title: Kalman filter

text: Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is a concept much applied in time series analysis used for topics such as signal processing and econometrics. Kalman filtering is also one of the main topics of robotic motion planning and control and can be used for trajectory optimization. Kalman filtering also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, the use of Kalman filters provides a realistic model for making estimates of the current state of a motor system and issuing updated commands.


title: Kalman filter

text: The algorithm works by a two-phase process. For the prediction phase, the Kalman filter produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with greater certainty. The algorithm is recursive. It can operate in real time, using only the present input measurements and the state calculated previously and its uncertainty matrix; no additional past information is required.


title: Kalman filter

text: Optimality of Kalman filtering assumes that errors have a normal (Gaussian) distribution. In the words of Rudolf E. Kálmán: "In summary, the following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Though regardless of Gaussianity, if the process and measurement covariances are known, the Kalman filter is the best possible "linear" estimator in the minimum mean-square-error sense.


title: Kalman filter

text: Extensions and generalizations of the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The basis is a hidden Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Kalman filtering has been used successfully in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filtering.


title: Kalman filter

text: The filtering method is named for Hungarian émigré Rudolf E. Kálmán, although Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. Richard S. Bucy of the Johns Hopkins Applied Physics Laboratory contributed to the theory, causing it to be known sometimes as Kalman–Bucy filtering.


title: Kalman filter

text: Stanley F. Schmidt is generally credited with developing the first implementation of a Kalman filter. He realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements. It was during a visit by Kálmán to the NASA Ames Research Center that Schmidt saw the applicability of Kálmán's ideas to the nonlinear problem of trajectory estimation for the Apollo program resulting in its incorporation in the Apollo navigation computer.


title: Kalman filter

text: This Kalman filtering was first described and developed partially in technical papers by Swerling (1958), Kalman (1960) and Kalman and Bucy (1961).


title: Kalman filter

text: Kalman filters have been vital in the implementation of the navigation systems of U.S. Navy nuclear ballistic missile submarines, and in the guidance and navigation systems of cruise missiles such as the U.S. Navy's Tomahawk missile and the U.S. Air Force's Air Launched Cruise Missile. They are also used in the guidance and navigation systems of reusable launch vehicles and the attitude control and navigation systems of spacecraft which dock at the International Space Station.


title: Kalman filter

text: Kalman filtering uses a system's dynamic model (e.g., physical laws of motion), known control inputs to that system, and multiple sequential measurements (such as from sensors) to form an estimate of the system's varying quantities (its state) that is better than the estimate obtained by using only one measurement alone. As such, it is a common sensor fusion and data fusion algorithm.


title: Kalman filter

text: Noisy sensor data, approximations in the equations that describe the system evolution, and external factors that are not accounted for, all limit how well it is possible to determine the system's state. The Kalman filter deals effectively with the uncertainty due to noisy sensor data and, to some extent, with random external factors. The Kalman filter produces an estimate of the state of the system as an average of the system's predicted state and of the new measurement using a weighted average. The purpose of the weights is that values with better (i.e., smaller) estimated uncertainty are "trusted" more. The weights are calculated from the covariance, a measure of the estimated uncertainty of the prediction of the system's state. The result of the weighted average is a new state estimate that lies between the predicted and measured state, and has a better estimated uncertainty than either alone. This process is repeated at every time step, with the new estimate and its covariance informing the prediction used in the following iteration. This means that Kalman filter works recursively and requires only the last "best guess", rather than the entire history, of a system's state to calculate a new state.


title: Kalman filter

text: The measurements' certainty-grading and current-state estimate are important considerations. It is common to discuss the filter's response in terms of the Kalman filter's "gain". The Kalman-gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance. With a high gain, the filter places more weight on the most recent measurements, and thus conforms to them more responsively. With a low gain, the filter conforms to the model predictions more closely. At the extremes, a high gain close to one will result in a more jumpy estimated trajectory, while a low gain close to zero will smooth out noise but decrease the responsiveness.


title: Kalman filter

text: When performing the actual calculations for the filter (as discussed below), the state estimate and covariances are coded into matrices because of the multiple dimensions involved in a single set of calculations. This allows for a representation of linear relationships between different state variables (such as position, velocity, and acceleration) in any of the transition models or covariances.


title: Kalman filter

text: As an example application, consider the problem of determining the precise location of a truck. The truck can be equipped with a GPS unit that provides an estimate of the position within a few meters. The GPS estimate is likely to be noisy; readings 'jump around' rapidly, though remaining within a few meters of the real position. In addition, since the truck is expected to follow the laws of physics, its position can also be estimated by integrating its velocity over time, determined by keeping track of wheel revolutions and the angle of the steering wheel. This is a technique known as dead reckoning. Typically, the dead reckoning will provide a very smooth estimate of the truck's position, but it will drift over time as small errors accumulate.


title: Kalman filter

text: For this example, the Kalman filter can be thought of as operating in two distinct phases: predict and update. In the prediction phase, the truck's old position will be modified according to the physical laws of motion (the dynamic or "state transition" model). Not only will a new position estimate be calculated, but also a new covariance will be calculated as well. Perhaps the covariance is proportional to the speed of the truck because we are more uncertain about the accuracy of the dead reckoning position estimate at high speeds but very certain about the position estimate at low speeds. Next, in the update phase, a measurement of the truck's position is taken from the GPS unit. Along with this measurement comes some amount of uncertainty, and its covariance relative to that of the prediction from the previous phase determines how much the new measurement will affect the updated prediction. Ideally, as the dead reckoning estimates tend to drift away from the real position, the GPS measurement should pull the position estimate back toward the real position but not disturb it to the point of becoming noisy and rapidly jumping.


title: Kalman filter

text: The Kalman filter is an efficient recursive filter estimating the internal state of a linear dynamic system from a series of noisy measurements. It is used in a wide range of engineering and econometric applications from radar and computer vision to estimation of structural macroeconomic models, and is an important topic in control theory and control systems engineering. Together with the linear-quadratic regulator (LQR), the Kalman filter solves the linear–quadratic–Gaussian control problem (LQG). The Kalman filter, the linear-quadratic regulator, and the linear–quadratic–Gaussian controller are solutions to what arguably are the most fundamental problems of control theory.


title: Kalman filter

text: In most applications, the internal state is much larger (has more degrees of freedom) than the few "observable" parameters which are measured. However, by combining a series of measurements, the Kalman filter can estimate the entire internal state.


title: Kalman filter

text: For the Dempster–Shafer theory, each state equation or observation is considered a special case of a linear belief function and the Kalman filtering is a special case of combining linear belief functions on a join-tree or Markov tree. Additional methods include belief filtering which use Bayes or evidential updates to the state equations.


title: Kalman filter

text: A wide variety of Kalman filters exists by now, from Kalman's original formulation - now termed the "simple" Kalman filter, the Kalman–Bucy filter, Schmidt's "extended" filter, the information filter, and a variety of "square-root" filters that were developed by Bierman, Thornton, and many others. Perhaps the most commonly used type of very simple Kalman filter is the phase-locked loop, which is now ubiquitous in radios, especially frequency modulation (FM) radios, television sets, satellite communications receivers, outer space communications systems, and nearly any other electronic communications equipment.


title: Kalman filter

text: Kalman filtering is based on linear dynamic systems discretized in the time domain. They are modeled on a Markov chain built on linear operators perturbed by errors that may include Gaussian noise. The state of the target system refers to the ground truth (yet hidden) system configuration of interest, which is represented as a vector of real numbers. At each discrete time increment, a linear operator is applied to the state to generate the new state, with some noise mixed in, and optionally some information from the controls on the system if they are known. Then, another linear operator mixed with more noise generates the measurable outputs (i.e., observation) from the true ("hidden") state. The Kalman filter may be regarded as analogous to the hidden Markov model, with the difference that the hidden state variables have values in a continuous space as opposed to a discrete state space as for the hidden Markov model. There is a strong analogy between the equations of a Kalman Filter and those of the hidden Markov model. A review of this and other models is given in Roweis and Ghahramani (1999) and Hamilton (1994), Chapter 13.


title: Kalman filter

text: In order to use the Kalman filter to estimate the internal state of a process given only a sequence of noisy observations, one must model the process in accordance with the following framework. This means specifying the matrices, for each time-step "k", following:


title: Kalman filter

text: The Kalman filter model assumes the true state at time "k" is evolved from the state at ("k" − 1) according to


title: Kalman filter

text: The initial state, and the noise vectors at each step {x, w, ..., w, v, ... ,v} are all assumed to be mutually independent.


title: Kalman filter

text: Many real-time dynamic systems do not exactly conform to this model. In fact, unmodeled dynamics can seriously degrade the filter performance, even when it was supposed to work with unknown stochastic signals as inputs. The reason for this is that the effect of unmodeled dynamics depends on the input, and, therefore, can bring the estimation algorithm to instability (it diverges). On the other hand, independent white noise signals will not make the algorithm diverge. The problem of distinguishing between measurement noise and unmodeled dynamics is a difficult one and is treated as a problem of control theory using robust control.


title: Kalman filter

text: The Kalman filter is a recursive estimator. This means that only the estimated state from the previous time step and the current measurement are needed to compute the estimate for the current state. In contrast to batch estimation techniques, no history of observations and/or estimates is required. In what follows, the notation formula_6 represents the estimate of formula_7 at time "n" given observations up to and including at time .


title: Kalman filter

text: The algorithm structure of the Kalman filter resembles that of Alpha beta filter. The Kalman filter can be written as a single equation; however, it is most often conceptualized as two distinct phases: "Predict" and "Update". The predict phase uses the state estimate from the previous timestep to produce an estimate of the state at the current timestep. This predicted state estimate is also known as the "a priori" state estimate because, although it is an estimate of the state at the current timestep, it does not include observation information from the current timestep. In the update phase, the innovation (the pre-fit residual), i.e. the difference between the current "a priori" prediction and the current observation information, is multiplied by the optimal Kalman gain and combined with the previous state estimate to refine the state estimate. This improved estimate based on the current observation is termed the "a posteriori" state estimate.


