How to populating matrices in the Apache Commons Kalman filter Implementation

Question

Background : To give everyone some background I am trying to smoothen GPS data received from a device using Kalman filter (Apache Common implementation). What kind of dynamic noises should I include in my implementation with respect to matrix P0, Q and R knowing that the only input I have apart from position(X and Y) is horizontal accuracy and velocity for X and Y components. This is not a constant velocity example since the velocity might change from one ping to another ping.

Implementation Library : Apache Common
- http://commons.apache.org/proper/commons-math/userguide/filter.html

Usage : I am only considering 2D space for now

Inputs that I have with me : 1. latitude
2. longitude
3. horizontal accuracy or Horizontal Dilution of precision (HDOP) in meters/sec
4. Time between two pings (dt) = 30 seconds

Outputs I care about
1. new Latitude
2. new Longitude

Calculated values : Vx (velocity in X direction) Vy (velocity in Y direction) The object will be constantly moving but with varying velocities so I can calculate Vx and Vy using the formulate V * sin(theta) and V * Cosine(theta)

How should I map my values to the Apache Common implementation.?

Current setup :

X = Initial State = [  

     {X Y X-Vel Y-Vel}

    ]  

 // I only care about X and Y coordinates so this is a 2 * 4 matrix  
 H = Observation variables = [   

     {1, 0, 0, 0},  
     {0, 1, 0, 0} 



 ]  

 // This is a 4 * 4 matrix  
 P0 = Cov(X) = [     

     {(horizontal accuracy from i/p), 0, 0, 0},  
     {0, (horizontal accuracy from i/p), 0, 0},  
     {0, 0, (some initial value for VY), 0},  
     {0, 0, 0, (some initial value for VX) }

    ]  

 // Copied this from somewhere. What values should I have in this?   //
 This is a 4 * 4 matrix  
 Q = Cov(Dynamic noise) = [          

     { Math.pow(dt, 4d)/4d, 0d, Math.pow(dt, 3d)/2d, 0d },  
     { 0d, Math.pow(dt, 4d)/4d, 0d, Math.pow(dt, 3d)/2d },  
     { Math.pow(dt, 3d)/2d, 0d, Math.pow(dt, 2d), 0d },  
     { 0d, Math.pow(dt, 3d)/2d, 0d, Math.pow(dt, 2d) }

    ]  

 // This is a 2 * 2 matrix  
 R = Cov(measurement noise) = [  

     { Math.pow((horizontal accuracy from i/p), 2d) , 0},  
     { 0, Math.pow((horizontal accuracy from i/p), 2d)} 

 ]  

 // This is a 4 * 4 matrix  
 A = State transition matrix =   [

     { 1d, 0d, dt, 0d },  
     { 0d, 1d, 0d, dt },  
     { 0d, 0d, 1d, 0  },  
     { 0d, 0d, 0d, 1d }  

 ]

Are my matrices correct for what I am trying to do? When I run them I keep getting MatrixDimensionMismatchException and hence I decided to ask a question. Any help would be appreciated.

Please reformat your question. No need of fancy formating. Use code formating for code, and quote formating for quotes. — Ander Biguri, Mar 14 '16 at 19:41
I think it is unusual, but well formatted, no need to change the formatting — AlexWien, Mar 14 '16 at 20:15
GPS coordinates are already heavily kalman filtered. Smoothing will make them less accurate. Think whether you might need filtering of unwanted locations instead of smoothing. — AlexWien, Mar 14 '16 at 20:17
I removed the MATLAB tag as the Apache Commons Math library is a **Java** library. It has nothing to do with MATLAB. In addition, the code appears to be Java (i.e. `Math.pow`) so the retagging is justified. — rayryeng, Mar 14 '16 at 21:26
@AlexWien - The device might be a watch which might not have a kalman filter on board the chip. Also what if pings are received from WIFI and hence I think I would need filtering. — andybandy12, Mar 14 '16 at 22:23
@rayryeng - That makes sense. Thank you for removing the tag though my intention was to involve folks who have worked on Kalman filter using matlab since the matrices would be similar. — andybandy12, Mar 14 '16 at 22:24

score 0 · Accepted Answer · answered Mar 16 '16 at 14:51

I was able to solve this problem by using the latest version of Apache Commons Math library.

It turns out that Apache Commons Math 3.2 and earlier version had a major bug
reported here : https://issues.apache.org/jira/browse/MATH-1033

The problem was measNoise column dimension always had to be 1 which means matrix R should always have only 1 column

// row dimension of R must be equal to row dimension of H
if (measNoise.getRowDimension() != measurementMatrix.getRowDimension() ||
    measNoise.getColumnDimension() != 1) {  
    throw new MatrixDimensionMismatchException(measNoise.getRowDimension(), measNoise.getColumnDimension(), measurementMatrix.getRowDimension(), 1); 
}

How to populating matrices in the Apache Commons Kalman filter Implementation

1 Answers1