A sensor network's motes observe the environment, make estimates based on observations with spatially correlated noise sources, and then send/relay these estimates to a Cluster-Head (CH). A novel scheme based on dithered quantization and channel compensation is used to ensure that each mote's local estimate received by the CH is unbiased. Based on an upper bound of the noise covariance matrix, the CH fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). We evaluate the mean square error(MSE) of the final estimate by both analysis and simulation.

In clustered networks of wireless sensors, each sensor collects noisy observations of the environment, quantizes these observations into a local estimate of finite length, and forwards them through one or more noisy wireless channels to the cluster head (CH). The measurement noise is assumed to be zero-mean and have finite variance, and each wireless hop is modeled as a binary symmetric channel (BSC) with a known crossover probability. A novel scheme is proposed that uses dithered quantization and channel compensation to ensure that each sensor's local estimate received by the CH is unbiased. The CH fuses these unbiased local estimates into a global one, using a best linear unbiased estimator (BLUE). Analytical and simulation results show that the proposed scheme can achieve much smaller mean square error (MSE) than two other common schemes, while using the same amount of energy. The sensitivity of the proposed scheme to errors in estimates of the crossover probability of the BSC channel is studied by both analysis and simulation. We then determine both the minimum energy required for the network to produce an estimate with a prescribed error variance and how this energy must be allocated amongst the sensors in the multihop network.

The motes in a wireless sensor network observe the environment, make estimates based on their observations, and then send these estimates to a Cluster-Head (CH). A novel scheme based on dithered quantization and channel compensation is used to ensure that each mote's local estimate received by the CH is unbiased. Then the CH fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). We determine the number of bits each node should transmit to reach a prescribed error variance at the CH subject to per-node limits on the energy that can be used and the per-node cost of forwarding a bit to the CH.

A sensor network's motes observe the environment, make estimates based on their observations, and send/relay these estimates to a Cluster-Head (CH). There are two sources of error in these multi-hop networks: observations are corrupted by noise and transmissions suffer communication errors. A novel scheme based on dithered quantization and channel compensation is used to ensure that each mote's local estimate received by the CH is unbiased. The CH fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). We determine both the minimum energy required for the network to produce a BLUE estimate with a prescribed error variance and show how this energy should be allocated across the rings of a multi-hop network and the motes in each ring.

A set of mobile wireless sensors observe their environment as they move about. We consider the subset of these sensors that each made observations when they were all at approximately the same time/location. As they continue to move, one of them processes its observations and decides that an event that must be reported has taken place. To reduce the probability of a false alarm, this sensor assumes the role of a Cluster-Head (CH) and requests that all other sensors that collected observations at that time/location send it their decisions. The motion of each sensor determines how many hops its decision data must make to reach the CH. We analyze this effect of motion in the 1D case by modeling each sensor's motion as a Correlated Random Walk (CRW), which can account for transient behavior, geographical restrictions, and nonzero drift. Quantities, such as the energy required to collect the decision from all relevant sensors, can then be determined as a function of time.

To ensure that a multi-hop cluster of batterypowered, wireless sensor motes can complete all of its tasks, each task must minimize its use of communication and processing resources. For event detection tasks that are subject to both measurement errors by sensors and communication errors in the wireless channel, this implies that: (i) the Cluster-Head (CH) must optimally fuse the decisions received from its cluster in order to reduce the effect of measurement errors; (ii) the CH and all motes that relay other motes' decisions must adopt lowcomplexity processing and coding algorithms that minimize the effects of communication errors. This paper combines a Maximum a Posteriori (MAP) approach for local and global decisions in multi-hop sensor networks with low-complexity repetition codes and processing algorithms. It is shown by analysis and confirmed by simulation that there exists an odd integer M and an integer KMsuch the decision error probability at the CH is reduced when: (1) nodes in rings k ≤ KMhops from the CH directly relay their decisions to the CH; (2) nodes in rings k > KMlocally fuse groups of M decisions and then use a repetition code to forward these fused decisions to the CH; and (3) KMis a nondecreasing function of M. This algorithm - and hybrid, hierarchical, and compression approaches based on it - enable tradeoffs amongst the probability of error, energy usage, compression ratio, complexity, and time to decision.

In clustered networks of wireless sensor motes, each mote collects noisy observations of the environment, quantizes these observations into a local estimate of finite length, and forwards them through one or more noisy wireless channels to the Cluster Head (CH). The measurement noise is assumed to be zero-mean and have finite variance. Each wireless hop is assumed to be a Binary Symmetric Channel (BSC) with a known crossover probability. We propose a novel scheme that uses dithered quantization and channel compensation to ensure that each motes' local estimate received by the CH is unbiased. The CH then fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). The energy allocation problem at each mote and among different sensor motes are also discussed. Simulation results show that the proposed scheme can achieve much smaller mean square error (MSE) than two other common schemes while using the same amount of energy. The sensitivity of the proposed scheme to errors in estimates of the crossover probability of the BSC channel is studied by both analysis and simulation.

The model of hinging hyperplanes (HH) can approximate a large class of nonlinear functions to arbitrary precision, but represent only a small part of continuous piecewise-linear (CPWL) functions in two or more dimensions. In this correspondence, the influence of this drawback for black-box modeling is first illustrated by a simple example. Then it is shown that the above shortcoming can be amended by adding a sufficient number of linear functions to current hinges. It is proven that any CPWL function of n variables can be represented by a sum of hinges containing at most n+1 linear functions. Hence the model of a sum of such expanded hinges is a general representation for all CPWL functions. The structure of the novel general representation is much simpler than the existing generalized canonical representation that consists of nested absolute-value functions. This characteristic is very useful for black-box modeling. Based on the new general representation, an upper bound on the number of nestings of nested absolute-value functions of a generalized canonical representation is established, which is much smaller than the known result.