title: Kalman filter

text: Typically, the two phases alternate, with the prediction advancing the state until the next scheduled observation, and the update incorporating the observation. However, this is not necessary; if an observation is unavailable for some reason, the update may be skipped and multiple prediction procedures performed. Likewise, if multiple independent observations are available at the same time, multiple update procedures may be performed (typically with different observation matrices H).


title: Kalman filter

text: The formula for the updated ("a posteriori") estimate covariance above is valid for the optimal K gain that minimizes the residual error, in which form it is most widely used in applications. Proof of the formulae is found in the "derivations" section, where the formula valid for any K is also shown.


title: Kalman filter

text: If the model is accurate, and the values for formula_20 and formula_21 accurately reflect the distribution of the initial state values, then the following invariants are preserved:


title: Kalman filter

text: where formula_23 is the expected value of formula_24. That is, all estimates have a mean error of zero.


title: Kalman filter

text: Practical implementation of a Kalman Filter is often difficult due to the difficulty of getting a good estimate of the noise covariance matrices Q and R. Extensive research has been done to estimate these covariances from data. One practical method of doing this is the "autocovariance least-squares (ALS)" technique that uses the time-lagged autocovariances of routine operating data to estimate the covariances. The GNU Octave and Matlab code used to calculate the noise covariance matrices using the ALS technique is available online using the GNU General Public License. Field Kalman Filter (FKF), a Bayesian algorithm, which allows simultaneous estimation of the state, parameters and noise covariance has been proposed. The FKF algorithm has a recursive formulation, good observed convergence, and relatively low complexity, thus suggesting that the FKF algorithm may possibly be a worthwhile alternative to the Autocovariance Least-Squares methods.


title: Kalman filter

text: It follows from theory that the Kalman filter is the optimal linear filter in cases where a) the model matches the real system perfectly, b) the entering noise is "white" (uncorrelated) and c) the covariances of the noise are known exactly. Correlated noises can also be treated using Kalman filters.


title: Kalman filter

text: Several methods for the noise covariance estimation have been proposed during past decades, including ALS, mentioned in the section above. After the covariances are estimated, it is useful to evaluate the performance of the filter; i.e., whether it is possible to improve the state estimation quality. If the Kalman filter works optimally, the innovation sequence (the output prediction error) is a white noise, therefore the whiteness property of the innovations measures filter performance. Several different methods can be used for this purpose. If the noise terms are distributed in a non-Gaussian manner, methods for assessing performance of the filter estimate, which use probability inequalities or large-sample theory, are known in the literature.


title: Kalman filter

text: Consider a truck on frictionless, straight rails. Initially, the truck is stationary at position 0, but it is buffeted this way and that by random uncontrolled forces. We measure the position of the truck every Δ"t" seconds, but these measurements are imprecise; we want to maintain a model of the truck's position and velocity. We show here how we derive the model from which we create our Kalman filter.


title: Kalman filter

text: We assume that between the ("k" − 1) and "k" timestep, uncontrolled forces cause a constant acceleration of "a" that is normally distributed with mean 0 and standard deviation "σ". From Newton's laws of motion we conclude that


title: Kalman filter

text: (there is no formula_30 term since there are no known control inputs. Instead, "a" is the effect of an unknown input and formula_31 applies that effect to the state vector) where


title: Kalman filter

text: The matrix formula_35 is not full rank (it is of rank one if formula_36). Hence, the distribution formula_37 is not absolutely continuous and has no probability density function. Another way to express this, avoiding explicit degenerate distributions is given by


title: Kalman filter

text: At each time phase, a noisy measurement of the true position of the truck is made. Let us suppose the measurement noise "v" is also distributed normally, with mean 0 and standard deviation "σ".


title: Kalman filter

text: and to tell the filter that we know the exact position and velocity, we give it a zero covariance matrix:


title: Kalman filter

text: If the initial position and velocity are not known perfectly, the covariance matrix should be initialized with suitable variances on its diagonal:


title: Kalman filter

text: The filter will then prefer the information from the first measurements over the information already in the model.


title: Kalman filter

text: A similar equation holds if we include a non-zero control input. Gain matrices formula_15 evolve independently of the measurements formula_48. From above, the four equations needed for updating the Kalman gain are as follows:


title: Kalman filter

text: Since the gain matrices depend only on the model, and not the measurements, they may be computed offline. Convergence of the gain matrices formula_15 to an asymptotic matrix formula_51 applies for conditions established in Walrand and Dimakis. Simulations establish the number of steps to convergence. For the moving truck example described above, with formula_52. and formula_53, simulation shows convergence in formula_54 iterations.


title: Kalman filter

text: Using the asymptotic gain, and assuming formula_55 and formula_56 are independent of formula_57, the Kalman filter becomes a linear time-invariant filter:


title: Kalman filter

text: The asymptotic gain formula_51, if it exists, can be computed by first solving the following discrete Riccati equation for the asymptotic state covariance formula_60:


title: Kalman filter

text: Additionally, a form of the asymptotic Kalman filter more commonly used in control theory is given by


title: Kalman filter

text: This formula (sometimes known as the Joseph form of the covariance update equation) is valid for any value of K. It turns out that if K is the optimal Kalman gain, this can be simplified further as shown below.


title: Kalman filter

text: The Kalman filter is a minimum mean-square error estimator. The error in the "a posteriori" state estimation is


title: Kalman filter

text: We seek to minimize the expected value of the square of the magnitude of this vector, formula_78. This is equivalent to minimizing the trace of the "a posteriori" estimate covariance matrix formula_79. By expanding out the terms in the equation above and collecting, we get:


title: Kalman filter

text: The trace is minimized when its matrix derivative with respect to the gain matrix is zero. Using the gradient matrix rules and the symmetry of the matrices involved we find that


title: Kalman filter

text: This gain, which is known as the "optimal Kalman gain", is the one that yields MMSE estimates when used.


title: Kalman filter

text: The formula used to calculate the "a posteriori" error covariance can be simplified when the Kalman gain equals the optimal value derived above. Multiplying both sides of our Kalman gain formula on the right by SK, it follows that


title: Kalman filter

text: This formula is computationally cheaper and thus nearly always used in practice, but is only correct for the optimal gain. If arithmetic precision is unusually low causing problems with numerical stability, or if a non-optimal Kalman gain is deliberately used, this simplification cannot be applied; the "a posteriori" error covariance formula as derived above (Joseph form) must be used.


title: Kalman filter

text: The Kalman filtering equations provide an estimate of the state formula_10 and its error covariance formula_9 recursively. The estimate and its quality depend on the system parameters and the noise statistics fed as inputs to the estimator. This section analyzes the effect of uncertainties in the statistical inputs to the filter. In the absence of reliable statistics or the true values of noise covariance matrices formula_88 and formula_89, the expression


title: Kalman filter

text: no longer provides the actual error covariance. In other words, formula_91. In most real-time applications, the covariance matrices that are used in designing the Kalman filter are different from the actual (true) noise covariances matrices. This sensitivity analysis describes the behavior of the estimation error covariance when the noise covariances as well as the system matrices formula_56 and formula_55 that are fed as inputs to the filter are incorrect. Thus, the sensitivity analysis describes the robustness (or sensitivity) of the estimator to misspecified statistical and parametric inputs to the estimator.


title: Kalman filter

text: This discussion is limited to the error sensitivity analysis for the case of statistical uncertainties. Here the actual noise covariances are denoted by formula_94 and formula_95 respectively, whereas the design values used in the estimator are formula_96 and formula_89 respectively. The actual error covariance is denoted by formula_98 and formula_99 as computed by the Kalman filter is referred to as the Riccati variable. When formula_100 and formula_101, this means that formula_102. While computing the actual error covariance using formula_103, substituting for formula_104 and using the fact that formula_105 and formula_106, results in the following recursive equations for formula_98 :


title: Kalman filter

text: While computing formula_99, by design the filter implicitly assumes that formula_111 and formula_112. The recursive expressions for formula_98 and formula_99 are identical except for the presence of formula_115 and formula_116 in place of the design values formula_96 and formula_89 respectively. Researches have been done to analyze Kalman filter system's robustness.


title: Kalman filter

text: One problem with the Kalman filter is its numerical stability. If the process noise covariance Q is small, round-off error often causes a small positive eigenvalue to be computed as a negative number. This renders the numerical representation of the state covariance matrix P indefinite, while its true form is positive-definite.


title: Kalman filter

text: Positive definite matrices have the property that they have a triangular matrix square root P = S·S. This can be computed efficiently using the Cholesky factorization algorithm, but more importantly, if the covariance is kept in this form, it can never have a negative diagonal or become asymmetric. An equivalent form, which avoids many of the square root operations required by the matrix square root yet preserves the desirable numerical properties, is the U-D decomposition form, P = U·D·U, where U is a unit triangular matrix (with unit diagonal), and D is a diagonal matrix.


title: Kalman filter

text: Between the two, the U-D factorization uses the same amount of storage, and somewhat less computation, and is the most commonly used square root form. (Early literature on the relative efficiency is somewhat misleading, as it assumed that square roots were much more time-consuming than divisions, while on 21st-century computers they are only slightly more expensive.)


title: Kalman filter

text: Efficient algorithms for the Kalman prediction and update steps in the square root form were developed by G. J. Bierman and C. L. Thornton.


title: Kalman filter

text: The L·D·L decomposition of the innovation covariance matrix S is the basis for another type of numerically efficient and robust square root filter. The algorithm starts with the LU decomposition as implemented in the Linear Algebra PACKage (LAPACK). These results are further factored into the L·D·L structure with methods given by Golub and Van Loan (algorithm 4.1.2) for a symmetric nonsingular matrix. Any singular covariance matrix is pivoted so that the first diagonal partition is nonsingular and well-conditioned. The pivoting algorithm must retain any portion of the innovation covariance matrix directly corresponding to observed state-variables H·x that are associated with auxiliary observations in


title: Kalman filter

text: y. The l·d·l square-root filter requires orthogonalization of the observation vector. This may be done with the inverse square-root of the covariance matrix for the auxiliary variables using Method 2 in Higham (2002, p. 263).


