A general model-based filter initialization approach for linear and nonlinear dynamic systems

Tracking performance significantly relies on the quality of filter initialization, including accuracy and consistency, especially in a nonlinear filtering system. Most existing methods are built on assumptions that the target position varies linearly with time or the dynamic model is linear. In practical applications where the assumptions are violated, these methods may suffer from performance degradation or cannot be applied. To address this limitation, a general model-based initialization method for both linear and nonlinear dynamic systems is proposed. According to the dynamic model, the relationships between the first several measurements and the state to be initialized are analyzed and several equations are constructed to solve the initial state estimate. When transcendental equations are involved, numeric root-finding methods are employed to find numeric solutions. In cases with linear analytic solutions, the initial state covariance can be derived explicitly. In other cases, the unscented transformation is employed to calculate the initial covariance. Two commonly used linear dynamic models and three representative nonlinear dynamic models are used as examples to illustrate the procedure of the proposed algorithm. Monte Carlo simulation results demonstrate the effectiveness of the proposed filter initialization algorithm.