Magnetic object tracking based on direct observation of magnetic sensor measurements

A magnetic object tracking algorithm, that may be implemented as an apparatus or a method, that permits kinematic tracking of magnetized objects, or targets, using magnetic field strength measurements derived from one or more vector magnetometers. The magnetic object tracking algorithm effectively tracks a maneuvering magnetic dipole target using an extended Kalman filter directly observing (processing) real magnetic field strength data.

BACKGROUND
 The present invention relates generally to the tracking of magnetic source
 objects, and more particularly, to a data processing algorithm that
 permits kinematic tracking in real time of one or more magnetized objects,
 using a series of magnetic field strength measurements, vector components
 or total field, collected from one or more magnetometers.
 Numerous opportunities exist for sensor systems that can track objects
 which generate magnetic fields. All types of land vehicles, ships, and
 aircraft have structural and power systems capable of generating
 substantial magnetic signatures. Even small inert objects such as firearms
 and hard tools may exhibit sufficient magnetization to be observed from a
 distance. Over the past several years, the assignee of the present
 invention has developed various types of magnetic sensor data processing
 algorithms and systems capable of localizing, quantifying, and classifying
 such objects based on their magnetostatic fields. The present invention
 extends this capability to real time tracking in a way that greatly
 simplifies solution of the nonlinear field equations.
 A magnetostatic field may be generated by any combination of three physical
 phenomena: permanent or remanent magnetization, magnetostatic induction,
 and electromagnetic induction. The first occurs in objects that contain
 metals of the ferromagnetic group, which includes iron, nickel, cobalt,
 and their alloys. These may be permanently magnetized either through
 manufacture or use. Second, the Earth's magnetostatic field may induce a
 secondary field in ferromagnetic structures and also paramagnetic
 structures if the mass and shape sufficiently enhance the susceptibility.
 Third, the object may comprise a large direct current loop that induces
 its own magnetic field. This is often the case with land vehicles that use
 the vehicle chassis as a ground return.
 Tracking objects by sensing and data processing their magnetostatic fields
 offers several advantages over other methods. One is that the process is
 passive rather than active. This eliminates potential health and safety
 hazards that could be associated with some types of active sensor systems,
 such as those which use various types of electromagnetic radiation. A
 passive system also permits covert observation, useful to military and
 intelligence operations as well as law enforcement. Another advantage is
 that the field is mostly unaffected by natural boundaries, such as space
 above and the sea or land surface below. It is also unaffected by many
 adverse environmental conditions such as wind, fog, thunderstorms, and
 temperature extremes. Yet another advantage is that the magnetostatic
 field of the tracked object is difficult to conceal or countermeasure, and
 is therefore useful against hostile subjects.
 RELATED ART
 As a result of continuing research and development, the assignee of the
 present invention has previously filed developed inventions relating to
 magnetic sensor systems and data processing of magnetic field
 measurements. To date these have been primarily concerned with detecting,
 locating, and classifying magnetic objects based on a large set of
 measurements distributed over space and/or time. The first method to be
 introduced was the dipole detection and localization (DMDL) algorithm
 disclosed in U.S. Pat. No. 5,239,474, issued Aug. 24, 1993. This algorithm
 assumes that the field of a magnetic source object is well represented as
 the field of a magnetic dipole moment at distances far removed from the
 source. The location of the dipole is determined by maximizing an
 objective function over a grid of search points that spans the search
 volume. Two limitations of this method are the assumption of a linear
 array of sensors and the need to search over all possible dipole
 orientations if the orientation is unknown.
 This original invention was augmented by two subsequent inventions. The
 first invention, disclosed in U.S. Pat. No. 5,337,259, issued Aug. 9,
 1994, provided for three improvements to DMDL processing. The first
 improves spatial resolution yielding a more definitive localization; the
 second uses higher order mutipole terms in the Anderson function expansion
 to increase the signal to noise ratio (SNR); and the third introduces a
 multiple-pass, multiple-target localization method. The next invention,
 disclosed in U.S. Pat. No. 5,388,803, issued Feb. 17, 1995, extended the
 DMDL process to use in synthetic aperture arrays. This method permits a
 set of magnetic field measurements to be collected from a single moving
 sensor over a period of time in lieu of a large number of fixed sensors in
 a single instant.