title: Kalman filter

text: The Kalman filter is efficient for sequential data processing on central processing units (CPUs), but in its original form it is inefficient on parallel architectures such as graphics processing units (GPUs). It is however possible to express the filter-update routine in terms of an associative operator using the formulation in Särkkä (2021). The filter solution can then be retrieved by the use of a prefix sum algorithm which can be efficiently implemented on GPU. This reduces the computational complexity from formula_119 in the number of time steps to formula_120.


title: Kalman filter

text: The Kalman filter can be presented as one of the simplest dynamic Bayesian networks. The Kalman filter calculates estimates of the true values of states recursively over time using incoming measurements and a mathematical process model. Similarly, recursive Bayesian estimation calculates estimates of an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process model.


title: Kalman filter

text: In recursive Bayesian estimation, the true state is assumed to be an unobserved Markov process, and the measurements are the observed states of a hidden Markov model (HMM).


title: Kalman filter

text: Because of the Markov assumption, the true state is conditionally independent of all earlier states given the immediately previous state.


title: Kalman filter

text: Similarly, the measurement at the "k"-th timestep is dependent only upon the current state and is conditionally independent of all other states given the current state.


title: Kalman filter

text: Using these assumptions the probability distribution over all states of the hidden Markov model can be written simply as:


title: Kalman filter

text: However, when a Kalman filter is used to estimate the state x, the probability distribution of interest is that associated with the current states conditioned on the measurements up to the current timestep. This is achieved by marginalizing out the previous states and dividing by the probability of the measurement set.


title: Kalman filter

text: This results in the "predict" and "update" phases of the Kalman filter written probabilistically. The probability distribution associated with the predicted state is the sum (integral) of the products of the probability distribution associated with the transition from the ("k" − 1)-th timestep to the "k"-th and the probability distribution associated with the previous state, over all possible formula_124.


title: Kalman filter

text: The probability distribution of the update is proportional to the product of the measurement likelihood and the predicted state.


title: Kalman filter

text: The PDF at the previous timestep is assumed inductively to be the estimated state and covariance. This is justified because, as an optimal estimator, the Kalman filter makes best use of the measurements, therefore the PDF for formula_130 given the measurements formula_131 is the Kalman filter estimate.


title: Kalman filter

text: Related to the recursive Bayesian interpretation described above, the Kalman filter can be viewed as a generative model, i.e., a process for "generating" a stream of random observations z = (z, z, z, ...). Specifically, the process is


title: Kalman filter

text: This process has identical structure to the hidden Markov model, except that the discrete state and observations are replaced with continuous variables sampled from Gaussian distributions.


title: Kalman filter

text: In some applications, it is useful to compute the "probability" that a Kalman filter with a given set of parameters (prior distribution, transition and observation models, and control inputs) would generate a particular observed signal. This probability is known as the marginal likelihood because it integrates over ("marginalizes out") the values of the hidden state variables, so it can be computed using only the observed signal. The marginal likelihood can be useful to evaluate different parameter choices, or to compare the Kalman filter against other models using Bayesian model comparison.


title: Kalman filter

text: It is straightforward to compute the marginal likelihood as a side effect of the recursive filtering computation. By the chain rule, the likelihood can be factored as the product of the probability of each observation given previous observations,


title: Kalman filter

text: and because the Kalman filter describes a Markov process, all relevant information from previous observations is contained in the current state estimate formula_142 Thus the marginal likelihood is given by


title: Kalman filter

text: i.e., a product of Gaussian densities, each corresponding to the density of one observation z under the current filtering distribution formula_144. This can easily be computed as a simple recursive update; however, to avoid numeric underflow, in a practical implementation it is usually desirable to compute the "log" marginal likelihood formula_145 instead. Adopting the convention formula_146, this can be done via the recursive update rule


title: Kalman filter

text: An important application where such a (log) likelihood of the observations (given the filter parameters) is used is multi-target tracking. For example, consider an object tracking scenario where a stream of observations is the input, however, it is unknown how many objects are in the scene (or, the number of objects is known but is greater than one). For such a scenario, it can be unknown apriori which observations/measurements were generated by which object. A multiple hypothesis tracker (MHT) typically will form different track association hypotheses, where each hypothesis can be considered as a Kalman filter (for the linear Gaussian case) with a specific set of parameters associated with the hypothesized object. Thus, it is important to compute the likelihood of the observations for the different hypotheses under consideration, such that the most-likely one can be found.


title: Kalman filter

text: In the information filter, or inverse covariance filter, the estimated covariance and estimated state are replaced by the information matrix and information vector respectively. These are defined as:


title: Kalman filter

text: The main advantage of the information filter is that "N" measurements can be filtered at each time step simply by summing their information matrices and vectors.


title: Kalman filter

text: To predict the information filter the information matrix and vector can be converted back to their state space equivalents, or alternatively the information space prediction can be used.


title: Kalman filter

text: The optimal fixed-lag smoother provides the optimal estimate of formula_155 for a given fixed-lag formula_156 using the measurements from formula_157 to formula_48. It can be derived using the previous theory via an augmented state, and the main equation of the filter is the following:


title: Kalman filter

text: The optimal fixed-interval smoother provides the optimal estimate of formula_172 (formula_173) using the measurements from a fixed interval formula_157 to formula_175. This is also called "Kalman Smoothing". There are several smoothing algorithms in common use.


title: Kalman filter

text: The Rauch–Tung–Striebel (RTS) smoother is an efficient two-pass algorithm for fixed interval smoothing.


title: Kalman filter

text: The forward pass is the same as the regular Kalman filter algorithm. These "filtered" a-priori and a-posteriori state estimates formula_176, formula_67 and covariances formula_178, formula_99 are saved for use in the backward pass (for retrodiction).


title: Kalman filter

text: In the backward pass, we compute the "smoothed" state estimates formula_180 and covariances formula_181. We start at the last time step and proceed backward in time using the following recursive equations:


title: Kalman filter

text: formula_184 is the a-posteriori state estimate of timestep formula_57 and formula_186 is the a-priori state estimate of timestep formula_187. The same notation applies to the covariance.


title: Kalman filter

text: An alternative to the RTS algorithm is the modified Bryson–Frazier (MBF) fixed interval smoother developed by Bierman. This also uses a backward pass that processes data saved from the Kalman filter forward pass. The equations for the backward pass involve the recursive


title: Kalman filter

text: computation of data which are used at each observation time to compute the smoothed state and covariance.


title: Kalman filter

text: where formula_189 is the residual covariance and formula_190. The smoothed state and covariance can then be found by substitution in the equations


title: Kalman filter

text: An important advantage of the MBF is that it does not require finding the inverse of the covariance matrix.


title: Kalman filter

text: The minimum-variance smoother can attain the best-possible error performance, provided that the models are linear, their parameters and the noise statistics are known precisely. This smoother is a time-varying state-space generalization of the optimal non-causal Wiener filter.


title: Kalman filter

text: The smoother calculations are done in two passes. The forward calculations involve a one-step-ahead predictor and are given by


title: Kalman filter

text: The above system is known as the inverse Wiener-Hopf factor. The backward recursion is the adjoint of the above forward system. The result of the backward pass formula_194 may be calculated by operating the forward equations on the time-reversed formula_195 and time reversing the result. In the case of output estimation, the smoothed estimate is given by


title: Kalman filter

text: which is identical to the minimum-variance Kalman filter. The above solutions minimize the variance of the output estimation error. Note that the Rauch–Tung–Striebel smoother derivation assumes that the underlying distributions are Gaussian, whereas the minimum-variance solutions do not. Optimal smoothers for state estimation and input estimation can be constructed similarly.


title: Kalman filter

text: Expectation–maximization algorithms may be employed to calculate approximate maximum likelihood estimates of unknown state-space parameters within minimum-variance filters and smoothers. Often uncertainties remain within problem assumptions. A smoother that accommodates uncertainties can be designed by adding a positive definite term to the Riccati equation.


title: Kalman filter

text: In cases where the models are nonlinear, step-wise linearizations may be within the minimum-variance filter and smoother recursions (extended Kalman filtering).


title: Kalman filter

text: Pioneering research on the perception of sounds at different frequencies was conducted by Fletcher and Munson in the 1930s. Their work led to a standard way of weighting measured sound levels within investigations of industrial noise and hearing loss. Frequency weightings have since been used within filter and controller designs to manage performance within bands of interest.


title: Kalman filter

text: Typically, a frequency shaping function is used to weight the average power of the error spectral density in a specified frequency band. Let formula_198 denote the output estimation error exhibited by a conventional Kalman filter. Also, let formula_199 denote a causal frequency weighting transfer function. The optimum solution which minimizes the variance of formula_200 arises by simply constructing formula_201.


title: Kalman filter

text: The design of formula_199 remains an open question. One way of proceeding is to identify a system which generates the estimation error and setting formula_199 equal to the inverse of that system. This procedure may be iterated to obtain mean-square error improvement at the cost of increased filter order. The same technique can be applied to smoothers.


title: Kalman filter

text: The basic Kalman filter is limited to a linear assumption. More complex systems, however, can be nonlinear. The nonlinearity can be associated either with the process model or with the observation model or with both.


title: Kalman filter

text: The most common variants of Kalman filters for non-linear systems are the Extended Kalman Filter and Unscented Kalman filter. The suitability of which filter to use depends on the non-linearity indices of the process and observation model.


title: Kalman filter

text: In the extended Kalman filter (EKF), the state transition and observation models need not be linear functions of the state but may instead be nonlinear functions. These functions are of differentiable type.


title: Kalman filter

text: The function "f" can be used to compute the predicted state from the previous estimate and similarly the function "h" can be used to compute the predicted measurement from the predicted state. However, "f" and "h" cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian) is computed.


title: Kalman filter

text: At each timestep the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the nonlinear function around the current estimate.


