What Is the Kalman Filter Scalar Gain & Variance Update Calculator?
The Kalman filter provides real-time estimation of hidden state variables in the presence of noise.
The measurement update step optimally balances trust between model predictions and raw sensor data.
How Does the Kalman Filter Scalar Gain & Variance Update Calculator Work?
Calculates the innovation residual y = z - x_hat^-.
Determines the optimal Kalman gain K = P^- / (P^- + R).
Updates the state estimate x_hat and reduces error variance P.
Kalman Filter Scalar Gain & Variance Update Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Optimal Kalman measurement update equations for scalar linear observation.
How to Use the Kalman Filter Scalar Gain & Variance Update Calculator
- Enter prior predicted state and its associated uncertainty variance P^-.
- Enter the newly observed sensor measurement z.
- Provide the sensor noise variance R from sensor specifications.
Step-by-Step Example Calculation
GPS Velocity Tracking Fusion
Input Values:
Understanding Your Result
If sensor noise R is small, K approaches 1.0 and the filter trusts the measurement.
If model variance P^- is small, K approaches 0 and the filter rejects sensor noise.
Factors That Affect the Result
- Sensor accuracy R: Lower sensor noise accelerates filter response to sudden state changes.
- Process noise Q: Higher process uncertainty inflates prior variance P^-, increasing reliance on measurements.
When Should You Use This Calculator?
- Avionics navigation, missile guidance, and autonomous vehicle trajectory tracking.
- Sensor fusion combining IMU accelerometers, gyroscopes, and GPS receivers.
Assumptions & Limitations
- Assumes linear observation model and zero-mean Gaussian white noise.
- Applies to scalar (single-variable) state observations.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Proven mathematically optimal minimum mean-square error estimator for linear Gaussian systems.