Cooperative Vehicle Target Tracking 22.1 General Theoretical Framework 501
Part B | 22.1
or coordination with careful attention to interdependencies that may lead to an unstable overall
system.
For realistic scenarios, the quantitative evaluation of
the effectiveness of cooperative target tracking systems
with tractable decision rules for their operation is a subject of current research. Rigorous analytical solutions
exist only at the level of methodological ideas, rather
far from implementations, and numerical simulations
are challenging. To gain insight into the performance
advantages (or disadvantages) of such systems and
assess trade-offs and sensitivities, a simplified framework must be constructed that models essential features
at tractable levels of complexity. Repeatable experimentation within this simplified framework provides
sensitivity analysis and uncertainty estimation. When
transitioning from single-sensor systems to distributed,
mobile systems, an essential feature is the coordination mechanism between spatially separated sensors
that may not have the same information due to limited communication between them. The behavior of
complex adaptive systems is often nonlinear. A small
change in one specific variable, such as the coordination mechanism, may result in large changes in system
performance. Modeling the behavior of the overall system as a function of this specific variable is critical for
assessing system stability and determining overall measures of effectiveness (MoE) from component measures
of performance (MoP).
Four approaches are commonly used for analysis of
cooperative target tracking:
Control and estimation (CE)
Multiagent systems (MAS)
Cellular automata (CA)
Probabilistic graphical models (PGM).
22.1.1 Control and Estimation Approach
In a state space approach, there is a model for the
evolution over time of the state of each player. This evolution is corrupted by noise which randomly pushes the
player in uncontrolled directions [22.12]. For cooperative target tracking, there is a coupling among all state
variables, modeled by a set of stochastic differential
equations. In addition to the motion or control equations
in the state space mode, there is a set of estimation equations describing the uncertainty of each player about
the state of all state variables of all players. Control
design and estimation design can be separated, that is,
each control equation is conditioned by the result of the
estimation process for each state variable [22.13]. For
example, the state of a member of the surveillance team
will probably change when a target is detected nearby.
How each player reacts to the knowledge about the
states is defined by the control equations. The performance of the system is modeled by a multiple-objective
cost function with multiple constraints. Such a cost
function can be expressed in terms of risk. For cooperative tracking of a reactive target, the surveillance team
will try to minimize the risk of the target passing undetected, while the target will act such that its own risk of
detection is minimized.
Mathematically this risk can be calculated as a function of the MoP of the components of the systems.
MoPs can be combined into attributes of the system
specific to a task. The degree to which overall risk is
minimized can be defined as the system’s MoE. The
art of system design is to create from expert knowledge of the system the attributes which are then used
to optimize the setting of free parameters, including
parameters that govern coordination. The proof that
a chosen combination of MoPs is a good cost function to increase the MoE is possible for mathematically tractable setups [22.14], for example, for linearquadratic forms [22.12]. However, this simplification is
unrealistic since the main features of the motion, control, decisions, and estimation cannot be represented
accurately by linear-quadratic equations. A coupled
physical-mechanical-fluids control model is a better
choice [22.15]. Tools from applied physics can then be
used for further analysis including simplification and
approximation techniques for the analytical treatment
of stochastic differential equations. Other approaches to
generating a proper functional representation of the risk
are via learning (trial-and-error or more sophisticated
reinforced learning [22.16, 17]).
MoE values for specific scenarios can be statistically derived through Monte Carlo simulations. A large
number of degrees of freedom in realistic scenarios
make such simulations a formidable task, and one that
is more likely to yield insight into the sensitivities of
specific constraints in specific scenarios rather than the
impact of different coordination mechanisms for more
generalized application classes.
The impact of coordination mechanisms can be appreciated by noting the advantages of complete data
exchange between two sensing platforms. The sensors could exploit the received signals in a coherent
or semicoherent manner. Collaborative coherent signal
processing allows for an increased signal-to-noise ratio.
Semicoherent techniques could, for example, exploit
complementary Doppler and target strength features of
a target. Joint estimation and classification can lead to
higher localization accuracy and a lower false alarm
rate. Collaborative signal-processing techniques can be
adaptive, or the motion of the sensing platforms preselected [22.18, 19].