 Subsequent to these inventions, a substantially changed and improved DMDL
 processing algorithm (IDMDL) was developed by the assignee of the present
 invention which is disclosed in a U.S. patent application Ser. No.
 08/611,291. The Anderson function expansion in spherical coordinates was
 replaced by a conventional electromagnetic field moment expansion in
 Cartesian coordinates. This change eliminates the requirement for a linear
 array of sensors and permits an arbitrary array geometry to be used. Also,
 range normalization and the search over unknown dipole orientations was
 eliminated by forming a unique estimate of the dipole moment within the
 objective function. An extension of the method estimates multiple dipole
 moment sources simultaneously.
 The fundamental algorithm change in IDMDL substantially generalized the
 process and led rapidly to new processing extensions on several fronts.
 The first was spatial-temporal processing, disclosed in U.S. Pat. No.
 5,684,396 issued Nov. 4, 1997. This extension permits the dipole source to
 be in motion and solves for the source object location as well as its
 velocity vector. When applied independently to short time intervals of
 measurements, it provides an approximate track of the object. The second
 extension was multipole dipole characterization, disclosed in U.S. Pat.
 No. 5,783,944 issued Jul. 21, 1998. This second extension replaces the
 dipole approximation with a set of spatially separated and independently
 oriented dipoles when the object is close or large. The dipole set
 provides a means of characterizing or classifying an object in the near
 field. A third extension permits both the remanent and induced components
 of the dipole source to be independently estimated as the source object
 rotates in the earth's magnetic field, and is disclosed in U.S. Patent
 application Ser. No. 08/789,032, filed Jan. 27, 1997.
 Accordingly, it is an objective of the present invention to provide for a
 data processing algorithm that permits kinematic tracking in real time of
 one or more magnetized objects, using a series of magnetic field strength
 measurements, vector components or total field, collected from one or more
 magnetometers.
 SUMMARY OF THE INVENTION
 To accomplish the above and other objectives, the present invention
 provides for an algorithm, which may be implemented as an apparatus or a
 method, that permits kinematic tracking of magnetized targets (objects)
 using magnetic field strength measurements from one or more vector or
 total field magnetometers (magnetic field strength sensors). While
 kinematic tracking of targets using a variety of observables including
 range, bearing, Doppler shift, for example, has been well established for
 many years, the kinematic tracking of magnetized targets using magnetic
 field strength measurements from one or more vector or total field
 magnetometers provided by the present invention is unique. The present
 magnetic object tracking algorithm has been shown to effectively track a
 maneuvering magnetic dipole target using an extended Kalman filter
 directly observing real magnetic field strength data.
 The present invention comprises a substantial change to algorithms of the
 prior art discussed above in that it is intended for use in tracking
 rather than in initially detecting or classifying the object. The present
 method begins with a source detection and approximate location provided by
 one of the prior methods and tracks the source continuously in real time
 as long as it is within range of the sensors. It is based on the
 conventional electromagnetic field moment equation but applies it to a
 Kalman filter observation equation instead of an objective function. It
 uses new measurement data sequentially over small sample intervals to
 track the source object and continuously improve the estimates of its
 location, velocity, and dipole moments.
 As mentioned in the Background section, tracking of magnetic dipole targets
 detected by the dipole detection and localization algorithm disclosed in
 U.S. Pat. No. 5,239,474 has primarily involved maximizing the correlation
 between a magnetic field response associated with a hypothesized straight
 line swath and a set of 3MN observed magnetic samples, where M is the
 number of vector sensors and N is the number of time samples. The present
 algorithm may be applied directly to the 3M spatially observed magnetic
 data samples at every time sample to improve the kinematic tracking of the
 magnetic dipole over the previous swath approach.
