Resolving Grating Lobe Ambiguities at the Tracking Stage : An IMM based approach using two tilted sparse antenna arrays

Sammanfattning

Sparse uniform linear arrays offer higher angular resolution and lower hardware cost than fully populated arrays of equal aperture, but their interelement spacing exceeding half a wavelength introduces grating lobe ambiguities that have traditionally been addressed at the array design stage. This thesis investigates whether those ambiguities can instead be resolved at the tracking stage. Three questions are addressed. First, whether an Interacting Multiple Model tracker combining constant velocity and constant acceleration Kalman filters can follow a representative set of manoeuvring targets. Second, whether grating lobe candidates from a single sparse array can be disambiguated from tracking statistics alone. Third, whether two sparse arrays oriented at a small relative tilt angle resolve the ambiguity when a single array cannot. Simulation results in MATLAB show that the IMM tracker achieves steady state position errors below 4 m across six trajectories spanning straight cruise, sharp turns, and sinusoidal manoeuvring. With a single sparse array, however, the innovation and Doppler error statistics are indistinguishable across the true target and its grating lobe replicas, making single array disambiguation infeasible. Introducing a second array at a relative tilt of phi = 2 degrees resolves the ambiguity reliably, achieving position RMSE below 4 m and angular RMSE below 0.5 mrad for standard deviation of angular noise below 0.084 degree and standard deviation of range noise below 12 m. Comparison with the Cramér Rao bound confirms that these noise levels are physically achievable with approximately 24 dB of angular and 50 dB of range SNR margin at standard radar operating conditions.