Velocity Estimation from noisy Measurements - Sensor fusion using modified Kalman filter

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Velocity Estimation from noisy Measurements

Sensor fusion using modified Kalman filter

www.controltrix.com


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

Objective


• Acceleration and velocity are measured using noisy sensor

• Direct velocity measurement is noisy (sv = 10m/s)

• Acceleration is measured with sa = 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

Problem specifics


Measured velocity noisy data (True velocity is smooth sine wave of amp 10, period 20 s)


• 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

Advantages


• Can be modified easily to make tradeoff between driftperformance (convergence) and noise reduction• Systematic technique for parameter calculations• No trial and error

Advantages.


Sl No metric Kalman Filter Modified Filter

1. Drift •Drift is a major problem (depends inversely on K)•Needs considerable characterization.(Offset, temperature calibration etc).

•Guaranteed automatic convergence. •No prior measurement of offset and characterization required.•Not sensitive to temperature induced variable drift etc.

2. Convergence •Non-Zero measurement and process noise covariance required else leads to singularity

•Always converges•No assumptions on variances required •Never leads to a singular solution

3. Method •Two distinct phases: Predict and update.

•Can be implemented in a few single difference equation or even in continuum.

Comparison


Comparison.

Note: The right column filter is a super set of a standard Kalman filter

Sl No metric Kalman Filter Modified Filter4. Computation •Need separate state

variables for position, velocity, etc which adds more computation.

•Highly optimized computation.•Only single state variable required

5. Gain value /performance

•In one dimension, •K = process noise / measurement noise. dt • ‘termed as optimal’

•Gains based on systematic design choices. •The gains are good though suboptimal (based on tradeoff)

6. Processor req. •Needs 32 Bit floating point computation for accuracy and plenty of MIPS/ computation

•Easily implementable in 16 bit fixed point processor 40 MIPS/computation is sufficient


velocity estimation error (v^ - v) vs time

Sim results std Kalman filter


error = v^ – v vs time

Sim results of proposed solution


Thank [email protected]

Technology

Velocity Estimation from noisy Measurements - Sensor fusion using modified Kalman filter