constvel

Constant velocity state update

Description

example

updatedstate = constvel(state) returns the updated state, state, of a constant-velocity Kalman filter motion model after a one-second time step.

example

updatedstate = constvel(state,dt) specifies the time step, dt.

updatedstate = constvel(state,w,dt) also specifies state noise, w.

Examples

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Update the state of two-dimensional constant-velocity motion for a time interval of one second.

state = [1;1;2;1];
state = constvel(state)
state = 4×1

2
1
3
1

Update the state of two-dimensional constant-velocity motion for a time interval of 1.5 seconds.

state = [1;1;2;1];
state = constvel(state,1.5)
state = 4×1

2.5000
1.0000
3.5000
1.0000

Input Arguments

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Kalman filter state vector for constant-velocity motion, specified as a real-valued 2N-element column vector where N is the number of spatial degrees of freedom of motion. The state is expected to be Cartesian state. For each spatial degree of motion, the state vector takes the form shown in this table.

Spatial DimensionsState Vector Structure
1-D[x;vx]
2-D[x;vx;y;vy]
3-D[x;vx;y;vy;z;vz]

For example, x represents the x-coordinate and vx represents the velocity in the x-direction. If the motion model is 1-D, values along the y and z axes are assumed to be zero. If the motion model is 2-D, values along the z axis are assumed to be zero. Position coordinates are in meters and velocity coordinates are in meters/sec.

Example: [5;.1;0;-.2;-3;.05]

Data Types: single | double

Time step interval of filter, specified as a positive scalar. Time units are in seconds.

Example: 0.5

Data Types: single | double

State noise, specified as a scalar or real-valued D-by-N matrix. D is the number of motion dimensions and N is the number of state vectors. For example, D = 2 for the 2-D motion. If specified as a scalar, the scalar value is expanded to a D-by-N matrix.

Data Types: single | double

Output Arguments

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Updated state vector, returned as a real-valued vector or real-valued matrix with same number of elements and dimensions as the input state vector.

Algorithms

For a two-dimensional constant-velocity process, the state transition matrix after a time step, T, is block diagonal as shown here.

$\left[\begin{array}{c}{x}_{k+1}\\ {v}_{x,k+1}\\ {y}_{k+1}\\ {v}_{y,k+1}\end{array}\right]=\left[\begin{array}{cccc}1& T& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& T\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{k}\\ v{x}_{k}\\ {y}_{k}\\ v{y}_{k}\end{array}\right]$

The block for each spatial dimension is:

$\left[\begin{array}{cc}1& T\\ 0& 1\end{array}\right]$

Extended Capabilities

Objects

Introduced in R2021a 