A Filter Implementation Using the Cubature Kalman Filter

The Cubature Kalman Filter (CKF) is an efficient state estimation algorithm designed for nonlinear systems. It approximates the statistical properties after nonlinear transformations through deterministic sampling points. Compared to the traditional Extended Kalman Filter (EKF), CKF avoids Jacobian matrix calculations, and offers better numerical stability than the Unscented Kalman Filter (UKF).

Core Implementation Logic: Initialization Phase: Set the system state vector, covariance matrix, and process/observation noise parameters. For nonlinear systems, clearly define the state transition function and observation function (typically implemented as separate MATLAB functions or class methods). Cubature Point Generation: Generate a set of symmetric cubature points (usually 2n points, where n is the state dimension) based on the current state mean and covariance. These points are determined through spherical-radial rules to accurately capture higher-order moment information (commonly implemented using matrix decomposition and point transformation algorithms). Prediction Step: Propagate cubature points through the nonlinear state equation to compute the predicted state mean and covariance. This process fully considers the system's nonlinear characteristics (in code, this involves function evaluations for each cubature point). Update Step: Transform predicted cubature points through the observation model, combine with actual sensor data, calculate Kalman gain, and update state estimates (requires matrix operations for covariance updates and gain calculations).

Advantages and Application Scenarios: Suitable for strongly nonlinear systems (e.g., UAV positioning, robot SLAM) Superior computational efficiency compared to Monte Carlo methods, with better accuracy than EKF's linear approximations Deterministic sampling avoids randomness issues inherent in particle filters

Parameter Tuning Essentials: Special attention should be paid to setting process noise matrix Q and observation noise matrix R, as these parameters directly affect the filter's convergence speed and anti-interference capability. In practical applications, these can be determined through sensor calibration data or offline optimization (often implemented as diagonal matrices with values tuned via experimental data).

For further discussion on specific matrix operation details in implementation or real-time optimization for engineering applications, please specify your requirements.