# Improving Velocity estimation

I have a sensor reduction model which gives me a velocity estimate of a suspension system(velocity 1) .

This suspension system estimate velocity is used to calculate another velocity(velocity 2) via a transfer function/plant model.

Can I use velocity 2 to improve my velocity estimate (velocity 1) through Kalman filtering or through some feedback system.?? V1 is "estimated" using these two sensors.That is fed into a geroter pump (Fs in diagram) which pumps fluid to manupulate the damper viscous fluid thereby applying resistance to the forces applied to the car body. There is no problem did I have an velocity sensor on the spring.I could measure it accurately but now I only have an estimate. I am trying to make the estimate better.Assume I have a model/plant or transfer function already that gives me the V2 given a V1.

• Can you provide a one-line diagram of your pump system? I'm not clear on how everything connects. Is the pump running the viscous damper between $m_s$ and $m_{us}$? Is V1 a control input to the pump? More information on your system is needed to give good advice. Jun 16 '15 at 18:36
• @Chuck V1 is "estimated" using these two sensors.That is fed into a geroter pump (Fs in diagram) which pumps fluid to manupulate the damper viscous fluid thereby applying resistance to the forces applied to the car body. There is no problem did I have an velocity sensor on the spring.I could measure it accurately but now I only have an estimate. I am trying to make the estimate better.Assume I have a model/plant or transfer function already that gives me the V2 given a V1. Jun 16 '15 at 18:44
• Welcome to robotics Lanny, but on stack exchange, it is better to edit your question to add information requested in comments, rather than adding more comments. Comments are for helping to improve questions and answers, and are distracting, so we try to keep them to a minimum. If all of the information needed to answer the question is contained within it, the comments can be tidied up (deleted). Jun 16 '15 at 21:22

If you have transfer function such that $$\frac{V_2}{V_1} = H \\ V_2 = H V_1 \\$$ Then wouldn't your estimate of $V_1$ be given by inverting the transfer function?

$$V_1 = H^{-1} V_2$$

The problem is that you can't use this to measure $V_1$, and here's why:

Your measurements are an estimate of $V_1$. $$V_{est} = f(V_1)$$ You feed that estimate into the pump and get a flow output. $$V_2 = H V_{est}$$ Now, if you invert the plant, you do NOT get a measurement of $V_1$, you get a measurement of your original estimate. $$V_{est} = H^{-1} V_2$$ It's like you are trying to draw your own ruler and then use that ruler to see if you drew the ruler correctly. It's a circular definition that's not going to get you anything useful.

• So now I have Actual V1,V1_est ,V_2 derived from V1_est. What if I were to introduce noise into the velocity esitimate.Doesnt it become a Kalman Filter problem? slideshare.net/antoniomorancardenas/… Jun 16 '15 at 19:29
• As I mentioned in the above post, anything you get from $V_2$, noisy or not, will only ever at best return your original estimate based on the two sensors. If you had a perfect measurement of $V_2$, with no noise, and a perfect model of the plant that was 100% correct, you still only get the sensor-based estimates. Now, you could of course always filter the sensor output to try to improve your initial estimate of $V_1$, but $V_2$ will never give you any useful information because it is a function of your estimate, not the actual velocity. Jun 16 '15 at 19:52
• How about this.Suppose I have an additional sensor to measure the actual $V_2 actual$. So Now I have $V_2 actual$ and $V_2 est$ got from $V_1 est$.And now I update the $V_1 estimate$ based on the error of $V_2 actual -V_2 estimate$ Jun 16 '15 at 20:36
• $V_2$ is always a function of your $V_1$ estimate, so it doesn't matter how precisely you can measure it, the best you can do with that information is to recover your original $V_1$ estimate. Jun 16 '15 at 20:47
• How about this. Let's assume a model of $y = 2x$. Based on my measurement, I think $x = 2$. I use $2$ as the input to my plant, which I have modeled. It doesn't matter if the model is absolutely correct or not. Let's further assume I measure $y = 4$ after I provide an $x = 2$. Does this mean that $x$ actually equaled $2$? No! It just means that the input to plant was $2$. The actual value could have been anything! Jun 16 '15 at 20:50