  In this paper, sensor selection problems for target tracking in large sensor
networks with linear equality or inequality constraints are considered. First,
we derive an equivalent Kalman filter for sensor selection, i.e., generalized
information filter. Then, under a regularity condition, we prove that the
multistage look-ahead policy that minimizes either the final or the average
estimation error covariances of next multiple time steps is equivalent to a
myopic sensor selection policy that maximizes the trace of the generalized
information gain at each time step. Moreover, when the measurement noises are
uncorrelated between sensors, the optimal solution can be obtained analytically
for sensor selection when constraints are temporally separable. When
constraints are temporally inseparable, sensor selections can be obtained by
approximately solving a linear programming problem so that the sensor selection
problem for a large sensor network can be dealt with quickly. Although there is
no guarantee that the gap between the performance of the chosen subset and the
performance bound is always small, numerical examples suggest that the
algorithm is near-optimal in many cases. Finally, when the measurement noises
are correlated between sensors, the sensor selection problem with temporally
inseparable constraints can be relaxed to a Boolean quadratic programming
problem which can be efficiently solved by a Gaussian randomization procedure
along with solving a semi-definite programming problem. Numerical examples show
that the proposed method is much better than the method that ignores dependence
of noises.
