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摘要: Kalman滤波在系统控制、信号处理和飞行器导航等领域有广泛应用.众所周知，Kalman滤波是建立在一组递推计算的滤波算法.不准确的初始值设置是否影响状态滤波结果，这是实际应用Kalman滤波时必须关注和解决的问题.本文在推导滤波初始值与系统真实初态之间偏差对滤波结果影响的基础上，建立了初始值偏差对后续滤波影响的传递关系，以及滤波结果收敛的充分条件；通过设置多组不同初始值偏差，分别对某三阶可观测系统和不可观测系统进行了仿真计算及结果分析，验证了滤波初始值偏差会导致滤波结果发生明显偏离.研究结果揭示，即使是可观测的线性系统，采用Kalman滤波时也必须尽可能选取准确的初始值.Abstract: Kalman filter is widely used in system control, signal processing, spacecraft navigation and other fields. It has come to light that the Kalman filter is composed of a series of recursion algorithms. When the filter is used in practical projects, it is an open problem whether the biased initialization is infectious to Kalman filtering results or not, which must be paid much attention to and solved down. In this paper, the effect of initialization deviation on the recursive Kalman filter is discussed, a transmission formula is built to analyze the Kalman filtering difference which comes from initialization deviation, and a sufficient condition is deduced for convergence of the Kalman filter of state vectors. Setting several kinds of initial deviation values for simulation, series of simulation results are given for a 3rd-order observable system as well as a 3rd-order unobservable linear system. Simulation results show that deviation of initial value may result in distinct difference of the state filtering. The results given in this paper reveal that the initial value must be carefully selected even if the dynamic system is an observable linear time-invariant systems.
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Key words:
- Kalman filter /
- initial value /
- initial deviation /
- convergence /
- eigenvalue
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图 1 初始值偏10%时的Kalman滤波比对差
Fig. 1 Difference of Kalman filtering states under 10% deviation from the initial state of dynamic system
图 2 初始值偏10%的滤波与实际状态比对差
Fig. 2 Difference of Kalman filtering and true states under 10% deviation from the initial state
图 3 初始值偏50%时的Kalman滤波比对差
Fig. 3 Difference of Kalman filtering states under 50% deviation from the initial state of dynamic system
图 4 初始值偏50%的滤波与实际状态比对差
Fig. 4 Difference of Kalman filtering and true states under 50% deviation from the initial state
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