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Velocity Estimation from noisy Measurements - Sensor fusion using modified Kalman filter
- 1. Velocity Estimation from noisy Measurements Sensor fusion using modified Kalman filter www.controltrix.com copyright 2011 controltrix corp www. controltrix.com
- 2. Objective Consider a vehicle moving • Desired to measure the velocity accurately • Velocity is directly measured but is noisy • Acceleration also measured using onboard accelerometers • Integrating acceleration data gives velocity • Offset errors in acc./random walk cause drift in velocity Standard solution • Kalman filter with optimal gain K for sensor data fusion • Estimate by combining velocity and acc. measurement copyright 2011 controltrix corp www. controltrix.com
- 3. Problem specifics • Acceleration and velocity are measured using noisy sensor • Direct velocity measurement is noisy ( v m/s) • Acceleration is measured with a = 0.1 m/s2 offset = 0.2 m/s2 (DRIFT) Superposed sine wave drive Amplitude A = 3 m/s2, frequency f = 0.05 Hz Sample time Ts = 0.1 s • Simulated time = 200s - 400s copyright 2011 controltrix corp www. controltrix.com
- 4. Measured velocity noisy data (True velocity is smooth sine wave of amp 10, period 20 s) copyright 2011 controltrix corp www. controltrix.com
- 5. Advantages • No matrix calculations • Easier computation, can be easily scaled • Equivalent to Kalman filter structure (easily proven) • No drift (the error converges to 0) • Estimate accelerometer drift in the system by default • Drift est. for calib. and real time comp. of accelerometers copyright 2011 controltrix corp www. controltrix.com
- 6. Advantages. • Can be modified easily to make tradeoff between drift performance (convergence) and noise reduction • Systematic technique for parameter calculations • No trial and error copyright 2011 controltrix corp www. controltrix.com
- 7. Comparison Sl No metric Kalman Filter Modified Filter 1. Drift •Drift is a major problem •Guaranteed automatic convergence. (depends inversely on K) •No prior measurement of offset and •Needs considerable characterization required. characterization.(Offset, •Not sensitive to temperature induced temperature calibration variable drift etc. etc). 2. Convergence •Non-Zero measurement •Always converges and process noise •No assumptions on variances required covariance required else •Never leads to a singular solution leads to singularity 3. Method •Two distinct phases: •Can be implemented in a few single Predict and update. difference equation or even in continuum. copyright 2011 controltrix corp www. controltrix.com
- 8. Comparison. Sl No metric Kalman Filter Modified Filter 4. Computation •Need separate state •Highly optimized computation. variables for position, •Only single state variable required velocity, etc which adds more computation. 5. Gain value •In one dimension, •Gains based on systematic design /performance •K = process noise / choices. measurement noise. dt •The gains are good though • ‘termed as optimal’ suboptimal (based on tradeoff) 6. Processor req. •Needs 32 Bit floating point •Easily implementable in 16 bit computation for accuracy fixed point processor 40 and plenty of MIPS/ MIPS/computation is sufficient computation Note: The right column filter is a super set of a standard Kalman filter copyright 2011 controltrix corp www. controltrix.com
- 9. Sim results std Kalman filter velocity estimation error (v^ - v) vs time copyright 2011 controltrix corp www. controltrix.com
- 10. Sim results of proposed solution error = v^ – v vs time copyright 2011 controltrix corp www. controltrix.com
- 11. Thank You consulting@controltrix.com copyright 2011 controltrix corp www. controltrix.com