Bi-Station Single Target Tracking Without Bearing Information

Ground Wave Over the Horizon Radar has been in service in many countries, this kind of radars usually have large antenna arrays, which are composed of tens or even hundreds of elements, it is very difficult for these large arrays to be mobile or concealed, so they could be easy targets for enemy missiles. In order to improve the survivability of the radar system, the using of small antennas has been proposed. But the smaller the antenna is, the lower bearing resolution we get [6]. To maintain a reasonable tracking ability with a very low bearing resolution, a bi-station no bearing observation tracking system has been proposed in this paper, which doesn't need the bearing observations of the targets. This system can track a target with two pairs of range and Doppler observations from two separately located radar stations, without the bearing information. The tracking performance of this tracking system, will not be affected by the poor bearing resolution of the small antennas. So we can use small antennas to make the whole system mobile and concealable.The tracking system described above has a very strong non-linearity, so the classical linear filters, such as EKF, will not get a good performance. The goal of this paper is to develop a new tracking algorithm, to track a maneuvering target under this non-linear background.In the beginning of this paper, a brief review to the classical linear algorithms, which are widely used in maneuvering target tracking, such as EKF and GHKF [13], is given. Then an introduction to the standard numerical integration methods is made. With these numerical integration methods as mathematics tools, the new tracking algorithm, non-linear estimators weighted fusion filter, is developed, we call it TNF. TNF is not a linear filter, its output will not be a linear combination of the inputs, its performance will not be bounded by the performance limit of the optimal linear filter, which could still perform poorly under a strong non-linear background. TNF uses numerical integrations to solve complicated integrations on line, and get the exact values of the conditional means of some state variables, which is impossible for the conventional linear filters, at the price of a very heavy computational load. TNF can get higher accuracy than EKF and other modified KFs, because it can use numerical methods to get exact numerical results of a state vector, instead of doing a linear approximation as EKF does, it can avoid the system error caused by the linear approximations. So TNF will get a better performance under a strong non-linear background.Simulations are run to test the performance of TNF, EKF and GHKF. Different target maneuvering and noise levels are simulated. The results shows that, in all circumstances, weak medium and strong noise, non-maneuvering low-maneuvering and high-maneuvering targets, TNF all has a better performance than GHKF, and far more better than EKF. Besides the superior tracking accuracy, TNF also has a better stability. When the noise is very strong, EKF could has a problem of divergence, which had never happened to TNF.In the final section of this paper, a brief comparison is made between the bi-station no bearing observation tracking system and the conventional single base tracking system. The results shows that, with the same range and Doppler resolution, the bi-station no bearing observation tracking system can get the same accuracy as the conventional single base tracking system, when the locations of the two radar stations are properly chosen.