Consideration on how the covariance of Kalman filter affects the tracking effect of deepsort

One 、 Preface

We know deepsort The idea of Kalman filter is used in the implementation of , Used to predict the trajectory of motion , That is, tracking objects in real time .

From the five formulas of Kalman filter , It involves three covariance matrices , Namely P,Q,R.
So how do the values of these three covariances affect the tracking effect ？

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Two 、 Covariance matrix analysis of Kalman filter

According to the principle of implementation , covariance P、Q、R It's a two-dimensional matrix .

• Variance is quantity ⼀ The degree of dispersion of the group data , In probability theory, variance is used to measure random variables and their mathematical expectations （ mean value ） Between .
• covariance （Covariance） In probability theory and statistics, it is used to measure the total error of two variables .

   So covariance P Used to represent the predicted state vector and the real expected value mean Deviation between . So covariance P The bigger it is , It shows that there is a large deviation between the predicted result and the real value , That is, the reliability of the estimated value is low ; The smaller the covariance , It shows that the predicted result is close to the real value , That is, the reliability of the estimated value is high . stay deepsort In the implementation of , Here's the picture , covariance P How to set the initial value of .

   For the covariance matrix Q, This parameter is used to represent the error between the state transition matrix and the actual process , As a matrix for simulating external influences . However, it is often difficult to find an accurate and feasible assignment method for the initial value setting of the matrix . So in order to better solve this problem , I did a series of experiments , it turns out to be the case that , If in the scene of pedestrian movement , Such as roadside pedestrians , Walking in one direction , Then if the speed deviation is kept small , So the covariance matrix Q The value of can be given very small , But if the scene in the hospital , Such as waiting outside the door , Then patients usually move back and forth , Stop now and then , Sometimes accelerate your movement , Then in this scenario , Assign values according to the previous uniform velocity model , The effect not beautiful . We can attribute this non-uniform state to covariance Q To correct .
   Because covariance Q It is used to deal with the deviation between reality and reality , Covariance Q Set the internal initial value of to a larger initial value , To a certain extent, it can reduce the occurrence of loss , Set the value as shown in the figure below , The initial covariance of the speed weight is increased

   covariance R Discussion and Q similar .

   Last , If you want to reduce the loss of tracking at a low frame rate , The focus is on covariance Q Adjustment . On the whole , Reflected in Kalman gain K On ,P The smaller it is K The smaller it is , In the revised estimate , The proportion of observation value is small , The optimal modified estimate tends to the estimated value , On the contrary, it tends to measure . therefore , Increase the covariance difference between speed weight and speed , Make the speed closer to the measured value .
   that , because Q And P It's a linear relationship , that Q Adjustment of , Can affect K Value , Achieve the adjustment effect .

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3、 ... and 、 summary

Kalman filter function is still very powerful , Although it is a linear prediction system . stay deepsort In the implementation of , If the tracking effect is not good , To a large extent, it can be solved by adjusting relevant parameters in Kalman filter , Others, such as cascade matching 、iou Matching and other implementation principles , It's still perfect , Because when I try to improve the matching method , The original version is the best to change ！