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.
Cited by¶
13 citations across 13 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.
Supported in partVerified against the publisher's abstract
Kalman (1960) supplies the optimal linear filter and its estimation-error covariance equation — the mathematical frame — but says nothing about sensor fusion, robotics, accelerometers, gyroscopes, GPS, or pose.
“A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error.”
- 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.
- 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.
Supported in partVerified against the publisher's abstract
The abstract backs only the filtering/regulator duality for Kalman's estimator, not the plant-model embedding, the prediction-ahead-of-noise mechanism, or the four non-Kalman domains the claim lists.
“The filtering problem is shown to be the dual of the noise-free regulator problem.”
- 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.
- 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.
Supported in partVerified against the publisher's abstract
Kalman's abstract confirms a state-transition treatment of filtering and prediction, but never mentions object permanence and does not state the predict/update mapping the claim asserts.
“The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems.”
- 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.
- 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.
Supported in partVerified against the publisher's abstract
The abstract establishes the state-transition formulation of the optimal linear filter; it states no gain formula, precision weighting, sensor fusion, or meta-analysis items.
“The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems.”
- 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.
- 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.
Supported in partVerified against the publisher's abstract
Kalman's abstract establishes the optimal linear filter and its error-covariance equation, but does not state the innovation-minus-prediction or gain formulation.
“(2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation 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.
Supported in partVerified against the publisher's abstract
Its abstract shows the paper re-examines filtering and prediction for random processes, backing the Kalman-filter clause only, not the time-series or spectrum clause.
“The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems.”
- 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.
Domain-specific¶
Mechanisms¶
- Bayesian State Estimation
- Under the hood this is a Kalman filter
This sourceDevelops the recursive prediction-and-correction equations now known as the Kalman filter.
- Under the hood this is a Kalman filter
- 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.
- 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.
- Learning Rate Schedule
- Its strength is that it converts the vague instinct "we should probably adjust" into a governed step size, and — by adapting to volatility rather than holding the rate fixed — it beats any constant gain across a changing world.
This sourceDerives a recursive filter gain from evolving uncertainty covariances rather than requiring one fixed gain.
- Its strength is that it converts the vague instinct "we should probably adjust" into a governed step size, and — by adapting to volatility rather than holding the rate fixed — it beats any constant gain across a changing world.
- Map Matching and Recalibration
- The disciplined version of "correct the estimate against measurements" is formalized by the Kalman filter, which optimally blends a drifting prediction with a noisy fix.
This sourceDerives a recursive Kalman estimator that corrects a model-based state prediction with noisy measurements using gains determined by error covariance.
- The disciplined version of "correct the estimate against measurements" is formalized by the Kalman filter, which optimally blends a drifting prediction with a noisy fix.
- Predictive State Filter
- The recursive machinery it descends from, the Kalman filter,
This sourceDerives the Kalman filter as a recursive optimal linear estimator under a specified linear stochastic model and noise-covariance assumptions.
- The recursive machinery it descends from, the Kalman filter,
- State-Estimation Filter
- A state-estimation filter — canonically a Kalman filter
This sourceDerives a recursive state estimator that combines model prediction with noisy observations and sets its correction coefficients from error covariance.
- A state-estimation filter — canonically a Kalman filter
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
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