singermeas
Measurement function for Singer acceleration motion model
Syntax
Description
returns the measurements
= singermeas(states
)measurements
in rectangular coordinates for the Singer
motion model based on the current states
.
specifies the measurement output coordinate system, measurements
= singermeas(states
,frame
)frame
.
also specifies the sensor position, measurements
= singermeas(states
,frame
,sensorpos
,sensorvel
)sensorpos
, and the sensor velocity,
sensorvel
.
specifies the measurement parameters, measurements
= singermeas(states
,measurementParameters
)measurementParameters
.
[
returns the measurement bounds, used by a tracking filter (measurements
,bounds
] = singermeas(___)trackingEKF
, trackingUKF
, trackingCKF
,trackingIMM
, trackingMSCEKF
, or trackingGSF
) in residual
calculations.
Examples
Measurements for Singer Model
Define a state for a 2D Singer acceleration motion.
state = [1;10;3;2;20;5];
Obtain the measurement in a rectangular frame.
measurement = singermeas(state)
measurement = 3×1
1
2
0
Obtain the measurement in a spherical frame.
measurement = singermeas(state, 'spherical')
measurement = 4×1
63.4349
0
2.2361
22.3607
Obtain the measurement in a spherical frame relative to a stationary sensor located at [1;2;0].
measurement = singermeas(state, 'spherical', [1;2;0], [0;0;0])
measurement = 4×1
90
0
4
20
Obtain the measurement in a spherical frame relative to a stationary sensor located at [1;2;0] that is rotated by 90 degrees around the z axis relative to the global frame.
laxes = [0 1 0; 1 0 0; 0 0 1];
measurement = singermeas(state, 'spherical', [1;2;0], [0;0;0], laxes)
measurement = 4×1
0
0
4
20
Obtain measurements from multiple 2D states in a rectangular frame.
states = [1 2 3; 10 20 30; 2 4 5; 20 30 40; 5 6 11; 1 3 1.5]; measurements = singermeas(states)
measurements = 3×3
1 2 3
20 30 40
0 0 0
Display Residual Wrapping Bounds for singermeas
Specify a 2D state and specify a measurement structure such that the function outputs azimuth, range, and rangerate measurements.
state = [10 1 0 10 1 0]'; % [x vx ax y vy ay]' mp = struct("Frame","Spherical", ... "HasAzimuth",true, ... "HasElevation",false, ... "HasRange",true, ... "HasVelocity",false);
Output the measurement and wrapping bounds using the singermeas
function.
[measure,bounds] = singermeas(state,mp)
measure = 2×1
45.0000
14.1421
bounds = 2×2
180 180
Inf Inf
Input Arguments
states
— Current states
realvalued 3Nby1 vector  realvalued 3NbyM matrix
Current states, specified as a realvalued 3Nby1 vector or a realvalued 3NbyM matrix. N is the spatial degree of the state, and M is the number of states.
The state vector in each column takes different forms based on its spatial dimensions.
Spatial Degrees  State Vector Structure 

