the
Acknowledgements
The authors are grateful to Dr. S. Immediata (AMS) for providing the drawing in Fig. 1. Also they gratefully acknowledge the cooperation of Prof. Y. Bar-Shalom and Dr. M. Yeaddanapudi for their assistance in exploiting their work referenced in [6].
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