While appreciating the vast and extensive mathematical analysis carried out by the authors of [1], I would like to submit the following points. The authors used pseudo measurements for recasting the observability problem into a linear framework. They treated the bearings-only passive target tracking system (except in Section IX) as a deterministic system. It is already established in [2-4] that for deterministic systems, the pseudo measurements are linear functions of the states of the system, though the coefficient matrix is a non-linear function of the original measurements, By using the pseudo measurements in a linear observer, global stability can be shown [5], However, if the pseudo measurement observer, for which the analysis is mostly carried out by the authors [1], is used in a noisy environment as a Pseudo Measurement Filter (PMF), biased estimates are arrived [2-4], As the noise in the bearing measurement increases, the ability to estimate the states through the measurement decreases and the PMF departs appreciably from the Maximum Likelihood Estimator (MLE) and Modified Instrumental Variable (MIV) estimator, both of which remain nearer the ideal. Detailed analysis of PMF, MLE and MIV was carried out by S. C. Nardone, A. G. Lindgren and K. F. Gong in [6]. The departure of the PMF takes place at the break point where the measurement noise begins to dominate the smallest eigenvalue [6]. Hence PMF has not gained widespread acceptance within the TMA Community [7]. Instead, research efforts have been focused upon the analysis and development of other possible estimation schemes which are both stable and asymptotically unbiased. In this process bearings only tracking using Modified polar coordinates [7], Modified gain extended Kalman filter [5] and Hybrid filtering [8] obtained recognition, in which modified gain extended Kalman filter is extensively being used. The authors considered the same pseudo measurements while discussing stochastic observability and estimability in Section IX of [1]. A full-fledged stochastic analysis was carried out by T. L. Song and J. L. Speyer in [5] for bearings only target tracking. They developed an algorithm called modified gain extended Kalman biter (MGEKF). In this it was proved that the bearing measurements are modifiable and differentiable, In PMF, the gain is a function of present and past measurements. In MGEKF, the gain structure is modified in such a way that it is a function of only past measurements and thereby gain and measurement noise process are made uncorrelated, leading to unbiasedness in the estimates. Hence, though the approach of authors [1] is quite direct and provides insides about the algebraic structure of the BOT problem, as pseudo measurements are used throughout, the analysis is not of much use to TMA community, as the nonlinear measurement equation alongwith measurement noise are required to be considered in the BOT problem to obtain unbiased results. I would also like to discuss about the FIM determinant analysis carried out by authors [1] to optimize the observer trajectory. The authors of [1] have not clearly brought out the observer maneuver required in its course or speed or in both for the maximization of the determinant of FIM, It is mentioned in page 193 of [1] that "Hence, the above results allow us to optimize the observer trajectory without any prior knowledge about the sourer: trajectory." This statement is debatable. In my view, the observer trajectory can be optimized if the source trajectory knowledge is available. II it is so, if we can derive the formula for bearing rate and use it in finding out the observability of the range, so that it can he established that maximizing bearing rate is not sufficient to observe the speed of the target. The target angle (the angle difference between target course and bearing) plays an important role in observing the speed of the target. J. A. Fawcett [9] brought out the salient results of the course effects on only range estimation. In his paper, the variance of the error in the Cramer-Rao Lower Bound (CRLB) solution is used to find out a better maneuver from the available several ones. He assumed that the scenario is known. In reality, the geometry is not known and the required maneuver Is to be selected using the available bearings-only information. In this paper, a method is derived to utilize the bearing information to understand the geometry and choose an approximate maneuver. Fawcett recommended that observer maneuver should he in such a way that change in bearing rate should be maximum. This is adequate for the estimation of range alone, This criterion is not sufficient for the estimation of velocity. Here, his concepts are extended to obtain the entire solution namely range, course and speed estimation.
