Analysis of Limiting Factors in and Trade-offs for Positioning Performance Management

Positioning of an object with ranging, bearing, and/or range rate measurements is a nonlinear estimation problem underpinning such applications as target tracking and navigation. A position solution can be obtained using the classic least-squares (LS) method, which affords an explicit geometric interpretation when all sensor measurements are unified in terms of line of sight (LOS) vectors. Under the assumption of Gaussian errors, the LS solution is equivalent to the maximum likelihood estimate (MLE). With a prior, different formulations that lead to an essentially equivalent solution include the maximum a posteriori (MAP) estimate, ridge regression, least-squares with regularization, and LASSO among others. The first few formulations above are similar to a Kalman filter without the time updating step. The resulting positioning performance is limited by such factors as the number of sensors, type of sensors, accuracy and rate of sensor measurements, geometry of the object with respect to references, and the prior. In other words, they are related to the quantity and quality of sensor measurements. By quality, we mean not only the measurement errors but also the relative geometry among the sensor measurements in terms of their instantaneous spatial distribution and temporal availability. One of the goals of the paper is to explore the tradeoff of limiting factors (equivalent estimation aspects when subject to practical constraints) so as to achieve a desired level of performance.