ocation awareness is important to many pervasive computing applications. Unfortunately, no location sensor takes perfect measurements or works well in all situations. Thus, the motivation behind this article is twofold. First, we believe the pervasive computing community will benefit from a concise survey of Bayesian-filter techniques. Because no sensor is perfect, representing and operating on uncertainty with a statistical tool such as Bayes filters is key in any system using many sensors. Second, estimating an object's location is arguably the most fundamental sensing task in many pervasive computing scenarios. It is thus a natural domain in which to illustrate the application of Bayesian filter techniques. Representing locations statistically enables a unified interface for location information. This lets us write applications independent of the sensors used-even when using very different sensor types, such as GPS and infrared badges. (A comparative survey of location systems appears elsewhere. 1 ) Here, we illustrate fusing sensor data from ultrasound and infrared tags. We also discuss how to combine high-resolution location information from anonymous laser range finders with low-resolution location sensors that provide identification. Bayes filters 2 probabilistically estimate a dynamic system's state from noisy observations. In location estimation for pervasive computing, the state is a person's or object's location, and location sensors provide observations about the state. The state could be a simple 2D position or a complex vector including 3D position, pitch, roll, yaw, and linear and rotational velocities. Bayes filters represent the state at time t by random variables x t . At each point in time, a probability distribution over x t , called belief, Bel(x t ), represents the uncertainty. Bayes filters aim to sequentially estimate such beliefs over the state space conditioned on all information contained in the sensor data. To illustrate, let's assume that the sensor data consists of a sequence of time-indexed sensor observations z 1 , z 2 , …, z t . The belief Bel(x t ) is then defined by the posterior density over the random variable x t conditioned on all sensor data available at time t: Roughly speaking, the belief answers the question, "What is the probability that the person is at location x if the history of sensor measurements is z 1 , z 2 , …, z t ?" for all possible locations x. In general, the complexity of computing such posterior densities grows exponentially over time, because Bayesian-filter techniques provide a powerful statistical tool to help manage measurement uncertainty and perform multisensor fusion and identity estimation. The authors survey Bayes filter implementations and show their application to real-world location-estimation tasks common in pervasive computing.
Refer to REF for a survey of various implementations of Bayesian filters and how they are applied to location estimation with ultrasound and infrared technologies.
Bayesian filtering for location estimation
IEEE Pervasive Computing
Computer Science