Improved target tracking with the converted-measurement Kalman filter

For several decades, researchers have studied the problem of tracking a dynamic target given measurements in sensor coordinates. Since the sensor's measurement is a nonlinear function of the target's state corrupted by additive measurement noise, this problem properly qualifies as one of nonlinear estimation. Due to the mathematical intractability of the problem's theoretically optimal solution, researchers have developed numerous suboptimal but mathematically tractable approaches. The converted-measurement Kalman filter (CMKF), in which the sensor's measurement is converted to Cartesian coordinates and applied to the traditional Kalman filter's tracking algorithm, represents an approach popular in literature and in practice. This dissertation presents two significant contributions to the field of CMKF tracking.First, this dissertation corrects an error in the original algorithm for the debiased CMKF (CMKF-D), an early practical CMKF implementation. In particular, the original paper on the CMKF-D specified, with incorrect mathematical justification, a requirement for evaluating the average true converted-measurement-error bias and covariance with the best available polar target-position estimate. This dissertation provides the correct explanation for the tracking improvement obtained by using the specified requirement.Second, this dissertation contributes a CMKF algorithm employing expressions for the raw converted measurement's error bias and the debiased converted measurement's error covariance conditioned on the best practically available target-position estimate---either the sensor's measurement or the CMKF's Cartesian prediction. A simple test determines the more accurate target-position estimate for use in conditioning the bias and covariance. If the sensor's measurement is more accurate than the CMKF's Cartesian prediction, the resulting sensor-measurement-conditioned bias and covariance produce a CMKF mathematically equivalent to the modified unbiased CMKF (MUCMKF). If, however, the CMKF's prediction is more accurate than the sensor's measurement, two new approaches allow bias and covariance conditioning on the CMKF's prediction. In the first approach, the unscented transformation (UT) produces a target-position estimate in sensor coordinates from the CMKF's Cartesian position prediction and approximates the bias and covariance conditioned on that estimate. In the second approach, the UT approximately conditions the bias and covariance directly on the CMKF's Cartesian position prediction. Simulations demonstrate the improved performance of the new CMKF over the MUCMKF.