Sannsynlighetsfiltre

Sannsynlighetsfiltre, also known as probabilistic filters, are a class of algorithms used to estimate the state of a system based on a series of noisy measurements. They are particularly useful in situations where the system's dynamics are uncertain or the measurements are inaccurate. The core idea behind probabilistic filters is to maintain a probability distribution over the possible states of the system, rather than a single, precise estimate.

These filters work by iteratively updating this probability distribution. Initially, a prior probability distribution is established, representing the uncertainty about the system's state before any measurements are taken. When a new measurement arrives, the filter uses Bayes' theorem to update the prior distribution into a posterior distribution. This posterior distribution incorporates the information from the new measurement, effectively reducing the uncertainty. This process is repeated with each subsequent measurement, allowing the filter to track the system's state over time.

Common examples of probabilistic filters include the Kalman filter, the particle filter, and the Bayesian filter. The Kalman filter is optimal for linear systems with Gaussian noise, while particle filters are more general and can handle non-linear systems and non-Gaussian noise by approximating the probability distribution with a set of weighted samples. Probabilistic filters find applications in a wide range of fields, including robotics, navigation, signal processing, and econometrics, where they are crucial for tasks such as tracking objects, estimating sensor readings, and predicting future system behavior.