title: Kalman filter

text: When the state transition and observation models—that is, the predict and update functions formula_205 and formula_206—are highly nonlinear, the extended Kalman filter can give particularly poor performance. This is because the covariance is propagated through linearization of the underlying nonlinear model. The unscented Kalman filter (UKF)  uses a deterministic sampling technique known as the unscented transformation (UT) to pick a minimal set of sample points (called sigma points) around the mean. The sigma points are then propagated through the nonlinear functions, from which a new mean and covariance estimate are then formed. The resulting filter depends on how the transformed statistics of the UT are calculated and which set of sigma points are used. It should be remarked that it is always possible to construct new UKFs in a consistent way. For certain systems, the resulting UKF more accurately estimates the true mean and covariance. This can be verified with Monte Carlo sampling or Taylor series expansion of the posterior statistics. In addition, this technique removes the requirement to explicitly calculate Jacobians, which for complex functions can be a difficult task in itself (i.e., requiring complicated derivatives if done analytically or being computationally costly if done numerically), if not impossible (if those functions are not differentiable).


title: Kalman filter

text: where formula_218 is the mean estimate of formula_216. The vector formula_220 is the "j"th column of formula_221 where formula_222. Typically, formula_221 is obtained via Cholesky decomposition of formula_224. With some care the filter equations can be expressed in such a way that formula_221 is evaluated directly without intermediate calculations of formula_224. This is referred to as the "square-root unscented Kalman filter".


title: Kalman filter

text: formula_229 and formula_230 control the spread of the sigma points. formula_231 is related to the distribution of formula_232.


title: Kalman filter

text: Appropriate values depend on the problem at hand, but a typical recommendation is formula_233, formula_234, and formula_235. However, a larger value of formula_229 (e.g., formula_237) may be beneficial in order to better capture the spread of the distribution and possible nonlinearities. If the true distribution of formula_232 is Gaussian, formula_235 is optimal.


title: Kalman filter

text: As with the EKF, the UKF prediction can be used independently from the UKF update, in combination with a linear (or indeed EKF) update, or vice versa.


title: Kalman filter

text: Given estimates of the mean and covariance, formula_240 and formula_224, one obtains formula_242 sigma points as described in the section above. The sigma points are propagated through the transition function "f".


title: Kalman filter

text: where formula_245 are the first-order weights of the original sigma points, and formula_246 are the second-order weights. The matrix formula_247 is the covariance of the transition noise, formula_248.


title: Kalman filter

text: Given prediction estimates formula_176 and formula_178, a new set of formula_251 sigma points formula_252 with corresponding first-order weights formula_253 and second-order weights formula_254 is calculated. These sigma points are transformed through the measurement function formula_206.


title: Kalman filter

text: where formula_89 is the covariance matrix of the observation noise, formula_259. Additionally, the cross covariance matrix is also needed


title: Kalman filter

text: When the observation model formula_263 is highly non-linear and/or non-Gaussian, it may prove advantageous to apply Bayes' rule and estimate


title: Kalman filter

text: where formula_265 for nonlinear functions formula_266. This replaces the generative specification of the standard Kalman filter with a discriminative model for the latent states given observations.


title: Kalman filter

text: Note that this approximation requires formula_273 to be positive-definite; in the case that it is not,


title: Kalman filter

text: is used instead. Such an approach proves particularly useful when the dimensionality of the observations is much greater than that of the latent states and can be used build filters that are particularly robust to nonstationarities in the observation model.


title: Kalman filter

text: Adaptive Kalman filters allow to adapt for process dynamics which are not modeled in the process model formula_275, which happens for example in the context of a maneuvering target when a constant velocity (reduced order) Kalman filter is employed for tracking.


title: Kalman filter

text: Kalman–Bucy filtering (named for Richard Snowden Bucy) is a continuous time version of Kalman filtering.


title: Kalman filter

text: where formula_277 and formula_278 represent the intensities (or, more accurately: the Power Spectral Density - PSD - matrices) of the two white noise terms formula_279 and formula_280, respectively.


title: Kalman filter

text: The filter consists of two differential equations, one for the state estimate and one for the covariance:


title: Kalman filter

text: Note that in this expression for formula_283 the covariance of the observation noise formula_278 represents at the same time the covariance of the prediction error (or "innovation") formula_285; these covariances are equal only in the case of continuous time.


title: Kalman filter

text: The distinction between the prediction and update steps of discrete-time Kalman filtering does not exist in continuous time.


title: Kalman filter

text: The second differential equation, for the covariance, is an example of a Riccati equation. Nonlinear generalizations to Kalman–Bucy filters include continuous time extended Kalman filter.


title: Kalman filter

text: Most physical systems are represented as continuous-time models while discrete-time measurements are made frequently for state estimation via a digital processor. Therefore, the system model and measurement model are given by


title: Kalman filter

text: The prediction equations are derived from those of continuous-time Kalman filter without update from measurements, i.e., formula_290. The predicted state and covariance are calculated respectively by solving a set of differential equations with the initial value equal to the estimate at the previous step.


title: Kalman filter

text: For the case of linear time invariant systems, the continuous time dynamics can be exactly discretized into a discrete time system using matrix exponentials.


title: Kalman filter

text: The traditional Kalman filter has also been employed for the recovery of sparse, possibly dynamic, signals from noisy observations. Recent works utilize notions from the theory of compressed sensing/sampling, such as the restricted isometry property and related probabilistic recovery arguments, for sequentially estimating the sparse state in intrinsically low-dimensional systems.


title: Kalman filter

text: Since linear Gaussian state-space models lead to Gaussian processes, Kalman filters can be viewed as sequential solvers for Gaussian process regression.


title: Andy Milonakis

text: Andrew Michael Milonakis (; born January 30, 1976) is an American actor, comedian, rapper, and streamer. He is best known for his work on "The Andy Milonakis Show", a sketch comedy series that aired on MTV and MTV2 from 2005 to 2007. Other notable films and TV series Milonakis has appeared in include "Kroll Show", "Waiting..." and "Adventure Time".


title: Andy Milonakis

text: Milonakis was born in Katonah, New York, to a Greek-American family. His father was born in Greece. Milonakis was born with a growth hormone deficiency, causing him to have the appearance and voice of an adolescent. He attended John Jay High School in Lewisboro. Milonakis turned to comedy and humor as a preemptive defense mechanism.


title: Andy Milonakis

text: On January 26, 2003, the day of Super Bowl XXXVII, Milonakis decided not to attend a friend's Super Bowl party and instead recorded a video titled "The Super Bowl Is Gay". He posted the video to the website AngryNakedPat.com, and within two weeks it went viral. A writer for ABC's new late-night show, "Jimmy Kimmel Live!", spotted it and got Milonakis on the program. At the time, Milonakis was working as a tech support staffer at a Manhattan accounting firm.


title: Andy Milonakis

text: Milonakis first started rapping on YouTube; his first song was called "The Andy Milonakis Rap". He was in Three Loco, a group that also included rap artists Dirt Nasty and Riff Raff, but on September 26, 2014, he announced that the group had broken up.


title: Andy Milonakis

text: From 2014 to 2015, Milonakis hosted and starred in a cooking show called "Fat Prince" on Munchies, a YouTube channel that is part of the Vice network. In each episode, Milonakis and a changing cast of chefs combined cheap ingredients with expensive ingredients to make a unique meal.


title: Andy Milonakis

text: In December 2016, Milonakis announced he was joining the Baited podcast, with YouTubers Anything4views and Keemstar. According to Twitchmetrics on February 26, 2017, he was the fastest-growing streamer in the "IRL" category of the popular streaming website Twitch at that time.


title: Andy Milonakis

text: On May 30, 2020, Milonakis tweeted the sixth-most-liked tweet of all time on Twitter, writing "Congratulations to the Astronauts that left Earth today. Good choice" referring to the Crew Dragon Demo-2 launch during the George Floyd protests and the COVID-19 pandemic.


title: Andy Milonakis

text: After having lived in Los Angeles, California for much of his career, he currently lives in Astoria, Queens, New York City.


title: Zaporizhzhia

text: Zaporizhzhia (, ) or Zaporozhye () is a city in southeast Ukraine, situated on the banks of the Dnieper river. It is the administrative centre of the Zaporizhzhia Oblast (region). Zaporizhzhia has a population of


title: Zaporizhzhia

text: Zaporizhzhia is known for the historic island of Khortytsia; multiple power stations including Zaporizhzhia Nuclear Power Plant (the largest nuclear power station in Europe), Zaporizhzhia thermal power station and Dnieper Hydroelectric Station and for being an important industrial centre. Steel, aluminium, aircraft engines, automobiles, transformers for substations, and other heavy industrial goods are produced in the region.


title: Zaporizhzhia

text: Renderings of the name include: Zaporizhzhia, Zaporizhia, or Zaporizhzhya, pronounced , , from , . Also "Zaporozhye", , from , ).


title: Zaporizhzhia

text: The name "Zaporizhzhia" literally refers to the position of the city located "beyond the rapids" – down-river or south of the Dnieper River rapids, formerly a major impediment to navigation and the site of important portages (in 1932, the rapids on the Dnieper river were flooded to become part of the reservoir of the Dnieper Hydroelectric Station).


title: Zaporizhzhia

text: Before it was changed in 1921, the city's name was Aleksandrovsk ( ) or Oleksandrivsk ( ) after the name of a fortress (; ) that formed a part of the of the Russian Empire.


title: Zaporizhzhia

text: The city is located in south-eastern Ukraine. The Dnieper river splits the city in two; between them is Khortytsia island. The city covers at an elevation of above sea level.


title: Zaporizhzhia

text: There are two streams around Khortytsia island; New and Old Dnieper. The is about wide while the is about wide. The island has sizes. There are also several small rivers in the city, which enter the Dnieper: and , , and .


title: Zaporizhzhia

text: The flora of Khortytsia island is unique and diverse due to the dry steppe air and a large freshwater basin, which cleans the air polluted by industry. Khortytsia Island is a national park. The island surface is cut by large ravines ("balka"), hiking routes and historical monuments. The island is a very popular recreational area for both kids and adults. There are a large number of sanatoriums, resorts and health centres. There are also sandy beaches with swimming access.


