1. Velocity Estimation from noisy Measurements
Sensor fusion using modified Kalman filter

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

3. Problem specifics
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 = Hz
Sample time Ts = 0.1 s
Simulated time = 200s - 400s

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

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

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

7. Comparison 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.

8. Comparison. Sl No metric Kalman Filter Modified Filter 4. 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
Note: The right column filter is a super set of a standard Kalman filter

9. Sim results std Kalman filter
velocity estimation error (v^ - v) vs time

10. Sim results of proposed solution
error = v^ – v vs time

11. Thank You