Parameter Estimation Of Kalman Filter Model For One - Dimensional Discrete Data And Improvement Of Adaptive Filtering Algorithm

The paper reviews the research background and status quo of the Kalman filter, detailedly studies the linear Kalman filtering and nonlinear Kalman filtering,analyzes the respective advantages and disadvantages and discusses their application ranges.First of all, based on one-dimensional discrete state data and observational data, the parameter estimation algorithm(SPL) for state equation and the parameter estimation algorithm(OSL)for observation equation are proposed. The first method is to calculate the probability distribution of the next status data relevant to the current status data, then to estimate the parameter in the state equation by the least square method and to deduce the state equation; the second method is to estimate the measurement matrix by using the least square method of each interval based on equant status data and observation data, to construct the function relationship between the state variable and the measurement matrix and to deduce the observation equation.Secondly, two improvements about the simplified Sage-Husa self-adaptive filtering algorithm are made. The first point: substitute observation noise Rk-1 for observation noise Rk to calculate Calman gainKK, solving the infinite loop problem in the original algorithm; the second point: increase two steps on the basis of original algorithm. The first step is to recalculate Calman gainKK by using the obtained observation noise Rk; the second step is to recalculate the estimated value xk by the use of the new Calman gain Kk.Then, for the single time delay system, the specific Kalman filtering algorithm is given, and a method to estimate observation delay time when the state process and the observation process are stationary is proposedFinally, these methods in this paper are analyzed empirically. It deduces the relevant parameter and the observation delay time of state equation and observation equation, and verifies the effectiveness of above methods by the use of evaluation function R(s) proposed in this paper.