title: Zaporizhzhia

text: Zaporizhzhia is a regional seat of Zaporizhzhia Oblast and a city of regional significance meaning that it has a form of self-rule within the oblast (region).


title: Zaporizhzhia

text: The city population has been declining since the first years of the state independence. In 2014–2015 the rate of the population decrease was −0.56%/year.


title: Zaporizhzhia

text: The total reduction of the population of the city during the state independence is around 146 thousand people (the years 2017–2018 are not included in this estimation)


title: Zaporizhzhia

text: Most of the citizens are Orthodox Christians of Ukrainian Orthodox Church (Moscow Patriarchate) or Orthodox Church of Ukraine. Among the Orthodox churches the , which is under the Moscow Patriarchate, is most popular. There are also St. Nicholas Church and St. Andrew's Cathedral in the city.


title: Zaporizhzhia

text: In the Zaporizhzhia district there are five communities which are part of the Spiritual Administration of Muslims of Ukraine and four independent Muslim communities.


title: Zaporizhzhia

text: Zaporizhzhia is an important industrial centre of Ukraine, the country's main car manufacturing company, the Motor-Sich world-famous aircraft engine manufacturer. Well supplied with electricity, Zaporizhzhia forms, together with the adjoining Donets Basin (Donbas) and the Nikopol manganese and Kryvyi Rih iron mines, one of Ukraine's leading industrial complexes.


title: Zaporizhzhia

text: The city is a home of Ukraine's main automobile production centre, which is based at the Zaporizhzhia Automobile Factory (ZAZ), producing Ukrainian car brands such as "Zaporozhets" and "Tavria".


title: Zaporizhzhia

text: After the end of the Russian Revolution, the city became an important industrial centre. The presence of cheap labor and the proximity of deposits of coal, iron ore, and manganese created favorable conditions for large-scale enterprises of the iron and mechanical engineering industries. Today Zaporizhzhia is an important industrial centre of the region with heavy industry (particularly metallurgy), aluminium, and chemical industry. Cars, avia motors and radioelectronics are manufactured in the city. The port of Zaporizhzhia is important for transshipment for goods from the Donbas.


title: Zaporizhzhia

text: Zaporizhstal, Ukraine's fourth largest steel maker, and ranking 54th in the world, is based in the city.


title: Zaporizhzhia

text: Zaporizhzhia is a large electricity generating hub. There are hydroelectric power plant known as "DniproHES" Dnieper Hydroelectric Station and the largest nuclear power plant in Europe. Zaporizhzhia plants generate about 25% of the whole Ukrainian electricity consumption. The Zaporizhzhia Nuclear Power Plant is located near the Enerhodar (meaning "energy gifter"), around from Zaporizhzhia, which is the largest nuclear power plant in Europe. Also in Enerhodar, is the Zaporizhzhia Thermal Power Station.


title: Zaporizhzhia

text: There are a number of small amateur groups of folk music bands, art galleries in Zaporizhzhia. The city regularly holds festivals and feasts, competitions of the Cossack martial arts and art exhibitions.


title: Zaporizhzhia

text: Zaporizhzhia has an open-air exhibition-and-sale of Zaporizhzhia city association of artists «Kolorit» near the 'Fountain of Life' at the . A daily exhibition of artists' organizations of the city is a unique place in Zaporizhzhia, where people can communicate with craftsmen and artists, watch classes of carving, embroidery, beading and other creative works, receive lessons from professional artists, designers, and cartoonists.


title: Zaporizhzhia

text: The x island Khortytsia is located in the geographical centre of the city. The city embraces the island by banks of the New and Old Dnieper streams.


title: Zaporizhzhia

text: They have been designed and constructed by the engineer Boris N. Preobrazhensky in 1952. Two level bridges have height about 54 meters. High level of the bridges is intended for rail and bottom – for cars and pedestrians.


title: Zaporizhzhia

text: The historical and cultural museum "Zaporizka Sich" is placed on the northern rocky part of the island Khotritsa.


title: Zaporizhzhia

text: The museum is the reconstructed stronghold of the Zaporizhzhian Cossacks. All features of the military cossack's camp life and their lifestyle are presented in the museum.


title: Zaporizhzhia

text: The smaller islands are located between the dam and the island Khortytsia. Each of these islands has its own legend. On one of them named Durnya Scala ("Rock of the Fool") Tzar Peter the Great punished the Cossacks by flogging for their betrayal on the side of Charles XII of Sweden during the Great Northern War between Russia and Sweden.


title: Zaporizhzhia

text: Another small island, named Stolb ("Pillar"), has a geological feature, which looks like a large bowl in granite slabs, its diameter equals , the depth . This bowl is named Cossack's bowl. People say that in summer days under the hot sun, it is easy to boil water in this "bowl" and the Cossacks used it for cooking galushki (boiled dough in a spicy broth).


title: Zaporizhzhia

text: The straight and long Sobornyi avenue () ends in the SotsGorod near the Dam, which built up of the constructivist architecture of the 20th century.


title: Zaporizhzhia

text: The city of Zaporizhzhia is an important transportation hub in Ukraine and has deeply developed transportation system that includes roadway, rail, river and air options for passenger, freight as well as public utilities transit. Public city transport includes buses, minivans, trams, trolleybuses and railways.


title: Zaporizhzhia

text: On the eastern outskirts Zaporizhzhia is passed by a major national highway M18 which connects Kharkiv with Simferopol. The H08 which starts just outside Kyiv and travels southeast along the Dnieper through Kremenchuk, Kamianske, Dnipro and passes through Zaporizhzhia on to Mariupol. Two other highways terminate in the city, the H15 which arrives from Donetsk and the which starts in Kropyvnytskyi and through Kryvyi Rih ends in Zaporizhzhia.


title: Zaporizhzhia

text: There are four road bridges over Dnieper and two rail bridges. All bridges but one connect the city with Khortytsia island. The other bridge goes over the river dam of DniproHES. Early in 2022, President Volodymyr Zelenskyy opened the first stage of the new New Zaporizhzhia Dniper Bridge.


title: Zaporizhzhia

text: Zaporizhzhia city has two railway stations, Zaporizhzhia-the-First and Zaporizhzhia-the-Second. The First is the central station. It is located in the southern part of the city and is a part of the "north-south" transit route Simferopol-Kharkiv. The line of the Zaporizhzhia-the-Second station connects the Donbas coalfield with Kryvyi Rih iron ore site.


title: Zaporizhzhia

text: The city's two river ports are part of the national water transportation infrastructure that connects Kyiv to Kherson along Dnieper river and utilizes some freight ships as well as cutter boats to travel between Zaporizhzhia and nearby villages. The large island of Khortytsia splits the Dnieper into two branches (channels) the main branch that passes the island on its eastern side and the alternative branch also known as "Staryi Dnipro" (Old Dnieper) that flows past the island on its western side.


title: Zaporizhzhia

text: The city's sole airport located to the east of the city on the left-bank of the Dnieper serves both domestic and international flights. To the west of the city on the right-bank of the Dnieper there is a smaller airfield called Shyroke.


title: Zaporizhzhia

text: Zaporizhzhia is an important setting in two Axis victory in World War II short fictions by the American author Harry Turtledove: "Ready for the Fatherland" (1991) and "The Phantom Tolbukhin" (1998). Turtledove always uses the Zaporozhye spelling.


title: Zaporizhzhia

text: In addition, in 1969 the city renamed one of its streets "Wrocław", the Wrocław communist government acknowledging that they should honour the Ukrainian city in a similar way and a part of the Sudecka – Grabiszyńska street towards the square of the Silesian Insurgents – was renamed to Zaporoska street. It is about long.


title: El Clásico

text: El Clásico or el clásico (; , ; ) is the name given to any football match between rival clubs FC Barcelona and Real Madrid. Originally referring to competitions held in the Spanish championship, the term now includes every match between the clubs, such as those in the UEFA Champions League and Copa del Rey. It is considered one of the biggest club football games in the world, and is among the most viewed annual sporting events. A fixture known for its intensity, it has featured memorable goal celebrations from both teams, often involving mocking the opposition.


title: El Clásico

text: The rivalry comes about as Madrid and Barcelona are the two largest cities in Spain, and they are sometimes identified with opposing political positions, with Real Madrid viewed as representing Spanish nationalism and Barcelona viewed as representing Catalan nationalism. The rivalry is regarded as one of the biggest in world sport. The two clubs are among the richest and most successful football clubs in the world; in 2014 "Forbes" ranked Barcelona and Real Madrid the world's two most valuable sports teams. Both clubs have a global fanbase; they are the world's two most followed sports teams on social media.


title: El Clásico

text: Real Madrid leads in head-to-head results in competitive matches with 101 wins to Barcelona's 97 with 52 draws; Barcelona leads in exhibition matches with 20 victories to Madrid's 4 with 10 draws and in total matches with 117 wins to Madrid's 105 with 62 draws as of the match played on 16 October 2022. Along with Athletic Bilbao, they are the only clubs in La Liga to have never been relegated.


title: El Clásico

text: The conflict between Real Madrid and Barcelona has long surpassed the sporting dimension, so much that elections to the clubs' presidencies have been strongly politicized. Phil Ball, the author of "Morbo: The Story of Spanish Football", says about the match; "they hate each other with an intensity that can truly shock the outsider".


title: El Clásico

text: As early as the 1930s, Barcelona "had developed a reputation as a symbol of Catalan identity, opposed to the centralising tendencies of Madrid". In 1936, when Francisco Franco started the "coup d'état" against the democratic Second Spanish Republic, the president of Barcelona, Josep Sunyol, member of the Republican Left of Catalonia and Deputy to The Cortes, was arrested and executed without trial by Franco's troops (Sunyol was exercising his political activities, visiting Republican troops north of Madrid). During the dictatorships of Miguel Primo de Rivera and especially Francisco Franco, all regional languages and identities in Spain were frowned upon and restrained. As such, most citizens of Barcelona were in strong opposition to the fascist-like regime. In this period, Barcelona gained their motto "Més que un club" ("English: More than a club") because of its alleged connection to Catalan nationalist as well as to progressive beliefs.


