Kalman Filters

Geospatial stuff

Quantitative Methods in Ecosystem Distribution Mapping:
The Use of Remote Sensing for Ecosystem Risk Assessment:
The Changing Drivers of Coastal Ecosystem Change and New Opportunities for Conservation:
Advancing Global-Scale Remote Sensing to Meet Conservation Needs:
Detecting Ecosystem Degradation from Space:
Global Barriers of Tidal Inundation:
Fine-Scale Detection of Coastal Wetland Change in South-East Asia:
Developing New Performance Measures of Nature-Based Coastal Defenses:
Forecasting Coastal Change: Connecting Spatial Simulations to Earth Observation:

Kalman Filter in Bayesian vs. Frequentist Approaches

Aspect	Bayesian Approach	Frequentist Approach
Theory	Bayesian methods involve updating the probability distribution of a system's state based on new data.	Frequentist methods focus on estimating the state of a system by minimizing error without directly involving probability distributions for the state.
Model Type	Typically used with non-linear models (e.g., Extended Kalman Filter, Unscented Kalman Filter).	Often applied to linear models, although non-linear adaptations exist.
Uncertainty Handling	Uncertainty is explicitly modeled as probability distributions.	Uncertainty is often handled through error terms in the model.
Parameter Estimation	Parameters can be treated as random variables with their distributions updated iteratively.	Parameters are usually fixed values estimated from the data.
Use Cases	Common in robotics and autonomous systems for navigation and tracking where model uncertainty is significant.	Widely used in signal processing, econometrics, and systems control with clear, well-defined models.
Example Studies	Case studies in robotics often employ Bayesian Kalman Filters for real-time updating of system states in uncertain environments.	Studies in signal processing might use frequentist Kalman Filters to accurately track signals in noisy environments.

Note:

The distinction between Bayesian and frequentist approaches is based more on how uncertainty and parameters are treated rather than the linearity or non-linearity of the model.
While specific case studies could not be retrieved, the use cases and theoretical foundations provide a general understanding of how Kalman filters are applied in different statistical paradigms.

Kalman Filters in TensorTide

To incorporate Kalman filters into the TensorTide project, which focuses on advanced analytics in marine ecology, we need to identify areas where dynamic state estimation and time-series analysis are crucial. Kalman filters excel in situations where you need to track or estimate changing states over time, especially in the presence of uncertainty or noise in the data. Here's how Kalman filters can be integrated into different aspects of TensorTide: