基于Bancroft算法的GPS动态定位非线性滤波法

由于系统线性化时存在忽略项,扩展卡尔曼滤波成为一种次优的梯度下降算法.当滤波方程病态时,求解存在发散倾向,且估计量为有偏的,而非最优估计.即使动态系统噪声为高斯噪声时,残差也不是高斯噪声.在伪距定位中,由于线性化后的伪距方程是局部解,这有可能丢失正确解值.针对GPS动态导航扩展卡尔曼滤波定位问题,基于美国Bancroft的全局性非线性"闭合式求解"最小二乘算法(Bancroft算法),本文提出一种闭合式GPS非线性代数解的卡尔曼滤波法(两步算法).该方法将GPS滤波问题中的空间与时间分离,较好地解决了非线性GPS动态定位求解问题,且获得稳定可靠的动态定位解.

NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM

Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm-Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.