title: El Clásico

text: There's an ongoing controversy as to what extent Franco's rule (1939–75) influenced the activities and on-pitch results of both Barcelona and Real Madrid. Fans of both clubs tend to exaggerate the myths favouring their narratives. Most historians agree than Franco did not have a preferred football team, but his Spanish nationalist beliefs led him to associate himself with the establishment teams, such as Atlético Aviación and Madrid FC (that recovered its "royal" name after the fall of the Republic). On the other hand, he also wanted the renamed "CF Barcelona" succeed as "Spanish team" rather than a Catalan one. During the early years of Franco's rule, Real Madrid weren't particularly successful, winning two Copa del Generalísimo titles and a Copa Eva Duarte; Barcelona claimed three league titles, one Copa del Generalísimo and one Copa Eva Duarte. During that period, Atlético Aviación were believed to be the preferred team over Real Madrid. The most contested stories of the period include Real Madrid's 11–1 home win against Barcelona in the Copa del Generalísimo, where the Catalan team alleged intimidation, and the controversial transfer of Alfredo Di Stéfano to Real Madrid despite his agreement with Barcelona. The latter transfer was part of Real Madrid chairman Santiago Bernabéu's "revolution" that ushered in the era of unprecedented dominance. Bernabéu, himself a veteran of the Civil War who fought for Franco's forces, saw Real Madrid on top not only of Spanish but also European football, helping create the European Cup, the first true competition for Europe's best club sides. His vision was fulfilled when Real Madrid not only started winning consecutive league titles but also swept the first five editions of the European Cup in the 1950s. These events had a profound impact on Spanish football and influenced Franco's attitude. According to historians, during this time he realized the importance of Real Madrid for his regime's international image, and the club became his preferred team until his death. Fernando Maria Castiella, who served as Minister of Foreign Affairs under Franco from 1957 until 1969, noted that "[Real Madrid] is the best embassy we have ever had." Franco died in 1975, and the Spanish transition to democracy soon followed. Under his rule, Real Madrid had won 14 league titles, 6 Copa del Generalísimo titles, 1 Copa Eva Duarte, 6 European Cups, 2 Latin Cups and 1 Intercontinental Cup. In the same period, Barcelona had won 8 league titles, 9 Copa del Generalísimo titles, 3 Copa Eva Duarte titles, 3 Inter-Cities Fairs Cups and 2 Latin Cups.


title: El Clásico

text: The image for both clubs was further affected by the creation of Ultras groups, some of which became hooligans. In 1980, Ultras Sur was founded as a far-right-leaning Real Madrid ultras group, followed in 1981 by the foundation of the initially left-leaning and later on far-right, Barcelona ultras group Boixos Nois. Both groups became known for their violent acts, and one of the most conflictive factions of Barcelona supporters, the "Casuals", became a full-fledged criminal organisation.


title: El Clásico

text: For many people, Barcelona is still considered as "the rebellious club", or the alternative pole to "Real Madrid's conservatism". According to polls released by CIS (Centro de Investigaciones Sociológicas), Real Madrid is the favorite team of most of the Spanish residents, while Barcelona stands in the second position. In Catalonia, forces of all the political spectrum are overwhelmingly in favour of Barcelona. Nevertheless, the support of the blaugrana club goes far beyond from that region, earning its best results among young people, sustainers of a federal structure of Spain and citizens with left-wing ideology, in contrast with Real Madrid fans which politically tend to adopt right-wing views.


title: El Clásico

text: On 13 June 1943, Real Madrid beat Barcelona 11–1 at the Chamartín in the second leg of the Copa del Generalísimo semi-finals (the Copa del Presidente de la República having been renamed in honour of General Franco). The first leg, played at the Les Corts in Catalonia, had ended with Barcelona winning 3–0. Madrid complained about all the three goals that referee Fombona Fernández had allowed for Barcelona, with the home supporters also whistling Madrid throughout, whom they accused of employing roughhouse tactics, and Fombona for allowing them to. Barça’s Josep Escolà was stretchered off in the first half with José María Querejeta’s stud marks in his stomach. A campaign began in Madrid. The newspaper "Ya" reported the whistling as a "clear intention to attack the representatives of Spain." Barcelona player Josep Valle recalled: "The press officer at the DND and ABC newspaper wrote all sorts of scurrilous lies, really terrible things, winding up the Madrid fans like never before". Former Real Madrid goalkeeper Eduardo Teus, who admitted that Madrid had "above all played hard", wrote in a newspaper: "the ground itself made Madrid concede two of the three goals, goals that were totally unfair".


title: El Clásico

text: Barcelona fans were banned from traveling to Madrid. Real Madrid released a statement after the match which former club president Ramón Mendoza explained, "The message got through that those fans who wanted to could go to El Club bar on Calle de la Victoria where Madrid's social center was. There, they were given a whistle. Others had whistles handed to them with their tickets." The day of the second leg, the Barcelona team were insulted and stones were thrown at their bus as soon as they left their hotel. Barcelona's striker Mariano Gonzalvo said of the incident, "Five minutes before the game had started, our penalty area was already full of coins." Barcelona goalkeeper Lluis Miró rarely approached his line—when he did, he was armed with stones. As Francisco Calvet told the story, "They were shouting: "Reds! Separatists!"... a bottle just missed Sospedra that would have killed him if it had hit him. It was all set up."


title: El Clásico

text: Real Madrid went 2–0 up within half an hour. The third goal brought with it a sending off for Barcelona's Benito García after he made what Calvet claimed was a "completely normal tackle". Madrid's José Llopis Corona recalled, "At which point, they got a bit demoralized," while Ángel Mur countered, "at which point, we thought: 'go on then, score as many as you want'." Madrid scored in minutes 31', 33', 35', 39', 43' and 44', as well as two goals ruled out for offside, made it 8–0. Juan Samaranch wrote: "In that atmosphere and with a referee who wanted to avoid any complications, it was humanly impossible to play... If the azulgranas had played badly, really badly, the scoreboard would still not have reached that astronomical figure. The point is that they did not play at all." Both clubs were fined 2,500 pesetas by the Royal Spanish Football Federation and, although Barcelona appealed, it made no difference. Piñeyro resigned in protest, complaining of "a campaign that the press has run against Barcelona for a week and which culminated in the shameful day at Chamartín".


title: El Clásico

text: The match report in the newspaper "La Prensa" described Barcelona's only goal as a "reminder that there was a team there who knew how to play football and that if they did not do so that afternoon, it was not exactly their fault". Another newspaper called the scoreline "as absurd as it was abnormal". According to football writer Sid Lowe, "There have been relatively few mentions of the game [since] and it is not a result that has been particularly celebrated in Madrid. Indeed, the 11–1 occupies a far more prominent place in Barcelona's history. This was the game that first formed the identification of Madrid as the team of the dictatorship and Barcelona as its victims." Fernando Argila, Barcelona's reserve goalkeeper from the game, said, "There was no rivalry. Not, at least, until that game."


title: El Clásico

text: The rivalry was intensified during the 1950s when the clubs disputed the signing of Alfredo Di Stéfano. Di Stéfano had impressed both Barcelona and Real Madrid while playing for Los Millionarios in Bogotá, Colombia, during a players' strike in his native Argentina. Soon after Millonarios' return to Colombia, Barcelona directors visited Buenos Aires and agreed with River Plate, the last FIFA-affiliated team to have held Di Stéfano's rights, for his transfer in 1954 for the equivalent of 150 million Italian lira ($200,000 according to other sources). This started a battle between the two Spanish rivals for his rights. FIFA appointed Armando Muñoz Calero, former president of the Spanish Football Federation as mediator. Calero decided to let Di Stéfano play the 1953–54 and 1955–56 seasons in Madrid, and the 1954–55 and 1956–57 seasons in Barcelona. The agreement was approved by the Football Association and their respective clubs. Although the Catalans agreed, the decision created various discontent among the Blaugrana members and the president was forced to resign in September 1953. Barcelona sold Madrid their half-share, and Di Stéfano moved to "Los Blancos", signing a four-year contract. Real paid 5.5 million Spanish pesetas for the transfer, plus a 1.3 million bonus for the purchase, an annual fee to be paid to the Millonarios, and a 16,000 salary for Di Stéfano with a bonus double that of his teammates, for a total of 40% of the annual revenue of the Madrid club.


title: El Clásico

text: Di Stéfano became integral in the subsequent success achieved by Real Madrid, scoring twice in his first game against Barcelona. With him, Madrid won the first five editions of the European Cup. The 1960s saw the rivalry reach the European stage when Real Madrid and Barcelona met twice in the European Cup, with Madrid triumphing en route to their fifth consecutive title in 1959–60 and Barcelona prevailing en route to losing the final in 1960–61.


title: El Clásico

text: In 2000, Real Madrid's then-presidential candidate, Florentino Pérez, offered Barcelona's vice-captain Luís Figo $2.4 million to sign an agreement binding him to Madrid if he won the elections. If the player broke the deal, he would have to pay Pérez $30 million in compensation. When his agent confirmed the deal, Figo denied everything, insisting, "I'll stay at Barcelona whether Pérez wins or loses." He accused the presidential candidate of "lying" and "fantasizing". He told Barcelona teammates Luis Enrique and Pep Guardiola he was not leaving and they conveyed the message to the Barcelona squad.


title: El Clásico

text: On 9 July, "Sport" ran an interview in which he said, "I want to send a message of calm to Barcelona's fans, for whom I always have and always will feel great affection. I want to assure them that Luís Figo will, with absolute certainty, be at the Camp Nou on the 24th to start the new season... I've not signed a pre-contract with a presidential candidate at Real Madrid. No. I'm not so mad as to do a thing like that."


title: El Clásico

text: The only way Barcelona could prevent Figo's transfer to Real Madrid was to pay the penalty clause, $30 million. That would have effectively meant paying the fifth highest transfer fee in history to sign their own player. Barcelona's new president, Joan Gaspart, called the media and told them, "Today, Figo gave me the impression that he wanted to do two things: get richer and stay at Barça." Only one of them happened. The following day, 24 July, Figo was presented in Madrid and handed his new shirt by Alfredo Di Stéfano. His buyout clause was set at $180 million. Gaspart later admitted, "Figo's move destroyed us."