Part B | 22.1
or coordination with careful attention to interdependencies that may lead to an unstable overall
system.
For realistic scenarios, the quantitative evaluation of
the effectiveness of cooperative target tracking systems
with tractable decision rules for their operation is a subject of current research. Rigorous analytical solutions
exist only at the level of methodological ideas, rather
far from implementations, and numerical simulations
are challenging. To gain insight into the performance
advantages (or disadvantages) of such systems and
assess trade-offs and sensitivities, a simplified framework must be constructed that models essential features
at tractable levels of complexity. Repeatable experimentation within this simplified framework provides
sensitivity analysis and uncertainty estimation. When
transitioning from single-sensor systems to distributed,
mobile systems, an essential feature is the coordination mechanism between spatially separated sensors
that may not have the same information due to limited communication between them. The behavior of
complex adaptive systems is often nonlinear. A small
change in one specific variable, such as the coordination mechanism, may result in large changes in system
performance. Modeling the behavior of the overall system as a function of this specific variable is critical for
assessing system stability and determining overall measures of effectiveness (MoE) from component measures
of performance (MoP).
Four approaches are commonly used for analysis of
cooperative target tracking:
Control and estimation (CE)
Multiagent systems (MAS)
Cellular automata (CA)
Probabilistic graphical models (PGM).
22.1.1 Control and Estimation Approach
In a state space approach, there is a model for the
evolution over time of the state of each player. This evolution is corrupted by noise which randomly pushes the
player in uncontrolled directions [22.12]. For cooperative target tracking, there is a coupling among all state
variables, modeled by a set of stochastic differential
equations. In addition to the motion or control equations
in the state space mode, there is a set of estimation equations describing the uncertainty of each player about
the state of all state variables of all players. Control
design and estimation design can be separated, that is,
each control equation is conditioned by the result of the
estimation process for each state variable [22.13]. For
example, the state of a member of the surveillance team
will probably change when a target is detected nearby.
How each player reacts to the knowledge about the
states is defined by the control equations. The performance of the system is modeled by a multiple-objective
cost function with multiple constraints. Such a cost
function can be expressed in terms of risk. For cooperative tracking of a reactive target, the surveillance team
will try to minimize the risk of the target passing undetected, while the target will act such that its own risk of
detection is minimized.
Mathematically this risk can be calculated as a function of the MoP of the components of the systems.
MoPs can be combined into attributes of the system
specific to a task. The degree to which overall risk is
minimized can be defined as the system’s MoE. The
art of system design is to create from expert knowledge of the system the attributes which are then used
to optimize the setting of free parameters, including
parameters that govern coordination. The proof that
a chosen combination of MoPs is a good cost function to increase the MoE is possible for mathematically tractable setups [22.14], for example, for linearquadratic forms [22.12]. However, this simplification is
unrealistic since the main features of the motion, control, decisions, and estimation cannot be represented
accurately by linear-quadratic equations. A coupled
physical-mechanical-fluids control model is a better
choice [22.15]. Tools from applied physics can then be
used for further analysis including simplification and
approximation techniques for the analytical treatment
of stochastic differential equations. Other approaches to
generating a proper functional representation of the risk
are via learning (trial-and-error or more sophisticated
reinforced learning [22.16, 17]).
MoE values for specific scenarios can be statistically derived through Monte Carlo simulations. A large
number of degrees of freedom in realistic scenarios
make such simulations a formidable task, and one that
is more likely to yield insight into the sensitivities of
specific constraints in specific scenarios rather than the
impact of different coordination mechanisms for more
generalized application classes.
The impact of coordination mechanisms can be appreciated by noting the advantages of complete data
exchange between two sensing platforms. The sensors could exploit the received signals in a coherent
or semicoherent manner. Collaborative coherent signal
processing allows for an increased signal-to-noise ratio.
Semicoherent techniques could, for example, exploit
complementary Doppler and target strength features of
a target. Joint estimation and classification can lead to
higher localization accuracy and a lower false alarm
rate. Collaborative signal-processing techniques can be
adaptive, or the motion of the sensing platforms preselected [22.18, 19].