I want to implement a Kalman Filter for predicting x/y positions. I have a sensor which gives me the current position (noisy). Now I want to smooth and predict the position. Thus Kalman Filter came to my mind.How do I have to design the filter taking the time in regards? I want to predict the next state which is ahead of the upcoming measurement. Moreover since i do not have a velocity, I'd like to estimate the velocity by the kalman as well.State := [xpos,ypos,xvelocity,yvelocity]Measurement := [xpos,ypos]ControlInput := predictionTimeI would run the following algorithm, whenever i get a measurement:1. Measure2. Update kalman gain3. Predict4. Get State estimateNow, when i use a predictionTime which is newer than the next measurement, the next measurement does not fit to the predicted state.Is there a strategy to solve this issue? My predicted state and my next measurement do not fit, how could I fix this?

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I want to implement a Kalman Filter for predicting x/y positions. I have a sensor which gives me the current position (noisy). Now I want to smooth and predict the position. Thus Kalman Filter came to my mind.How do I have to design the filter taking the time in regards? I want to predict the next state which is ahead of the upcoming measurement. Moreover since i do not have a velocity, I&#039;d like to estimate the velocity by the kalman as well.State := [xpos,ypos,xvelocity,yvelocity]Measurement := [xpos,ypos]ControlInput := predictionTimeI would run the following algorithm, whenever i get a measurement:1. Measure2. Update kalman gain3. Predict4. Get State estimateNow, when i use a predictionTime which is newer than the next measurement, the next measurement does not fit to the predicted state.Is there a strategy to solve this issue? My predicted state and my next measurement do not fit, how could I fix this?

pressacvt · Accepted Answer

Basically what you would do is the following:Let:  X  =  [  x  ,  y  ,  v  x  ,  v  y  ]  P  =                              σ          x          2                            0                    0                    0                            0                              σ          y          2                            0                    0                            0                    0                              σ                      v            x                    2                            0                            0                    0                    0                              σ                      v            y                    2                      Δ  tBe your state vector, state covariance matrix, and time interval between two measurements respectively.How can you transition from one state K to another state K+1,, which is Dt seconds later? Taking the simple equation.distance(meters)=speed(meters/sec)∗time(secs)You see that transitioning from one state to another is done in the following way:      F    k    =                    1                    0                    Δ        t                    0                            0                    1                    0                    Δ        t                            0                    0                    1                    0                            0                    0                    0                    1            Because, when you do the state prediction, you apply the following equation (simplyfication with no input control vector):      X    k    =      F    k    ∗      X          k      −      1      Multiplying both matrixes together yields back the following equations:      x    k    =      x          k      −      1        +  v      x          k      −      1        ∗  Δ  t      y    k    =      y          k      −      1        +  v      y          k      −      1        ∗  Δ  t  v      x    k    =  v      x          k      −      1        v      y    k    =  v      y          k      −      1      If you need further clarification on another aspect, please do not hesitate to ask.

I want to implement a Kalman Filter for predicting x/y positions. I have a sensor which gives me the

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