title: El Clásico

text: On his return to Barcelona in a Real Madrid shirt, banners with "Judas", "Scum" and "Mercenary" were hung around the stadium. Thousands of fake 10,000 peseta notes had been printed and emblazoned with his image, were among the missiles of oranges, bottles, cigarette lighters, even a couple of mobile phones were thrown at him. In his third season with Real Madrid, the 2002 Clásico at Camp Nou produced one of the defining images of the rivalry. Figo was mercilessly taunted throughout; missiles of coins, a knife, a whisky bottle, were raining down from the stands, mostly from areas populated by the Boixos Nois where he had been taking a corner. Among the debris was a pig's head.


title: El Clásico

text: During the last three decades, the rivalry has been augmented by the modern Spanish tradition of the "pasillo", where one team is given the guard of honor by the other team, once the former clinches the La Liga trophy before El Clásico takes place. This has happened in three occasions. First, during El Clásico that took place on 30 April 1988, where Real Madrid won the championship on the previous round. Then, three years later, when Barcelona won the championship two rounds before El Clásico on 8 June 1991. The last "pasillo", and most recent, took place on 7 May 2008, and this time Real Madrid had won the championship. In May 2018, Real Madrid refused to perform "pasillo" to Barcelona even though the latter had already wrapped up the championship a round prior to their meeting. Real Madrid's coach at the time, Zinedine Zidane, reasoned that Barcelona also refused to perform it five months earlier, on 23 December 2017, when Real Madrid were the FIFA Club World Cup champions.


title: El Clásico

text: The two teams met again in the UEFA Champions League semi-finals in 2002, with Real winning 2–0 in Barcelona and drawing 1–1 in Madrid, resulting in a 3–1 aggregate win for "Los Blancos". The tie was dubbed by Spanish media as the "Match of the Century".


title: El Clásico

text: While El Clásico is regarded as one of the fiercest rivalries in world football, there have been rare moments when fans have shown praise for a player on the opposing team. In 1980, Laurie Cunningham was the first Real Madrid player to receive applause from Barcelona fans at Camp Nou; after excelling during the match, and with Madrid winning 2–0, Cunningham left the field to a standing ovation from the locals. On 26 June 1983, during the second leg of the Copa de la Liga final at the Santiago Bernabéu in Madrid, having dribbled past the Real Madrid goalkeeper, Barcelona star Diego Maradona ran towards an empty goal before stopping just as the Madrid defender came sliding in an attempt to block the shot and crashed into the post, before Maradona slotted the ball into the net. The manner of Maradona's goal led to many Madrid fans inside the stadium start applauding. In November 2005, Ronaldinho became the second Barcelona player to receive a standing ovation from Madrid fans at the Santiago Bernabéu. After dribbling through the Madrid defence twice to score two goals in a 3–0 win, Madrid fans paid homage to his performance with applause. On 21 November 2015, Andrés Iniesta became the third Barcelona player to receive applause from Real Madrid fans while he was substituted during a 4–0 away win, with Iniesta scoring Barça's third. He was already a popular figure throughout Spain for scoring the nation's World Cup winning goal in 2010.


title: El Clásico

text: A 2007 survey by the Centro de Investigaciones Sociológicas showed that 32% of the Spanish population supported Real Madrid, while 25% supported Barcelona. In third place came Valencia, with 5%. According to an Ikerfel poll in 2011, Barcelona is the most popular team in Spain with 44% of preferences, while Real Madrid is second with 37%. Atlético Madrid, Valencia and Athletic Bilbao complete the top five.


title: El Clásico

text: The rivalry intensified in 2011, when Barcelona and Real Madrid were scheduled to meet each other four times in 18 days, including the Copa Del Rey final and UEFA Champions League semi-finals. Several accusations of unsportsmanlike behaviour from both teams and a war of words erupted throughout the fixtures which included four red cards. Spain national team coach Vicente del Bosque stated that he was "concerned" that due to the rising hatred between the two clubs, that this could cause friction in the Spain team.


title: El Clásico

text: A fixture known for its intensity and indiscipline, it has also featured memorable goal celebrations from both teams, often involving mocking the opposition. In October 1999, Real Madrid forward Raúl silenced 100,000 Barcelona fans at the Camp Nou when he scored before he celebrated by putting a finger to his lips as if telling the crowd to be quiet. In 2009 Barcelona captain Carles Puyol kissed his Catalan armband in front of Madrid fans at the Bernabéu. Cristiano Ronaldo twice gestured to the hostile crowd to "calm down" after scoring against Barcelona at the Camp Nou in 2012 and 2016. In April 2017, Messi celebrated his 93rd-minute winner for Barcelona against Real Madrid at the Bernabéu by taking off his Barcelona shirt and holding it up to incensed Real Madrid fans – with his name and number facing them. Later that year, in August, Ronaldo was subbed on in the first leg of the Supercopa de España, proceeded to score in the 80th minute and took his shirt off before holding it up to Barça's fans with his name and number facing them.


title: El Clásico

text: The passion of the rivalry has extended to women's football, although Real Madrid Femenino was only formed officially in 2020 whereas FC Barcelona Femení is 30 years older and had been one of the country's leading clubs for much of that time. The second leg of the UEFA Women's Champions League quarter-finals between the clubs at Camp Nou on 30 March 2022 was attended by 91,553 spectators; at the time, this was the largest known attendance for a women's football match since the 1971 Mexico–Denmark game (110,000).<ref name="GOAL.com/SPOX.com"></ref> Reigning continental champions Barça won 5–2 on the day and 8–3 on aggregate. The attendance was later surpassed in the semi-finals match between Barcelona and VfL Wolfsburg.


title: El Clásico

text: Until the early 1950s, Real Madrid was not a regular title contender in Spain, having won only two Primera División titles between 1929 and 1953. However, things changed for Real after the arrival of Alfredo Di Stéfano in 1953, Paco Gento in the same year, Raymond Kopa in 1956, and Ferenc Puskás in 1958. Real Madrid's strength increased in this period until the team dominated Spain and Europe, while Barcelona relied on its Hungarian star László Kubala and Luis Suárez, who joined in 1955 in addition to the Hungarian players Sándor Kocsis and Zoltán Czibor and the Brazilian Evaristo. With the arrival of Kubala and Di Stéfano, Barcelona and Real Madrid became among the most important European clubs in those years, and the players represented the turning point in the history of their teams.


title: El Clásico

text: With Kubala and Di Stéfano, a rivalry was born, but it would still take a long time to become what it is today. This period was characterized by the abundance of matches in different tournaments, as they faced each other in all the tournaments available at the time, especially at the European level, where they met twice in two consecutive seasons. In their period, El Clásico was played 26 times: Real won 13 matches, Barcelona 10 matches, and 3 ended in a draw. Di Stéfano scored 14 and Kubala scored 4 goals in those matches.


title: El Clásico

text: The rivalry between Lionel Messi and Cristiano Ronaldo between 2009 and 2018 has been the most competitive in El Clásico history, with both players being their clubs' all-time top scorers. In their period, many records were broken for both clubs; the two players alternated as top scorers in La Liga and the Champions League during most seasons while they were with Real Madrid and Barcelona. During this period, Ronaldo won the European Golden Shoe three times, while Messi won it five times. In addition, they won the Ballon d'Or four times each.


title: El Clásico

text: During the nine years they played together in Spain, the two players scored a total of 922 goals, including 38 goals in El Clásico matches, 20 scored by Messi and 18 by Ronaldo. As of 2022, Ronaldo is the all-time top scorer in the UEFA Champions League, followed by Messi in the second place. In addition, Messi is the all-time top scorer of La Liga, and Ronaldo is ranked second. Both players contributed to their club's record for the most points in La Liga history, with 100 points in the 2011–12 and 2012–13 seasons, respectively.


title: El Clásico

text: The Messi–Ronaldo rivalry was characterized by a lot of goals scored by both players, in addition to many domestic and European titles that they were a major reason for achieving them. In their period, they contributed to the dominance of their clubs in Europe, as they won six Champions League titles in eight seasons, including five consecutive seasons between 2014 and 2018. In El Clásico matches, Messi has scored 26 goals in his career which is a record. Ronaldo has scored 18, which is the joint second most in the fixture's history alongside Di Stéfano. Ronaldo, on the other hand, has a slight advantage in terms of minutes per goal ratio, scoring a goal for every 141 minutes played in El Clásico matches. Only slightly behind is Messi, scoring a goal every 151.54 minutes.


title: El Clásico

text: In their period, the rivalry between Real Madrid and Barcelona has been encapsulated by the rivalry between Ronaldo and Messi. Following the star signings of Neymar and Luis Suárez by Barcelona, and Gareth Bale and Karim Benzema by Real, the rivalry was expanded to a battle of the clubs' attacking trios, nicknamed "BBC" (Bale, Benzema, Cristiano) and "MSN" (Messi, Suárez, Neymar). Ronaldo left Real for Juventus in 2018, and in the week prior to the first meeting of the teams in the 2018–19 La Liga, Messi sustained an arm injury ruling him out of the match. It would be the first time since 2007 that the "Clásico" had featured neither player, with some in the media describing it as the 'end of an era'. Barcelona won the match 5–1.


title: El Clásico

text: As of 20 March 2022, 21 different players have scored a hat-trick in official El Clásico matches. 14 of the 25 hat-tricks came from Real Madrid players.


title: El Clásico

text: Since the first match in 1902, the official Clásico matches have been held at thirteen stadiums, twelve of those in Spain. The following table shows the details of the stadiums that hosted the Clásico. The following table does not include other stadiums that hosted the friendly matches.