 More specifically, the present magnetic object tracking algorithm comprises
 the following steps. An array of magnetic field strength measurements
 derived from observing a magnetized target using a vector magnetometer is
 provided. State variables associated with the target that are to be
 tracked are selected. A Kalman filter is defined in terms of a plant
 equation that describes the evolution of the state of the target. A state
 vector of the target is defined by the state variables and an observation
 equation that describes a relationship between the observed magnetic field
 strength measurements and the state vector that is being tracked. The
 array of magnetometer measurements is processed using the Kalman filter
 based on the plant equation (describing the evolution of the state) and
 the observation equation to track the magnetic object.
 The dipole detection and localization algorithm of U.S. Pat. No. 5,239,474
 is not used in the present magnetic object tracking algorithm. The
 magnetic object tracking algorithm offers several advantages over current
 swath correlation techniques described in U.S. Pat. No. 5,684,396, for
 example. First, CPU processing time required for performing the Kalman
 filter prediction and update equations is significantly less than that
 required for swath processing. The swath technique requires a
 6-dimensional search (the swath starting and ending positions) to
 determine a dipole track. Second, the magnetic object detection and
 tracking algorithm provides an estimate of the dipole state or location at
 every time sample (reduced latency), whereas swath processing requires
 several (N) temporal samples before a track can be established. Third,
 swath processing is optimal only if the target truly follows a straight
 line, constant speed track over the entire N sample observation period and
 maintains a constant magnetic dipole during this sampling interval. Any
 deviation from this straight line path or the constant dipole assumption
 and the magnetic object detection and tracking algorithm described herein
 yields better tracking accuracy and results. Fourth, the present invention
 has modeling flexibility, wherein, if the relationship between a target's
 direction of travel (or vehicle axis) and its magnetic multipole response
 is known, such information can be incorporated into the Kalman filter
 plant equation to provide for improved kinematic tracking performance by
 the present magnetic object detection and tracking algorithm.

DETAILED DESCRIPTION
 Referring to the drawing figures, FIG. 1 is a flow diagram illustrating a
 magnetic object tracking algorithm 10 in accordance with the principles of
 the present invention. The magnetic object tracking algorithm 10, which
 may be implemented as an apparatus or a method, provides for kinematic
 tracking of a magnetized target (object) using observed magnetic field
 strength measurements.
 The magnetic object tracking apparatus 10 comprises one or more vector
 magnetometers 11 for providing an array of observed magnetic field
 strength measurements derived from detecting the object's magnetic field,
 a Kalman filter 13 defined by a plant equation that describes the
 evolution of a state vector of the object defined by state variables 12
 associated with the object that is to be tracked and an observation
 equation that describes a relationship between the observed magnetic field
 strength measurements and the state vector that is tracked. A processor 14
 is used to process the array of magnetometer measurements using the Kalman
 filter 13 to track the object.
 The algorithm 10 may also be implemented by the following method steps. An
 array of observed magnetic field strength measurements derived from
 detecting a magnetized target using one or more vector magnetometers 11 is
 provided. State variables 12 associated with the target that is to be
 tracked are selected. A Kalman filter 13 is defined in terms of a plant
 equation that describes the evolution of a state vector of the target
 defined by the state variables and an observation equation that describes
 a relationship between the observed magnetic field strength measurements
 and the state vector that is tracked. The array of magnetometer
 measurements is processed 14 using the Kalman filter based on the plant
 equation and the observation equation to track the object.
 The magnetic object tracking algorithm 10 provides for a general method
 that may be applied to any array of vector or total field (scalar)
 magnetometer measurements to improve tracking performance. The
 implementation of the Kalman filter used in the present magnetic object
 tracking algorithm 10 requires selection of the state variables to be
 tracked, a suitable plant equation to describe the evolution of the state,
 and an observation equation to describe the relationship between the
 observed magnetic field data and the state being tracked.
