English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This report provides a brief historical evolution of the concepts in theKalman filtering theory since ancient times to the present. A brief descriptionof the filter equations its aesthetics, beauty, truth, fascinating perspectivesand competence are described. For a Kalman filter design to provide optimalestimates tuning of its statistics namely initial state and covariance, unknownparameters, and state and measurement noise covariances is important. Theearlier tuning approaches are reviewed. The present approach is a referencerecursive recipe based on multiple filter passes through the data without anyoptimization to reach a `statistical equilibrium' solution. It utilizes the apriori, a posteriori, and smoothed states, their corresponding predictedmeasurements and the actual measurements help to balance the measurementequation and similarly the state equation to help form a generalized likelihoodcost function. The filter covariance at the end of each pass is heuristicallyscaled up by the number of data points is further trimmed to statisticallymatch the exact estimates and Cramer Rao Bounds (CRBs) available with noprocess noise provided the initial covariance for subsequent passes. Duringsimulation studies with process noise the matching of the input and estimatednoise sequence over time and in real data the generalized cost functions helpedto obtain confidence in the results. Simulation studies of a constant signal, aramp, a spring, mass, damper system with a weak non linear spring constant,longitudinal and lateral motion of an airplane was followed by similar but moreinvolved real airplane data was carried out in MATLAB. In all cases the presentapproach was shown to provide internally consistent and best possible estimatesand their CRBs.

Introduction to the Kalman Filter and Tuning its Statistics for Near Optimal Estimates and Cramer Rao Bound