Applying a Kalman filter on a leg follower robot -

i asked create leg follower robot (i did it) , in second part of assignment have develop kalman filter in order improve following process of robot. robot gets person distance robot , angle (it relative angle, because reference robot itself, not absolute x-y coordinates)

about assignment have serious doubt. have read, every sample have seen kalman filter has been in 1 dimension (a car running distance or rock falling building) , according task have apply in 2 dimensions. possible apply kalman filter this?

if possible calculate kalman filter in 2 dimensions understand asked follow legs in linnearized way, despite person walks weirdly (with random movements) --> have doubt of how establish function of state matrix, please tell me how or tell me can find more information this?

thanks.

well should read on kalman filter. estimate state through mean , variance separately. state can whatever want. can have local coordinates in state global coordinates.

note latter result in nonlinear system dynamics, in case use extended kalman filter, or more correct continuous-discrete kalman filter, treat system dynamics in continuous manner , measurements in discrete time.

example global coordinates:

assuming have small cubic mass can drive forward velocity v. model dynamics in local coordinates only, state s s = [v], linear model.

but, incorporate global coordinates x , y, assuming moving on plane only. have s = [x, y, phi, v]'. need phi keep track of current orientation since cube can move forward in respect orientation of course. let's define phi angle between cube's forward direction , x-axis. or in other words: phi=0 cube move along x-axis, phi=90° move along y-axis.

the nonlinear system dynamics global coordinates can written as

s_dot = [x_dot, y_dot, phi_dot, v_dot]'  

with

x_dot = cos(phi) * v y_dot = sin(phi) * v phi_dot = ... v_dot = ... (newton's law) 

in ekf (extended kalman filter) prediction step use (discretized) equations above predict mean of state in first step of , linearized (and discretized) equations prediction of variance.

there 2 things keep in mind when decide state vector s should like:

• you might tempted use linear example s = [v] , integrate velocity outside of kalman filter in order obtain global coordinate estimates. work, lose awesomeness of kalman filter since integrate mean of state, not variance. in other words, have no idea current uncertainties global coordinates are.
• the second step of kalman filter, measurement or correction update, requires can describe sensor output function of states. may have add states representation can express measurements correctly as z[k] = h(s[k], w[k]) z measurements , w noise vector gaussian distribution.