An Estimation Error Bound for Pixelated Sensing

This paper considers the ubiquitous problem of estimating the state (e.g., position) of an object based on a series of noisy measurements. The standard approach is to formulate this problem as one of measuring the state (or a function of the state) corrupted by additive Gaussian noise. This model assumes both (i) the sensor provides a measurement of the true target (or, alternatively, a separate signal processing step has eliminated false alarms), and (ii) The error source in the measurement is accurately described by a Gaussian model. In reality, however, sensor measurement are often formed on a grid of pixels – e.g., Ground Moving Target Indication (GMTI) measurements are formed for a discrete set of (angle, range, velocity) voxels, and EO imagery is made on ( , ) grids. When a target is present in a pixel, therefore, uncertainty is not Gaussian (instead it is a boxcar function) and unbisased estimation is not generally possible as the location of the target within the pixel defines the bias of the estimator. It turns out that this small modification to the measurement model makes traditional bounding approaches not applicable. This paper discusses pixelated sensing in more detail and derives the minimum mean squared error (MMSE) bound for estimation in the pixelated scenario. We then use this error calculation to investigate the utility of using non-threshoded measurements.