Kalman filter algorithm

山鸡哥张强

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Kalman filter algorithm

The Kalman filter algorithm uses a state space model of signals and noise, and uses the estimated value at the previous moment and the observed value at the current moment to update the estimate of the state variable and obtain the estimated value at the current moment.

The Kalman filter algorithm is a recursive filtering algorithm proposed by Kalman et al. in the 1960s. Its essence is to seek a set of recursive estimation algorithms with the minimum mean square error as the best criterion for estimation. This algorithm uses the state space model of signal and noise, and uses the estimated value of the previous moment and the observed value of the current moment to update the estimate of the state variable and find the estimated value of the current moment. It is widely used in inertial navigation systems. The noise just mentioned refers to the error between the calculated value and the actual value.

So why is Kalman filtering applied to inertial navigation systems? This is mainly because the "pure inertial" sensors of inertial navigation systems are not sufficient to achieve the required navigation accuracy. In order to compensate for the shortcomings of the navigation system, other navigation devices are often used to improve navigation accuracy and reduce navigation errors. Therefore, using the Kalman filtering algorithm, data from inertial navigation systems and other navigation devices (such as the position calculated by the inertial navigation system and the position information given by the GPS receiver) can be mixed and used to estimate and correct unknown inertial navigation system errors.

The Kalman filter algorithm has been widely used for more than 30 years, including robot navigation, control, sensor data fusion and even military radar systems and missile tracking.

For example, in radar, people are interested in tracking targets, but the measured values of the target's position, velocity, and acceleration are often noisy at any time. Kalman filtering uses the dynamic information of the target to try to remove the influence of noise and obtain an optimal estimate of the target's position. This estimate can be an estimate of the current target position (filtering), an estimate of the future position (prediction), or an estimate of the past position (interpolation or smoothing).

吾妻思萌

When I was in school, I saw a senior student using Kalman to make a small flying machine.

hellokitty_bean

I have seen people with ties to Tsinghua spend years researching Kalman filtering, applying for NSFC, getting many projects, and living a comfortable life.