Documentation

constturn

Constant turn-rate motion model

Description

example

updatedstate = constturn(state) returns the updated state, updatedstate, obtained from the previous state, state, after a one-second step time for motion modelled as constant turn rate. Constant turn rate means that motion in the x-y plane follows a constant angular velocity and motion in the vertical z directions follows a constant velocity model.

example

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

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

Examples

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Define an initial state for 2-D constant turn-rate motion. The turn rate is 12 degrees per second. Update the state to one second later.

state = [500,0,0,100,12].';
state = constturn(state)
state = 5×1

489.5662
-20.7912
99.2705
97.8148
12.0000

Define an initial state for 2-D constant turn-rate motion. The turn rate is 12 degrees per second. Update the state to 0.1 seconds later.

state = [500,0,0,100,12].';
state = constturn(state,0.1)
state = 5×1

499.8953
-2.0942
9.9993
99.9781
12.0000

Input Arguments

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State vector for a constant turn-rate motion model in two or three spatial dimensions, specified as a real-valued vector or matrix.

• When specified as a 5-element vector, the state vector describes 2-D motion in the x-y plane. You can specify the state vector as a row or column vector. The components of the state vector are [x;vx;y;vy;omega] where x represents the x-coordinate and vx represents the velocity in the x-direction. y represents the y-coordinate and vy represents the velocity in the y-direction. omega represents the turn rate.

When specified as a 5-by-N matrix, each column represents a different state vector N represents the number of states.

• When specified as a 7-element vector, the state vector describes 3-D motion. You can specify the state vector as a row or column vector. The components of the state vector are [x;vx;y;vy;omega;z;vz] where x represents the x-coordinate and vx represents the velocity in the x-direction. y represents the y-coordinate and vy represents the velocity in the y-direction. omega represents the turn rate. z represents the z-coordinate and vz represents the velocity in the z-direction.

When specified as a 7-by-N matrix, each column represents a different state vector. N represents the number of states.

Position coordinates are in meters. Velocity coordinates are in meters/second. Turn rate is in degrees/second.

Example: [5;0.1;4;-0.2;0.01]

Data Types: 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+1)-length -by-N matrix. D is the number of motion dimensions and N is the number of state vectors. The components are each columns are [ax;ay;alpha] for 2-D motion or [ax;ay;alpha;az] for 3-D motion. ax, ay, and az are the linear acceleration noise values in the x-, y-, and z-axes, respectively, and alpha is the angular acceleration noise value. If specified as a scalar, the value expands to a (D+1)-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.