1D  [x;vx;ax] 
2D  [x;vx;ax;y;vy;ay] 
3D  [x;vx;ax;y;vy;ay;z;vz;az] 
For example, x
represents the
xcoordinate, vx
represents the velocity in the
xdirection, and ax
represents the
acceleration in the xdirection. If the motion model is in
onedimensional space, the y and zaxes are
assumed to be zero. If the motion model is in twodimensional space, values along the
zaxis are assumed to be zero. Position coordinates are in
meters. Velocity coordinates are in meters/second. Acceleration coordinates are in
m/s^{2}.
Example: [5;0.1;0.01;0;0.2;0.01;3;0.05;0]
frame
— Measurement output frame
'rectangular'
(default)  'spherical'
Measurement output frame, specified as 'rectangular'
or
'spherical'
. When the frame is 'rectangular'
,
a measurement consists of x, y, and
z Cartesian coordinates. When specified as
'spherical'
, a measurement consists of azimuth, elevation,
range, and range rate.
Data Types: char
sensorpos
— Sensor position
[0;0;0]
(default)  realvalued 3by1 column vector
Sensor position with respect to the navigation frame, specified as a realvalued 3by1 column vector. Units are in meters.
Data Types: double
sensorvel
— Sensor velocity
[0;0;0]
(default)  realvalued 3by1 column vector
Sensor velocity with respect to the navigation frame, specified as a realvalued 3by1 column vector. Units are in m/s.
Data Types: double
laxes
— Local sensor coordinate axes
[1,0,0;0,1,0;0,0,1]
(default)  3by3 orthogonal matrix
Local sensor coordinate axes, specified as a 3by3 orthogonal matrix. Each column specifies the direction of the local x, y, and zaxes, respectively, with respect to the navigation frame. That is, the matrix is the rotation matrix from the global frame to the sensor frame.
Data Types: double
measurementParameters
— Measurement parameters
structure  array of structure
Measurement parameters, specified as a structure or an array of structures. For more details, see Measurement Parameters.
Data Types: struct
Output Arguments
measurements
— Measurements
Nby1 column vector of scalar  NbyM matrix of scalar
Measurement vector, returned as an Nby1 column vector of scalars or an NbyM matrix of scalars. The form of the measurement depends upon which syntax you use.
When the syntax does not use the
measurementParameters
argument, the measurement vector is[x,y,z]
when theframe
input argument is set to'rectangular'
and[az;el;r;rr]
when theframe
is set to'spherical'
.When the syntax uses the
measurementParameters
argument, the size of the measurement vector depends on the values of theFrame
,HasVelocity
, andHasElevation
fields in themeasurementParameters
structure.Frame Measurement 'spherical'
Specifies the azimuth angle,
az
, elevation angle,el
, range,r
, and range rate,rr
of the measurements.Spherical Measurements
HasElevation false true HasVelocity false [az;r]
[az;el;r]
true [az;r;rr]
[az;el;r;rr]
Angle units are in degrees, range units are in meters, and range rate units are in m/s.
'rectangular'
Specifies the Cartesian position and velocity coordinates of the measurements.
Rectangular Measurements
HasVelocity false [x;y;z]
true [x;y;z;vx;vy;vz]
Position units are in meters and velocity units are in m/s.
Data Types: double
bounds
— Measurement residual wrapping bounds
Mby2 realvalued matrix
Measurement residual wrapping bounds, returned as an Mby2 realvalued matrix, where M is the dimension of the measurement. Each row of the matrix corresponds to the lower and upper bounds for the specific dimension in the measurement
output.
The function returns different bound values based on the frame
input.
If the
frame
input is specified as'Rectangular'
, each row of the matrix is[Inf Inf]
, indicating the filter does not wrap the measurement residual in the filter.
If the
frame
input is specified as'Spherical'
, the returnedbounds
contains the bounds for specific measurement dimension based on the following:When
HasAzimuth
=true
, the matrix includes a row of[180 180]
, indicating the filter wraps the azimuth residual in the range of[180 180]
in degrees.When
HasElevation
=true
, the matrix includes a row of[90 90]
, indicating the filter wraps the elevation residual in the range of[90 90]
in degrees.When
HasRange
=true
, the matrix includes a row of[Inf Inf]
, indicating the filter does not wrap the range residual.When
HasVelocity
=true
, the matrix includes a row of[Inf Inf]
, indicating the filter does not wrap the range rate residual.
If you specify any of the options as false
, the returned
bounds
does not contain the corresponding row. For example, if
HasAzimuth
= true
, HasElevation
=
false
, HasRange
= true
,
HasVelocity
= true
, then bounds
is returned as
180 180 Inf Inf Inf Inf
The filter wraps the measuring residuals based on this equation:
$${x}_{wrap}=mod(x\frac{ab}{2},ba)+\frac{ab}{2}$$
where x is the residual to wrap, a is the lower bound, b is the upper bound, mod is the modules after division function, and x_{wrap} is the wrapped residual.
Data Types: single
 double
More About
Azimuth and Elevation Angle Definitions
Define the azimuth and elevation angles used in the toolbox.
The azimuth angle of a vector is the angle between the xaxis and its orthogonal projection onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xyplane. The angle is positive when going toward the positive zaxis from the xy plane.
Measurement Parameters
The MeasurementParameters
property consists of an array of
structures that describe a sequence of coordinate transformations from a child frame to a
parent frame or the inverse transformations (see Frame Rotation). If
MeasurementParameters
only contains one structure, then it represents
the rotation from one frame to the other. If MeasurementParameters
contains an array of structures, then it represents rotations between multiple frames.
The fields of MeasurementParameters
are shown here. Not all fields
have to be present in the structure.
Field  Description 
Frame  Enumerated type indicating the frame used to report measurements. When detections are
reported using a rectangular coordinate system, set 
OriginPosition  Position offset of the origin of the child frame relative to the parent frame, represented as a 3by1 vector. 
OriginVelocity  Velocity offset of the origin of the child frame relative to the parent frame, represented as a 3by1 vector. 
Orientation  Frame orientation, specified as a 3by3 realvalued orthonormal frame rotation matrix.
The direction of the rotation depends on the

IsParentToChild  A logical scalar indicating whether 
HasElevation  A logical scalar indicating if the measurement includes elevation. For measurements
reported in a rectangular frame, if 
HasAzimuth  A logical scalar indicating if the measurement includes azimuth. 
HasRange  A logical scalar indicating if the measurement includes range. 
HasVelocity  A logical scalar indicating if the reported detections include velocity measurements.
For measurements reported in a rectangular frame, if

References
[1] Singer, Robert A. "Estimating optimal tracking filter performance for manned maneuvering targets." IEEE Transactions on Aerospace and Electronic Systems 4 (1970): 473483.
[2] Blackman, Samuel S., and Robert Popoli. "Design and analysis of modern tracking systems." (1999).
[3] Li, X. Rong, and Vesselin P. Jilkov. "Survey of maneuvering target tracking: dynamic models." Signal and Data Processing of Small Targets 2000, vol. 4048, pp. 212235. International Society for Optics and Photonics, 2000.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
See Also
initsingerekf
 singer
 singerjac
 singermeasjac
 singerProcessNoise
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