Elsevier

Signal Processing

Volume 84, Issue 8, August 2004, Pages 1347-1358
Signal Processing

Radar fusion to detect targets. Part III

https://doi.org/10.1016/j.sigpro.2004.05.009Get rights and content

Abstract

In two previous papers [2,3] (Signal Processing 82 (8) (August 2002) 1096; 80 (9) (September 2000) 1833) the authors have described the concept of cueing a microwave radar (MR) by exploiting the detection of a low-frequency radar (LFR); the target of interest was an aircraft in [2] and a ballistic object in [3]. This study considers again the detection and tracking of a ballistic target by extending the cueing chain to include early measurements provided by a sensor (for instance an infrared camera) installed on board of low-orbit satellites. The mathematical approach, conceived in [3], aimed at obtaining detection and tracking performance of target, is then extended to the present study to analyse a more realistic scenario that involves the exploitation of early measurements provided by space-borne sensors. The advantage of the satellite cueing is put in evidence.

Section snippets

Problem statement

High-velocity ballistic targets may be characterised by rather low RCS (radar cross section) in the order of 0.1–0.01m2 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.

  • The MR is a multifunction phased-array operating at 10GHz. 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.

A Mathcad at worksheet has been written to perform calculations concerning all the phases of the target flight and working procedure of the sensor suite (for details see Appendix in this paper). The results achieved by applying the Mathcad at program are

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 (30m) 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 300MHz, the configuration i forms a track with 30m of location accuracy at 87km 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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