Proceedings of SPIE Conference on Signal and Data Processing
of Small Targets, San Diego, CA, USA, July-August 2001. (4473-41)
A Survey of Maneuvering Target Tracking—Part III: Measurement Models
X. Rong Li and Vesselin P. Jilkov
Department of Electrical Engineering
Abstract
This is the third part of a series of papers that provide a comprehensive survey of the techniques for tracking maneuvering
targets without addressing the so-called measurement-origin uncertainty. Part I [1] and Part II [2] deal with general target motion
models and ballistic target motion models, respectively. This part surveys measurement models, including measurement
model-based techniques, used in target tracking. Models in Cartesian, sensor measurement, their mixed, and other coordinates
are covered. The stress is on more recent advances —topics that have received more attention recently are discussed in
greater details.
KeyWords: Target Tracking, Measurement Model, Survey
1 Introduction
This paper is the third part of a series that provides a comprehensive survey of techniques for maneuvering target tracking
without addressing the so-called measurement-origin uncertainty.
Most maneuvering target tracking techniques are model based; that is, they rely on explicitly two descriptions: one for
the behaviors of the target, usually in the form of a motion (or dynamics) model, and the other for our observations of the
target, known as an observation model. A survey of target motion models in general and ballistic target motion models in
particular has been reported in Part I [1] and Part II [2], respectively. This part surveys the measurement models and the
relevant modeling techniques.
More precisely, this paper surveys the models of measurements characterized by the following: they are truly originated
from the “point target” under track (i.e., there is no origin uncertainty); and they are measurements, rather than observations
in a more general sense, which may contain other information, including target features as provided by an imaging sensor.
Also, this survey is concerned with the mathematical models as a basis for maneuvering target tracking. For example, their
other applications are not addressed and the actual sensor models are not of concern. Further, this survey includes some
aspects of estimation and filtering techniques that are highly dependent on and thus hardly separable from the measurement
models.
2 Models in Sensor Coordinates
3 Tracking in Various Coordinates
3.1 Tracking in Mixed Coordinates
3.2 Tracking in Cartesian Coordinates
3.3 Tracking in Sensor Coordinates3.4 Tracking in Other Coordinates
4.1 Derivative-Based
4.2 Difference-Based
4.3 Optimally Linearized Model
4.4 Linearization-Error Reduction Techniques
5 Models in Cartesian Coordinates
5.2 Standard Model of Converted Measurements
5.3 Linearized Conversion
5.4 Toward Better Conversions
5.5 Conditioning in Measurement Conversion
5.6 Debiased Conversions
5.7 Quasi-Monte-Carlo Transformations
6 Pseudomeasurement Models
6.1 Conventional Pseudolinear Models
6.2 Models Based on Universal Pseudo-Linearization
6.3 Superiority of Difference-Based Linearization Models
6.4 Pseudomeasurement Models for Kinematic Constraints
7 Concluding Remarks
Target motion models are best described by target state in Cartesian coordinates while measurements of the target state
are directly available in the original sensor coordinates (usually in spherical coordinates or in terms of range and direction
cosines). As a result, measurement models in a variety of coordinate systems have been developed.
The most natural and widely used measurement models are in the Cartesian-sensor mixed coordinates, where Cartesian
target state is measured in sensor coordinates. They are highly nonlinear due to the nonlinear relationship between the two
coordinate systems. Effective tracking with these models relies on nonlinear filtering. The most popular approach here is
EKF-based, which relies on derivative-based linearization of the nonlinear models. Many enhancement techniq
