Distributed maximum likelihood estimation for sensor networks

Abstract

The problem of finding the maximum likelihood estimator of a commonly observed model, based on data collected by a sensor network under power and bandwidth constraints is considered. In particular, a case where the sensors cannot fully share their data is treated. An iterative algorithm that relaxes the requirement of sharing all the data is given. The algorithm is based on a local Fisher scoring method and an iterative information sharing procedure. The case where the sensors share sub-optimal estimates is also analyzed. The asymptotic distribution of the estimates is derived and used to provide means of discrimination between estimates that are associated with different local maxima of the loglikelihood function. The results are validated by a simulation.

Distributed compression-estimation using wireless sensor networks

“…. , m K ) [6]. Indeed, since m k is an indicator variable, it is Bernoulli distributed with parameter given by the probability q := Pr{x k ∈ B c } = F w (τ c − θ).…”

SOI-KF: Distributed Kalman Filtering With Low-Cost Communications Using The Sign Of Innovations

“…In any event, estimating necessitates each sensor to communicate to the remaining sensors . This communication takes place over the shared wireless channel that we will assume can afford transmission of a single packet per time slot , leading to a one-to-one correspondence between time and sensor index and allowing us to drop the sensor argument in (4). The decision of which sensor is active at time , and consequently which observation gets transmitted, depends on the underlying scheduling algorithm-see, e.g., [11], [21].…”

“…Let and be the ECM of the filtered and predicted estimates of the SOI-KF in Proposition 2 when sampling period is used in (4). Then, the continuous-time ECM is defined as…”

“…Upon defining , we can solve the differential equation in (1) between and with initial condition to obtain (3) For simplicity, define the matrix and the white Gaussian driving noise input . With these definitions, the resultant discrete-time equivalent model is given by the vector time-varying autoregressive (AR) process (4) where and the observation noise is white Gaussian with pdf . Since sampling (2) requires passing through a lowor band-pass filter of bandwidth , the sampled covariance matrix satisfies [20,Sec.…”

“…Without explicitly considering quantization, spatial redundancy across sensor observations has been exploited to reduce communication requirements [3], [4], [9], [21], [23], [24]. Accounting for quantization, distributed estimation algorithms were explored in early works, see, e.g., [10] and [17]; and recently in the context of WSNs.…”