KalmanFilter< NX, NZ > Class Template Reference

A lightweight, fixed-size Kalman Filter for embedded state estimation. More...

#include <KalmanFilter.h>

Collaboration diagram for KalmanFilter< NX, NZ >:

Public Member Functions
void	predict ()
void	update (const Matrix< NZ, 1 > &z)

Public Attributes
Matrix< NX, 1 >	x
Matrix< NX, NX >	P
Matrix< NX, NX >	Fmat
Matrix< NX, NX >	Q
Matrix< NZ, NX >	H
Matrix< NZ, NZ >	R
Matrix< NX, NX >	I = Matrix<NX, NX>::identity()

Detailed Description

template<size_t NX, size_t NZ>
class tinyrobotics::KalmanFilter< NX, NZ >

A lightweight, fixed-size Kalman Filter for embedded state estimation.

This template class implements a discrete-time, linear Kalman Filter for real-time state estimation in embedded and robotics applications. It is designed for efficiency and simplicity, using static, fixed-size matrices and minimal dynamic memory. The filter estimates the internal state of a process given noisy measurements and a mathematical model of the system dynamics.

Features

• Fixed-size, stack-allocated matrices for predictable memory usage
• Suitable for microcontrollers and real-time systems
• Supports arbitrary state and measurement dimensions via template parameters
• Simple API: predict() for time update, update(z) for measurement update

Mathematical Model

The Kalman Filter models the system as:

x_k = F * x_{k-1} + w (state transition) z_k = H * x_k + v (measurement)

where:

• x: state vector (NX x 1)
• z: measurement vector (NZ x 1)
• F: state transition matrix (NX x NX)
• H: measurement matrix (NZ x NX)
• Q: process noise covariance (NX x NX)
• R: measurement noise covariance (NZ x NZ)
• w, v: process and measurement noise (zero-mean, Gaussian)

Usage Example

KalmanFilter<2, 1> kf;
kf.Fmat = ...; // set state transition
kf.H = ...;    // set measurement model
kf.Q = ...;    // set process noise
kf.R = ...;    // set measurement noise
kf.x = ...;    // set initial state
kf.P = ...;    // set initial covariance
kf.predict();
kf.update(z);

Template Parameters

Template Parameters

NX	Number of state variables (state vector dimension)
NZ	Number of measurement variables (measurement vector dimension)

Members

• x: State estimate vector (NX x 1)
• P: State covariance matrix (NX x NX)
• Fmat: State transition matrix (NX x NX)
• Q: Process noise covariance (NX x NX)
• H: Measurement matrix (NZ x NX)
• R: Measurement noise covariance (NZ x NZ)
• I: Identity matrix (NX x NX)

Methods

• predict(): Performs the time update (prediction) step
• update(z): Performs the measurement update (correction) step

Applications

• Sensor fusion (IMU, GPS, encoders)
• Robot localization
• Signal filtering and smoothing
• Any scenario requiring optimal state estimation from noisy data

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The documentation for this class was generated from the following file:

• src/TinyRobotics/control/KalmanFilter.h