 Although the implementation of the Kalman filter equations may be done in
 any coordinate system, the present invention is described in terms of a
 generalized rectangular coordinate system. The state is assumed to include
 target position, velocity, and magnetic dipole moment. The choice of state
 variables to be tracked is not limited to the parameters chosen for use in
 the disclosed embodiment. Target acceleration and/or time derivatives of
 the magnetic dipole may be incorporated into the state vector as well. The
 plant equation is based on a constant velocity model for the kinematics
 and a static model for the dipole characteristics of the target. The
 static model for the dipole moment implies no underlying physical model is
 being used to alter the state of the target's magnetic dipole moment. The
 equations of motion describing the evolution of the target state are given
 by:
EQU r.sub.du (k+1)=r.sub.du (k)+T.sub.s r.sub.du (k)u=i,j,k
EQU r.sub.du (k+1)=r.sub.du (k),u=i,j,k
EQU m.sub.u (k+1)=m.sub.u (k),u=i,j,k.
 In these equations, i,j,k represent orthogonal directions in a rectangular
 coordinate system, and the d subscript indicates these coordinates
 describe the position of the dipole. The equations describing the dynamics
 can be written more succinctly by defining a state vector and state
 transition matrix, respectively:
 x(k)=[r.sub.di (k) r.sub.di (k) r.sub.dj (k) r.sub.dj (k) r.sub.dk (k)
 r.sub.dk (k) m.sub.i (k) m.sub.j (k) m.sub.k (k)].sup.T
 ##EQU1##
 where a is a 2.times.2 submatrix given by
 ##EQU2##
 and I, is a 3.times.3 identity matrix. T.sub.s is the sampling period or
 time between observations. The plant equation is then given by
EQU x(k+1)=Ax(k)+v(k).
 The plant or acceleration noise term, v(k), is required to account for
 unknown target accelerations and/or changes in the dipole moment. The
 acceleration noise is defined in terms of its covariance matrix
 Q(k)=E{v(k)v.sup.T (k)} and is used in prediction equations defining the
 Kalman filter.
 The observed data are the outputs from M magnetometer sensors. Although the
 present invention may be applied to a 1, 2, or 3 dimensional magnetometer,
 the description of the magnetic object tracking algorithm 10 is given in
 terms of the 3 dimensional vector magnetometer. Let b represent the
 magnetic field responses from the M sensors:
EQU b=[b.sub.1i b.sub.1j b.sub.1k b.sub.2i b.sub.2i b.sub.2j b.sub.2k . . .
 b.sub.Mi b.sub.Mj b.sub.Mk ].sup.T
 As before, the subscripts i,j,k represent orthogonal directions in a
 rectangular coordinate system of the magnetic field at the sensor. The
 magnetic response b is related to the state vector x through a nonlinear
 transformation F:
EQU b=F(r.sub.d,r.sub.s)m
 The vectors r.sub.d and m represent the position and magnetic dipole
 components of the state vector x, respectively; r.sub.s is a vector of the
 M sensor positions. F is a 3M.times.3 position matrix that maps the dipole
 position and orientation to the magnetic response at each of the M
 sensors:
EQU F=[f.sub.1 f.sub.2 . . . f.sub.M ].sup.T
 where f.sub.1 represents the 3.times.3 position matrix associated with the
 l.sup.th sensor. The time index k has been left off the components of the
 sensor position vector r.sub.s to simplify notation.
 ##EQU3##
 The observed magnetic response, in the presence of noise, is given by:
EQU z(k)=b(k)+w(k),
 and substituting the expression for b(k) defined above,
EQU z(k)=F(r.sub.d (k),r.sub.s)m(k)+w(k).
