Multiple-Level Quantized Innovation Kalman Filter

Particle filtering for Quantized Innovations

“…We use the same problem setup as that used in [1,2]. We consider the sensor network configuration in which the fusion center has sufficient power to broadcast its predicted output and the corresponding error covariance to its sensors.…”

“…[1,2] propose methods to quantize (n) and use the quantized innovations to update the state estimate.…”

“…In this paper, we precisely try to answer this question. We present simulation results which seem to indicate that the optimal nonlinear filter (approximated by a Particle filter [8][9][10]) obeys the modified Riccatis of [1,2] while the SOI-KF and MLQ-KF diverge. This is quite surprising in that the Riccatis which are a pure artifact of the Gaussianity assumption predict the performance of the optimal nonlinear filter even when the Gaussian assumption clearly does not hold.…”

“…In [1], this limitation is overcome by developing an elegant distributed estimation approach based on quantizing the innovation to one bit (so called sign of innovation or SOI). In [2], this is generalized to handle multiple quantization levels. In both cases, it is assumed that the innovation is approximately Gaussian leading to a linear filter and very simple characterization of its error performance.…”

“…But simulations show that the actual filters do not. This leads one to investigate the relation between the modified Riccati recursions derived in [1,2] and the actual error performance of the filters. In this paper, we precisely try to answer this question.…”