Estimation Theory Essay

1875 Words8 Pages

CHAPTER 3 SIGNIFICANCE AND BACKGROUND 3.1 Introduction to Estimation Theory In estimation theory, the aim is to infer a parameter θ or parameter vector θ from some measurement data x. Towards that end, it is necessary to first find a good mathematical model for the data. In classical estimation theory, the parameters are assumed to be deterministic but unknown. Thus, the data can be described using the family of PDFs p(x; θ). In Bayesian estimation theory, in contrast, the unknown parameter to be estimated is assumed to be a realization of a random variable. Consequently, the data is described by the joint PDF p(x; θ)= p(x|θ)p(θ) composed of the prior PDF p(θ) and the conditional PDF p(x|θ). 3.2 Conventional Estimation Theory 3.2.1 Performance Metrics and Unbiased Estimators For a given …show more content…

In tracking, however, parameters are assumed to evolve in time. To clearly distinguish between fixed parameters and those that evolve in time, the latter ones are often referred to as a state. The task in tracking is then to infer the state s[n] from the measurements y[n] taken at time-step n. Obviously, we could implement tracking by estimating states at every time-step individually, using some of the earlier discussed methods. However, if an estimates ̂[n-1]is available at time-step n, this estimate can often be used as prior information for the estimation of s ̂[n]. When tracking the location of a pedestrian, as an example, the change in location is clearly determined by the pedestrian’s velocity. Thus, if we have obtained an estimate for the pedestrian’s location and velocity at time-step n-1, we can already estimate the pedestrian’s location at time-step n without taking any measurements. In order to exploit such knowledge, we obviously need a good model for the evolution of the state. In Kalman filtering this model is often referred to as the state transition and is given

Open Document