title: El Clásico

text: The rivalry reflected in El Clásico matches comes about as Barcelona and Real Madrid are the most successful football clubs in Spain. As seen below, Real Madrid leads Barcelona 99 to 97 in terms of official overall trophies. While the Inter-Cities Fairs Cup is recognised as the predecessor to the UEFA Cup, and the Latin Cup is recognised as one of the predecessors of the European Cup, both were not organised by UEFA. Consequently, UEFA does not consider clubs' records in the Fairs Cup nor Latin Cup to be part of their European record. However, FIFA does view the competitions as a major honour. The one-off Ibero-American Cup was later recognised as an official tournament organised by CONMEBOL and the Royal Spanish Football Federation.


title: James Patterson

text: James Brendan Patterson (born March 22, 1947) is an American author. Among his works are the "Alex Cross", "Michael Bennett", "Women's Murder Club", "Maximum Ride", "Daniel X", "NYPD Red", "Witch & Wizard", and "Private" series, as well as many stand-alone thrillers, non-fiction, and romance novels. His books have sold more than 425 million copies, and he was the first person to sell 1 million e-books. In 2016, Patterson topped "Forbes" list of highest-paid authors for the third consecutive year, with an income of $95 million. His total income over a decade is estimated at $700 million.


title: James Patterson

text: In November 2015, Patterson received the Literarian Award from the National Book Foundation, which cited him as a "passionate campaigner to make books and reading a national priority. A generous supporter of universities, teachers colleges, independent bookstores, school libraries, and college students, Patterson has donated millions of dollars in grants and scholarships with the purpose of encouraging Americans of all ages to read more books."


title: James Patterson

text: Patterson was born on March 22, 1947, in Newburgh, New York, the son of Isabelle (), a homemaker and teacher, and Charles Patterson, an insurance broker. The family was working-class and of Irish descent. He graduated "summa cum laude" with both a B.A. in English from Manhattan College and an M.A. in English from Vanderbilt University.


title: James Patterson

text: Patterson was a PhD candidate at Vanderbilt and acquired a job in advertising. He was an advertising executive at J. Walter Thompson. After he retired from advertising in 1996, he devoted his time to writing. His greatest influence, he said later, was probably Evan S. Connell's 1959 debut novel "Mrs. Bridge". He published his first novel in 1976 called "The Thomas Berryman Number." The novels featuring his character Alex Cross, a forensic psychologist formerly of the Washington DC. Metropolitan Police and Federal Bureau of Investigation, who now works as a private psychologist and government consultant, are his most popular and the top-selling U.S. detective series in the past ten years. Patterson has written more than 200 novels since 1976. He has had more than 114 "New York Times" bestselling novels, and holds "The New York Times" record for most #1 "New York Times" bestsellers by a single author, a total of 67, which is also a Guinness World Record. His novels account for one in 17, roughly 6%, of all hardcover novels sold in the United States; in recent years his novels have sold more copies than those of Stephen King, John Grisham, and Dan Brown combined. His books have sold approximately 305 million copies worldwide. In 2008, he replaced Jacqueline Wilson as the most borrowed author in Britain's libraries. He retained this position at least until 2013. In 2018, he worked with Stephen David Entertainment on the true crime television series "James Patterson's Murder Is Forever".


title: James Patterson

text: Patterson's awards include the Edgar Award, the BCA Mystery Guild's Thriller of the Year, the International Thriller of the Year award, and the Children's Choice Book Award for Author of the Year. He is the first author to have No. 1 new titles simultaneously on "The New York Times" adult and children's bestsellers lists, and to have two books on NovelTrackr's top-ten list at the same time. In 2019, Patterson was awarded a National Humanities Medal. He appeared on the Fox TV show "The Simpsons" (in the episode "Yokel Chords") and in various episodes of "Castle" as himself.


title: James Patterson

text: Patterson works with a variety of co-authors, such as J.D. Barker, Candice Fox, Maxine Paetro, Andrew Gross, Mark Sullivan, Ashwin Sanghi, Michael Ledwidge, and Peter de Jonge. In May 2017, it was announced that Patterson would also co-author a crime fiction book with former U.S. President Bill Clinton. Patterson said the novel, "The President Is Missing", would provide a level of detail that only a former U.S. president can offer. Patterson has often said that collaborating with others brings new and interesting ideas to his stories. Of his process, he has stated that he is simply more proficient at dreaming up plots than crafting sentence after sentence.


title: James Patterson

text: In September 2009, Patterson signed a deal to write or co-write 11 books for adults and 6 for young adults by the end of 2012. "Forbes" reported the deal was worth at least $150 million, but according to Patterson the estimate was inaccurate.


title: James Patterson

text: Patterson founded the James Patterson PageTurner Awards in 2005 to donate over $100,000 that year to people, companies, schools, and other institutions that find original and effective ways to spread the excitement of books and reading. The PageTurner Awards were put on hold in 2008 to focus on Patterson's new initiative, ReadKiddoRead.com, which helps parents, teachers, and librarians find the best books for their children. The social networking site for ReadKiddoRead is hosted by Ning. Patterson states that his own son, Jack, wasn't the best reader in the class. So, in Jack's 8th summer, Patterson said that Jack did not need to do chores, just read 1 hour a day. The first summer, he resisted, the second summer, he accepted it, and the third, Jack wanted to. Patterson wanted to give that opportunity to every child, so he started the ReadKiddoRead website, for parents who just can't seem to find any good books for their child. Patterson has also set up the James Patterson Teacher Education Scholarship in the schools of education at Appalachian State University, Michigan State University, Florida Atlantic University, and the University of Florida. Patterson also runs the College Book Bucks scholarship program. Recently, his JP Entertainment company signed a first-look deal with Entertainment One.


title: James Patterson

text: In June 2022 Patterson set off a controversy when he claimed in an interview that older white males find it difficult to find work in film, theater, television and publishing and that the problem is “just another form of racism.” Patterson's own publishing house, Hachette, has a workforce that is 65% white and 78% of senior positions are filled with whites. Following publication of data confirming that white males are overrepresented in the publishing field, Patterson apologized on Facebook for his accusations of racism. “I apologize for saying white male writers having trouble finding work is a form of racism.” “I absolutely do not believe that racism is practiced against white writers. Please know that I strongly support a diversity of voices being heard — in literature, in Hollywood, everywhere.”


title: James Patterson

text: Patterson has been criticized for co-authoring many of his books and for being more of a brand that focuses on making money than an artist who focuses on his craft.


title: James Patterson

text: In an interview for " USA Weekend", Stephen King referred to Patterson as "a terrible writer but he's very successful." King also implied, while being asked on "The Late Show with Stephen Colbert" about how many hours it takes him to write a book, that Patterson needed only 12 hours for two books, noting he and Patterson had "a mutual respect – sort of". Patterson said of King in a "Wall Street Journal" interview, "He's taken shots at me for years. It's fine, but my approach is to do the opposite with himto heap praise."


title: James Patterson

text: Legal thriller writer Lisa Scottoline said in a review of Patterson's "Kill Alex Cross", "They used to say that 50 million Elvis Presley fans couldn't be wrong, and James Patterson makes 50 million fans look like a good start. He has sold more than 230 million books, and his fans aren't wrong, either."


title: James Patterson

text: In 2013, Patterson took out ads titled "Who Will Save Our Books? Our Bookstores? Our Libraries?" in "Publishers Weekly" and "The New York Times Book Review", which employed the text "If there are no bookstores, no libraries, no serious publishers with passionate, dedicated, idealistic editors, what will happen to our literature? Who will discover and mentor new writers? Who will publish our important books? What will happen if there are no more books like these?" Patterson called the ads an attempt to "stir the pot a little bit." " Digital Book World" called the ads, "refreshing, really. And brave." Maureen Sullivan, president of the American Library Association, told the "Tampa Bay Times" she was in the process of writing James Patterson a thank-you letter.


title: James Patterson

text: In 2017, digital humanities scholars Simon Fuller and James O'Sullivan published research showing that Patterson does not do much actual writing when collaborating with other authors. O'Sullivan writes: "Patterson is all about story... 'author', in its widely accepted sense, isn't always the most appropriate term for his role within the writing process." O'Sullivan would later go on to conduct the same analysis on "The President is Missing", a collaboration between Patterson and Bill Clinton; here O'Sullivan concludes that Patterson did most of the writing, aside from the end of the novel.


title: James Patterson

text: Patterson, his wife, Susan, nicknamed "Sue", and their son, Jack, live in Lake Worth Beach in Palm Beach County, Florida. In 2015, Patterson established the James Patterson Pledge with Scholastic Book Clubs to put books in the hands of young readers.


title: Fawad Khan

text: Fawad Afzal Khan () (born 29 November 1981) is a Pakistani actor, producer, screenwriter, model and singer having received several awards including a Filmfare Award, two Lux Style Awards and six Hum Awards.


title: Fawad Khan

text: Khan began his acting career on the television sitcom, "Jutt and Bond". He formed an alternative rock band, Entity Paradigm, with the show's co-stars and began his music career as its lead singer. The band appeared on the finale of "Pepsi Battle of the Bands" in 2002 and Khan became known for its 2003 debut album, "Irtiqa". After about 250 performances, he left the band to pursue a film career. Khan made his film debut with a supporting role in Shoaib Mansoor's sociodrama, "Khuda Kay Liye" (2007), one of Pakistan's highest-grossing films.


title: Fawad Khan

text: He had his first success in the television period drama, "Dastaan" (2010), for which he received the Best Male Actor Award at the Pakistan Media Awards. Khan played a lead role in the Pakistani television serial "Humsafar" (2011), and appeared in Sultana Siddiqui's family drama "Zindagi Gulzar Hai" (2012). For both performances, he received the Lux Style Award for Best Actor - Satellite. Khan made his Bollywood film debut with the lead role in the romantic comedy, "Khoobsurat" (2014), for which he received the Filmfare Award for Best Male Debut. He was praised for his portrayal of a closeted homosexual in the critically and commercially successful family drama "Kapoor & Sons" (2016), which earned him a nomination for the Filmfare Award for Best Supporting Actor.


title: Fawad Khan

text: In addition to acting, Khan has raised money for charitable organizations throughout Pakistan. He has endorsed several popular brands and products. Khan has been listed among the "Sexiest Asian Males" by the British magazine "Eastern Eye".