 The sensor noise is modeled as a zero mean Gaussian process w(k) with
 covariance matrix R(k)=E{w(k)w.sup.T (k)}. Since the observation equation
 is nonlinear (with respect to the dipole position components of the state
 vector), a first order extended Kalman filter is used to linearly
 approximate the observation equation. This requires a gradient of F(r)m
 with respect to each of the state components to be computed, and is used
 in the state covariance and Kalman gain equations in place of the
 observation matrix itself.
 The set of prediction and update equations are given below. The prediction
 equations are as follows.
EQU x(k+1.vertline.k)=A(k)x(k.vertline.k) (predicted state)
EQU P(k+1.vertline.k)=A(k)P(k.vertline.k)A.sup.T (k)+Q(k) (predicted state
 error covariance matrix)
 where
EQU P(k.vertline.k)=E{[x(k)-x(k.vertline.k)][x(k)-x(k.vertline.k)].sup.T }
 The update equations are as follows.
EQU x(k-1.vertline.k+1)=x(k+1.vertline.k)+W(k+1){z(k+1)-F(r.sub.d
 (k+1),r.sub.s)m(k+1)}
EQU P.sup.-1 (k+1.vertline.k+1)=P.sup.-1 (k+1.vertline.k)+.gradient..sub.r
 [F(r)m].sub.r(k+1.vertline.k).sup.T R.sup.-1 (k+1).gradient..sub.r
 [F(r)m].sub.r(k+1.vertline.k)
EQU W(k+1)=P(k+1.vertline.k+1).gradient..sub.r
 [F(r)m].sub.r(k+1.vertline.k).sup.T R.sup.-1 (k+1)
 The term .gradient..sub.r [F(r)m].sub.x(k+1.vertline.k) represents the
 gradient of F(r)m with respect to each of the state components evaluated
 at the predicted state x(k+1.vertline.k). Since F(r)m is 3M.times.1, the
 gradient .gradient..sub.r [F(r)m].sub.r(k+1.vertline.k) is 3M.times.9 (one
 column for each partial derivative with respect to each of the 9 state
 vector components).
 There are any number of ways to initialize the tracking process, which
 usually follows a detection process that declares new targets (magnetic
 dipole sources) as they enter the sensor array domain. Such detectors
 normally provide an initial estimate of dipole source location and moment
 vector. The source velocity may be initialized to zero or, alternatively,
 sequential detector estimates of position may be used to estimate the
 velocity.
 The present invention is described in more detail below and performance
 results are presented for a specific application: the tracking of a motor
 vehicle using vector (3 axis) magnetic field data. The present invention
 was implemented in the MATLAB programming language and tested on a desktop
 Apple PowerMac.TM. 8100 computer.
 The state includes the target position, velocity, and dipole moment in
 geodetic coordinates (i.e., in North, East, and Down directions). As
 presented in the general case, the equation describing the dynamics of the
 target state is given by:
EQU x(k+1)=Ax(k)+v(k)
 where
EQU x(k)=[r.sub.dN (k) r.sub.dN (k) r.sub.dE (k) r.sub.dE (k) r.sub.dD (k)
 r.sub.dD (k) m.sub.N (k) m.sub.E (k) m.sub.D (k)].sup.T
 and
 ##EQU4##
 In this case, the sampling period T.sub.s is 0.215 seconds. The
 acceleration noise terms in Q(k)=E{v(k)v.sup.T (k)} need to be tuned for
 this application. In this case, the magnetized target being tracked is a
 car traveling at relatively low speeds. Thus, the noise terms are simply
 made large enough to account for expected maneuvers performed during the
 test: e.g., the vehicle decelerating from a speed of 20 mph to a complete
 stop, accelerating to about 20 mph, and making left or right turns at low
 speeds. These target dynamics are assumed to occur primarily in a
 North-East plane and not in a Down direction and are modeled as such in
 the Q matrix. Simultaneously, an acceleration term needs to be defined for
 the magnetic dipole moment. A turn can profoundly change the target's
 magnetic dipole when viewed in a fixed coordinate system.
