Plane Localization for MIMO Radar

We consider the problem of localizing a ground plane with respect to a multiple-input multiple-output (MIMO) radar within a three-dimensional environment. An example application is a low-visibility landing radar as described by Longstaff (“MIMO radar developments at Teledyne Australia,” Proc. Int. Conf. Radar, 2013). We propose an extension to the common tangent algorithm (COTA), which has been developed by the echo location community for localizing planes with single input multiple output (SIMO) audio systems. The method adopted for this paper is to generalize COTA for the multiple transmitters of the MIMO radar case. Generalizing the COTA equations generates a Non-Convex Quadratically Constrained Quadratic Program (NC-QCQP). We show that by first replacing the quadratic constraints by linear approximations we can solve the NC-QCQP problem by iteratively solving a series of quadratic programming problems. This method demonstrates both global convergence and convergence to the Cramér-Rao Lower Bound (CRLB). We then extend this approach to additionally linearize the quadratic objective function, which in turn reduces the iterate to a simple pseudoinverse. This method retains the global convergence properties of the previous method, but does not quite converge to the CRLB. We also investigate two methods which operate directly on the unconstrained cost function, the first a Newton-Raphson based method and the second a singular value decomposition (SVD)-based approach to solving the optimization problem. The SVD method exhibits approximately quadratic convergence and reaches the CRLB. However, it is only locally convergent. The Newton-Raphson method also achieves the CRLB. We use numerical simulations to demonstrate the validity of the techniques presented and show a comparison to the CRLB for the plane localization problem. Finally, we discuss a preprocessing technique that can be used to improve the estimation accuracy. We conclude by demonstrating the proposed algorithms on data collected from the low visibility landing aid radar (Longstaff , 2013) developed at Teledyne Defence Australia.