ues exist. If
simple models are desirable, it appears that the newly-developed difference-based linearized models have a better potential
than the derivative-based models. More important, these nonlinear models provide a framework particular suitable for most
more sophisticated nonlinear filtering techniques, covered in the subsequent parts of this survey. Consequently, most tracking
applications of advances in nonlinear filtering have appeared and will continue to appear in this framework without hidden
difficulty.
Most measurement models in Cartesian coordinates have an attractive “linear” structure. They rely on a proper conversion
of the measurement models in the original sensor coordinates to the Cartesian coordinate. Linear filters can be applied to
this model (but nonoptimally because its measurement noise is actually state dependent and highly non-Gaussian). The
emphasis here has been on finding the first two moments of the converted measurement noise with appropriate conditioning.
Several different debiasing techniques have been proposed based on a variety of conditional moments of the noise. The
state dependence of the converted measurement noise has been accounted for only through the conditional moments of the
noise. In fact it can be more effectively taken into account in an explicit manner. As pointed out in Sections 5.4 and 5.5, it
appears to be more fundamental and appealing to convert the measurement (residual) and the associated covariance directly,
not the noise moments, and all we need in the Cartesian coordinates is a measurement residual equivalent to the one in the
11Similar ideas have been used in other areas, such as power system state estimation [92], under the name “virtual measurements.”
12Rc of [91] would be proportional to s2, similarly as for the converted range rate measurement d of Sec. 3.2.
19
sensor coordinates. This approach circumvents the ambiguity in the conditioning for noise moments. Although incapable
of providing good insight, the quasi-Monte-Carlo method based transformations are attractive for its simplicity and accuracy
within this framework.
The pseudomeasurement approach goes one step further. To take advantage of a linear model, it builds a pseudolinear
model by constructing appropriate pseudomeasurements or finding a universally applicable pseudolinear representation of a
nonlinear function. The price is that the “linear” measurement matrices (and possibly noise) are actually state dependent.
Blind applications of linear filters to such disguised nonlinear problems have proven unsatisfactory. Numerous heuristic
techniques have been proposed for performance improvement. Few of them are, in our opinion, promising in terms of
accuracy and applicability due to their lack of theoretical support. As explained in Sec. 6.3, the universal pseudo-linearization
based models are substantially inferior to and should be replaced by the difference-based linearized models.
The approach to convert/express the target state in the sensor coordinates, where the measurement models are the simplest
possible, leads to highly nonlinear motion models with significant pseudoaccelerations that must be accounted for effectively.
From the nonlinear filtering viewpoint, this appears to be a much more difficult problem than the one with Cartesian state
measured in sensor coordinates: In order to (approximately) summarize past information the state in the sensor coordinates
must have a high dimension and, probably worse, the process noise is highly state dependent, although the measurement
models are linear. To our knowledge, few theoretical results are available for such proble