 It is known that the magnetic dipole moment of a vehicle is generally the
 vector sum of two sources: the permanent or remanent magnetization forms a
 dipole moment vector that is constant in magnitude and fixed in
 orientation with respect to the vehicle structure, usually aligned more or
 less with the longitudinal axis of the vehicle; the induced magnetization
 forms a dipole moment vector that is more or less parallel to the
 background field vector (Earth's magnetic field) and increases or
 decreases in magnitude as the vehicle longitudinal axis rotates to become
 more parallel or more perpendicular to the background field vector,
 respectively. Thus, an alternative model for the dipole moment may be
 incorporated in the plant equations based on this behavior.
 However, the present invention can be used in the absence of such a model.
 Given that a vehicle's magnetic dipole moment is nominally 1e6
 nT-ft.sup.3, changes in dipole strength on the order of 1e6 nT-ft.sup.3
 over several seconds need to be accounted for in the Q matrix since the
 transition matrix assumes a constant dipole moment over time. Based on
 these assumptions then, the following Q matrix was used on the data set in
 this case:
 ##EQU5##
 where q is a 2.times.2 submatrix associated with target accelerations along
 each dimension, and q.sub.M is a 3.times.3 submatrix which models the
 potential variation in magnetic dipole moment strength along each
 dimension. The terms in the q.sub.M matrix represent variances in the
 dipole moment and thus have units of (nT-ft.sup.3).sup.2
 ##EQU6##
 The observed magnetic response in this example is an 18.times.1 vector
 z(k):
EQU z(k)=F(r.sub.d (k),r.sub.s)m(k)+w(k).
 Since the noise samples from the 6 sensors are assumed to be uncorrelated
 and identically distributed, the covariance matrix R(k)=E{w(k)w.sup.T (k)}
 is given by an identity matrix scaled by the noise power at the sensor (k
 is dropped since stationarity is assumed in the noise process w(k)):
EQU R=.sigma..sub.n.sup.2 I.
 The sensor noise variance was set at 2nT.sup.2 in the covariance matrix R
 used for and Kalman gain updates. Having defined R(k),Q(k),T.sub.s, the
 Kalman filter prediction and update equations are applied in this case.
 The Kalman filter tracking capability was tested, and a summary of case
 runs is given in the following table, which is a summary of scenarios
 extracted from the test.

Event No. Vehicle Sample No. Course
 10 Celica 3000-3250 East to south
 11 Mazda 3250-3450 North to east
 12 Celica 3450-3700 North to east
 13 Celica 9120-9250 CCW outer loop
 14 Celica 9550-9750 CCW outer loop
 The Kalman tracking results of the target kinematics are presented in FIGS.
 2-6, along with position estimates associated with the prior art DMDL
 "snapshot" approach or algorithm for comparison to the Kalman tracker.
 In general, the Kalman tracker performs at least as well as the
 corresponding DMDL snapshot algorithm. In most cases, smoother kinematic
 estimates associated with the Kalman tracker are readily apparent,
 particularly in FIGS. 3, 5, and 6. All vehicle trajectories were tracked
 with the same set of acceleration noise terms, observation noise terms,
 state transition matrix, and threshold values, suggesting a degree of
 robustness with the Kalman filter employed in the present algorithm 10.
 In each of these cases, use of the magnetic object tracking algorithm 10
 with an array of magnetometers will improve the tracking of magnetized
 targets over other approaches. The magnetic object tracking algorithm 10
 requires less processing time, improves accuracy, and reduces latency over
 current swath tracking approaches, resulting in quicker response times in
 delivering time critical information to appropriate operators.
 Thus, an algorithm, that may be implemented as an apparatus or a method,
 and that permits kinematic tracking of magnetized targets using magnetic
 field strength measurements from one or more vector magnetometers has been
 disclosed. It is to be understood that the described embodiments are
 merely illustrative of some of the many specific embodiments that
 represent applications of the principles of the present invention.
 Clearly, numerous and other arrangements can be readily devised by those
 skilled in the art without departing from the scope of the invention.