A Basis Function Approach to Position Estimation Using Microwave Arrays

We consider the problem of estimating the bearing of a remote object given measurements on a particular type of non‐scanning radar, namely a focal‐plane array. Such a system focuses incoming radiation through a lens onto an array of detectors. The problem is to estimate the angular position of the radiation source given measurements on the array of detectors and knowledge of the properties of the lens. The training data are essentially noiseless, and an estimator is derived for noisy test conditions. An approach based on kernel basis functions is developed. The estimate of the basis function weights is achieved through a regularization or roughness penalty approach. Choosing the regularization parameter to be proportional to the inverse of the input signal‐to‐noise ratio leads to a minimum prediction error. Experimental results for a 12‐element detector array support the theoretical predictions.