A New Approach to Linear Filtering and Prediction Problems.

Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems. Transactions of the ASME—Journal of Basic Engineering, 82(1), 35-45.

Type

Journal article

Intellectual base

Primary research

Year

1960

DOI

10.1115/1.3662552

Link

https://doi.org/10.1115/1.3662552

Cited from

cognitive_science, mathematics, psychology, statistics_experimental_design, systems_cybernetics

Cited by

8 citations across 8 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Bayesian Cue Integration
  • In sensor fusion and robotics it is the Kalman filter, which combines accelerometer, gyroscope, GPS, and visual-odometry estimates of pose, weighting each by its covariance.

    This sourceDerives the Kalman filter: recursive inverse-covariance-weighted fusion of parallel noisy estimates of a latent state, with the fused covariance smaller than any input's.

• Good Regulator Theorem
  • The same structural relationship holds for a Kalman filter's estimate moving ahead of noisy readings, a grandmaster reading a position, a central bank shifting policy on leading indicators, a predator anticipating prey movement, and a deep-RL policy encoding its environment's dynamics in hidden representations.

    This sourceThe optimal recursive state estimator embeds a model of the plant, letting its estimate move ahead of noisy readings — the estimator that is a model.

• Object Permanence
  • Its formalization is well known: the Kalman filter, with its predict step that propagates latent state between measurements and its update step that re-binds incoming observations, is engineered object permanence, and state-space modeling generally is the latent-state grammar this prime names.

    This sourceIntroduces the Kalman filter, whose predict step propagates latent state between measurements and whose update step re-binds incoming observations — the engineered formalization of object permanence.

• Precision Weighting
  • Probability and statistics — Bayesian updating as precision-weighted prior plus likelihood; inverse-variance weighting combining studies in meta-analysis; weighted least squares. Engineering and control — Kalman filtering and sensor fusion, where the Kalman gain is the ratio of prior precision to total precision and redundant measurements are weighted by inverse noise.

    This sourceIntroduces the Kalman filter, whose gain is the ratio of measurement precision to total precision.

• Prediction Error
  • The Kalman filter makes the relationship explicit: the innovation is observed minus predicted observation, and the gain controls how strongly it changes the estimate.
• Stochastic Process
  • In signal processing and statistics, a time series is a realization of a stochastic process, and estimating its mean, autocovariance, and spectrum — and forecasting it — is inference about the underlying process; control theory's stochastic filtering (the Kalman filter) tracks a process observed through noise.

    This sourceIntroduces the Kalman filter for tracking a stochastic process observed through noise.

Domain-specific

• State variable
  • A state variable is a component of a chosen state vector: information about the present system that, under the model and inputs, is sufficient to determine future state and outputs without retaining the full past.

Mechanisms

• Innovation Residual Filter
  • This is the logic of the Kalman filter, where the innovation drives the update and the gain that weights it is set by the model's and the sensor's covariances.

    This sourceDefines the recursive filter update as a prior estimate corrected by a new-observation residual whose weighting is derived from model and observation covariances.

Verification

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