Table 1 The description and dimension of the EKF symbols, where \(s\) and \(r\) represent the feature and robot state size, \(v\) and \(f\) the robot and feature position, \(i\) the feature number and \(n\) the total number of features
From: A method to convert floating to fixed-point EKF-SLAM for embedded robotics
Sym. | Dimension | Description |
|---|---|---|
\(\mu \) | \((r+sn) \times 1\) | Both robot and feature positions |
\(\mu _v\) | \(r \times 1\) | Elements of \(\mu \) related to robot position |
\(\mu _f\) | \(sn \times 1\) | Elements of \(\mu \) related to feature position |
\(\Sigma _{vv}\) | \(r \times r\) | Robot position covariance |
\(\Sigma _{vf}\) | \(r \times (sn)\) | Cross robot-feature covariance |
\(\Sigma _{ff}\) | \((sn) \times (sn)\) | Cross feature-feature covariance |
\(\Sigma \) | \((r+sn) \times \) | Cross robot-feature |
\((r+sn)\) | and feature-feature covariance | |
\(\alpha \) | – | Prediction function |
\(\gamma \) | – | Measurement function |
\(u\) | \(r \times 1\) | Robot motion command |
\(F\) | \(r \times r\) | Robot motion Jacobian |
\(G\) | \(r \times r\) | Robot motion noise Jacobian |
\(Q\) | \(r \times r\) | Permanent motion noise |
\(H_v\) | \(s \times r\) | Measurement Jacobian with respect to \(v\) |
\(H_{fi}\) | \(s \times s\) | Measurement Jacobian with respect to \(f_i\) |
\(H\) | \(s \times (r+sn)\) | Compounded measurement Jacobian |
\(R\) | \(s \times s\) | Permanent measurement noise |
\(W\) | \((r+sn) \times s\) | Filter gain |
\(\nu \) | \(s \times 1\) | Mean innovation |
\(z\) | \(s \times 1\) | Sensor measurement |
\(z_\mathrm{pred}\) | \(s \times 1\) | Sensor measurement prediction |
\(S\) | \(s \times s\) | Covariance innovation |
\(Z_1\) | \(s \times (s(i-1))\) | Zero matrix |
\(Z_2\) | \(s \times (s(n-i))\) | Zero matrix |